ECO403 — Final Term Summary (Lectures 23–45)

📘 Lecture 23 — Economic Growth (Continued)

📖 Overview: This lecture continues the discussion of economic growth, examining policies to increase saving rates and how to allocate investment across different capital types. It then confronts the Solow model with real-world facts, introduces the concept of convergence, and presents endogenous growth theory as an alternative framework where growth rates are determined within the model rather than externally.

🗂️ Topics Covered

The lecture covers policies to increase saving rates including reducing deficits and tax incentives, then discusses allocating investment among private capital, public infrastructure, and human capital. It examines encouraging technological progress through patents and R&D incentives, presents growth empirics confronting the Solow model with facts about convergence, explains conditional convergence, and introduces endogenous growth theory including basic and two-sector models with their implications for knowledge and R&D.

📝 Lecture Summary

2. POLICIES TO INCREASE THE SAVING RATE

To raise the saving rate, governments can reduce the budget deficit or increase surpluses, which raises national saving. They can also increase incentives for private saving by reducing taxes that discourage saving such as capital gains tax, corporate income tax, and estate tax. Another approach is to replace the federal income tax with a consumption tax that taxes spending rather than income, and expand tax incentives for retirement accounts.

3. ALLOCATING THE ECONOMY’S INVESTMENT

In the real world, there are many types of capital divided into three categories: private capital stock, public infrastructure, and human capital (knowledge and skills workers acquire through education). The Solow model only has one type of capital, raising the question of how to allocate investment among these types.

Two viewpoints exist. The first is to equalize tax treatment of all capital types and let the market allocate investment to the type with the highest marginal product. The second is industrial policy, where the government actively encourages investment in certain capital types or industries because they may have positive externalities (by-products) that private investors don't consider.

🔑 Definition — Industrial policy: Government actively encouraging investment in specific capital types or industries due to positive externalities.

Possible problems with industrial policy include whether the government has the ability to "pick winners" (choose industries with highest return to capital or biggest externalities), and whether politics rather than economics would influence which industries get preferential treatment.

4. ENCOURAGING TECHNOLOGICAL PROGRESS

Methods to encourage technological progress include patent laws that grant temporary monopolies to inventors, tax incentives for R&D, grants to fund basic research at universities, and industrial policy targeting specific industries key for rapid technological progress (subject to concerns about government's ability to pick winners).

GROWTH EMPIRICS: CONFRONTING THE SOLOW MODEL WITH THE FACTS The Solow model's steady state exhibits balanced growth where many variables grow at the same rate. The model predicts that Y/L and K/L grow at the same rate (g), so K/Y should be constant, which is true in the real world. It also predicts that the real wage grows at the same rate as Y/L while the real rental price is constant, which is also confirmed by real-world data.

CONVERGENCE The Solow model predicts that, other things equal, "poor" countries with lower Y/L and K/L should grow faster than "rich" ones. If true, income gaps would shrink over time and living standards would "converge." However, in the real world, many poor countries do NOT grow faster than rich ones. This doesn't mean the Solow model fails because "other things" aren't equal.

🔑 Definition — Conditional convergence: Countries converge to their own steady states, which are determined by saving, population growth, and education.

In samples of countries with similar savings and population growth rates, income gaps shrink about 2% per year. In larger samples controlling for differences in saving, population growth, and human capital, incomes also converge by about 2% per year. This confirms the Solow model's prediction of conditional convergence.

FACTOR ACCUMULATION VS. PRODUCTION EFFICIENCY Two reasons explain why income per capita is lower in some countries: differences in capital (physical or human) per worker, and differences in the efficiency of production (the height of the production function). Studies show both factors are important. Countries with higher capital per worker also tend to have higher production efficiency. Possible explanations include that production efficiency encourages capital accumulation, capital accumulation has externalities that raise efficiency, or a third unknown variable causes both to be higher in some countries.

ENDOGENOUS GROWTH THEORY

In the Solow model, sustained growth in living standards is due to technological progress, but the rate of technological progress is exogenous (determined outside the model). Endogenous growth theory is a set of models where the growth rate of productivity and living standards is determined within the model.

A basic model The production function is: Y = A K, where A is the amount of output for each unit of capital (A is exogenous and constant). The key difference from the Solow model is that the marginal product of capital (MPK) is constant here while it diminishes in the Solow model.

📐 Formula: Investment = sY, Depreciation = δK, Equation of motion: ∆K = sY − δK

Dividing through by K and using Y = A K gives: ΔY/Y = ΔK/K = sA − δ

📌 Example: If sA > δ, then income will grow forever, and investment is the "engine of growth." The permanent growth rate depends on s, unlike in the Solow model where it does not.

💡 Why this matters: In endogenous growth theory, policies that affect the saving rate can permanently affect the growth rate, whereas in the Solow model they only affect the level of income.

DOES CAPITAL HAVE DIMINISHING RETURNS OR NOT? Yes, if "capital" is narrowly defined (plant and equipment). Perhaps not, with a broad definition of "capital" including physical and human capital and knowledge. Some economists believe knowledge exhibits increasing returns. In the endogenous growth model, the assumption of constant returns to capital is more plausible.

A TWO-SECTOR MODEL There are two sectors: manufacturing firms that produce goods, and research universities that produce knowledge increasing labor efficiency in manufacturing. Let u = fraction of labor in research (u is exogenous).

🔑 Definition: Manufacturing production function: Y = F[K, (1-u)EL] 🔑 Definition: Research production function: ΔE = g(u)E 📐 Formula: Capital accumulation: ∆K = sY − δK

In the steady state, manufacturing output per worker and the standard of living grow at rate ΔE/E = g(u). Key variables are: s which affects the level of income but not its growth rate (same as in Solow model), and u which affects both the level and growth rate of income.

📌 Example: Would an increase in u be unambiguously good for the economy? No, because while it raises the growth rate, it reduces the fraction of labor producing goods, potentially lowering current output.

THREE FACTS ABOUT R&D IN THE REAL WORLD

1. Much research is done by firms seeking profits.
2. Firms profit from research because new inventions can be patented, creating monopoly profits until the patent expires. There is an advantage to being first on the market with a new product.
3. Innovation produces externalities that reduce the cost of subsequent innovation.

IS THE PRIVATE SECTOR DOING ENOUGH R&D? The existence of positive externalities in knowledge creation suggests the private sector is not doing enough R&D. However, there is much duplication of R&D effort among competing firms. Estimates show the social return to R&D is at least 40% per year, leading many to believe government should encourage R&D.

⭐ Key Takeaways

Students must remember that endogenous growth theory differs from the Solow model by treating technological progress as determined within the model rather than externally, and the key distinction is that the marginal product of capital is constant (not diminishing) when capital is broadly defined. The basic endogenous growth model Y = AK shows that if sA > δ, income grows forever with the growth rate depending on the saving rate. Conditional convergence is the Solow model's correct prediction that countries converge to their own steady states determined by saving, population growth, and education, explaining why poor countries don't always grow faster than rich ones. The two-sector model shows that the fraction of labor in research (u) affects both the level and growth rate of income, while the saving rate (s) only affects the level. Finally, the social return to R&D is at least 40% per year, and positive externalities in knowledge creation suggest government encouragement of R&D may be justified despite duplication of effort.

🧠 Quick Revision Questions

1. What is the fundamental difference between the Solow model and endogenous growth theory regarding the marginal product of capital?
2. In the basic endogenous growth model Y = AK, what condition must hold for continuous growth, and what determines the growth rate?
3. What is conditional convergence, and why does it explain why some poor countries don't grow faster than rich ones?
4. In the two-sector model, how does the fraction of labor in research (u) affect the economy differently from the saving rate (s)?
5. What three facts about R&D in the real world does new endogenous growth theory attempt to incorporate?

📘 Lecture 24 — Aggregate Demand and Aggregate Supply

📖 Overview: This lecture introduces the Aggregate Demand-Aggregate Supply (AD-AS) model, the primary framework used by economists to analyze economic fluctuations and the effects of stabilization policies. It explains how the economy behaves differently in the short run when prices are sticky versus the long run when prices are flexible, and shows how monetary policy affects output and prices in each time horizon.

🗂️ Topics Covered

The lecture covers time horizons and the distinction between sticky and flexible prices, classical macroeconomic theory regarding output determination, the model of aggregate demand and supply, the quantity equation as a basis for aggregate demand, the downward-sloping AD curve and its shifts, long-run aggregate supply as a vertical curve, long-run effects of an increase in money supply, short-run aggregate supply as a horizontal curve, short-run effects of an increase in money supply, the transition from short-run to long-run equilibrium, and a summary of the short-run and long-run effects of an increase in the money supply.

📝 Lecture Summary

TIME HORIZONS

The economy behaves differently depending on the time frame considered. In the long run, prices are flexible and respond to changes in supply or demand. In the short run, many prices are "sticky" at some predetermined level. This stickiness is the key reason why economic fluctuations and stabilization policies matter.

CLASSICAL MACROECONOMIC THEORY

According to classical macroeconomic theory, output is determined by the supply side: the supplies of capital and labor, and technology. Changes in demand for goods and services (consumption, investment, government spending) only affect prices, not quantities. Complete price flexibility is a crucial assumption of this theory, so classical theory applies in the long run.

WHEN PRICES ARE STICKY

When prices are sticky, output and employment also depend on demand for goods and services. This demand is affected by: fiscal policy (government spending G and taxes T), monetary policy (money supply M), and other factors like exogenous changes in consumption C or investment I.

THE MODEL OF AGGREGATE DEMAND AND SUPPLY

The AD-AS model is the paradigm that most mainstream economists and policymakers use to think about economic fluctuations and policies to stabilize the economy. It shows how the price level and aggregate output are determined and how the economy's behavior differs in the short run and long run.

AGGREGATE DEMAND

The aggregate demand (AD) curve shows the relationship between the price level and the quantity of output demanded. For an introduction to the AD/AS model, a simple theory of aggregate demand based on the Quantity Theory of Money is used.

THE QUANTITY EQUATION AS AGGREGATE DEMAND

Recall the quantity equation: M × V = P × Y and the money demand function it implies: (M/P)ᵈ = k × Y, where V = 1/k = velocity. For given values of M and V, these equations imply an inverse relationship between P and Y.

🔑 Definition — Quantity Equation: M × V = P × Y, where M is the money supply, V is the velocity of money, P is the price level, and Y is real output.

THE DOWNWARD-SLOPING AD CURVE

An increase in the price level causes a fall in real money balances (M/P), causing a decrease in the demand for goods and services. This creates the downward-sloping AD curve.

💡 Why this matters: Higher prices reduce the purchasing power of money, leading to lower spending and output demanded.

SHIFTING THE AD CURVE

An increase in the money supply shifts the AD curve to the right. A decrease in the money supply would shift the AD curve to the left.

📌 Example: If the central bank increases M, then at any given price level P, the real money balances (M/P) are higher, increasing the demand for goods and services and shifting AD to the right.

AGGREGATE SUPPLY IN THE LONG RUN

In the long run, output is determined by factor supplies and technology: Y = F(K, L). Ȳ is the full-employment or natural level of output, the level of output at which the economy's resources are fully employed. "Full employment" means that unemployment equals its natural rate. Full-employment output does not depend on the price level, so the long-run aggregate supply (LRAS) curve is vertical.

🔑 Definition — Natural Rate of Output (Ȳ): The level of output at which the economy's resources are fully employed and unemployment equals its natural rate.

LONG-RUN EFFECTS OF AN INCREASE IN MONEY

An increase in the money supply M shifts the AD curve to the right. In the long run, this increases the price level but leaves output the same (at Ȳ). This demonstrates classical dichotomy and money neutrality in the long run.

📌 Example: The economy starts at equilibrium with price level P₁. The central bank increases M, shifting AD from AD₁ to AD₂. In the long run, the price level rises to P₂, but output remains at Ȳ.

AGGREGATE SUPPLY IN THE SHORT RUN

In the real world, many prices are sticky in the short run. For now, we assume that all prices are stuck at a predetermined level in the short run and that firms are willing to sell as much as their customers are willing to buy at that price level. Therefore, the short-run aggregate supply (SRAS) curve is horizontal. The price level is fixed at a predetermined level, and firms sell as much as buyers demand.

SHORT-RUN EFFECTS OF AN INCREASE IN M

In the short run when prices are sticky, an increase in the money supply shifts the AD curve to the right. Since the price level is fixed (P), the increase in aggregate demand causes output to rise from Y₁ to Y₂.

📌 Example: The economy is at Y₁ with sticky price level P. The central bank increases M, shifting AD from AD₁ to AD₂. Since prices cannot adjust, the only way to meet the higher demand is for firms to produce more, so output rises to Y₂.

FROM THE SHORT RUN TO THE LONG RUN

Over time, prices gradually become "unstuck." The adjustment process depends on the relationship between actual output Y and potential output Ȳ:

• If Y > Ȳ (output above potential), the price level will rise over time.
• If Y < Ȳ (output below potential), the price level will fall over time.
• If Y = Ȳ (output at potential), the price level will remain constant.

This adjustment of prices is what moves the economy to its long-run equilibrium.

THE SR & LR EFFECTS OF ΔM > 0

The full adjustment process for an increase in the money supply involves three stages:

• Point A: Initial equilibrium at Y = Ȳ with price level P₁.
• Point B: New short-run equilibrium after the central bank increases M. Output rises to Y₂, but the price level is still P₁ because prices are sticky.
• Point C: Long-run equilibrium. Since Y₂ > Ȳ, prices rise over time. The SRAS curve shifts upward until the economy returns to Ȳ at a higher price level P₂.

📌 Example: The economy starts at A. The central bank increases M, shifting AD to AD₂. In the short run (B), output rises to Y₂ at price P₁. Since output exceeds potential, prices gradually rise, shifting SRAS upward until the economy reaches long-run equilibrium at C, where output is back at Ȳ and the price level is P₂.

⭐ Key Takeaways

The most critical concept from this lecture is the distinction between short-run and long-run macroeconomic behavior. In the long run, prices are flexible, output is determined by supply-side factors (capital, labor, technology), and changes in money supply only affect prices (money neutrality). In the short run, prices are sticky, so changes in aggregate demand (from monetary or fiscal policy) affect output and employment. The AD curve slopes downward because higher prices reduce real money balances and demand. The LRAS is vertical at the natural rate of output, while the SRAS is horizontal at a predetermined price level. An increase in the money supply raises output in the short run but only raises prices in the long run, with the transition occurring as prices gradually adjust back toward full employment.

🧠 Quick Revision Questions

1. Why is the long-run aggregate supply curve vertical, while the short-run aggregate supply curve is horizontal?
2. Using the quantity equation M × V = P × Y, explain why the aggregate demand curve is downward-sloping.
3. What happens to output and the price level in both the short run and long run when the central bank increases the money supply?
4. If actual output (Y) is greater than potential output (Ȳ), what will happen to the price level over time, and why?
5. Explain the difference between classical theory (long run) and the sticky-price model (short run) regarding the role of aggregate demand in determining output.

📘 Lecture 25 — Aggregate Demand and Aggregate Supply (Continued)

📖 Overview: This lecture examines how exogenous shocks—unexpected changes in aggregate demand or supply—temporarily push the economy away from full-employment equilibrium. It explains the mechanics of demand shocks and supply shocks, analyzing their short-run and long-run effects on output, prices, and employment, using historical oil price shocks as real-world examples.

🗂️ Topics Covered

Shocks are defined as exogenous changes in aggregate supply or demand that temporarily push the economy away from full-employment. The lecture covers demand shocks (positive and negative) and their short-run vs. long-run adjustment paths along the AD-AS model. It then introduces supply shocks (adverse and favorable), explains the role of stabilization policy (especially monetary accommodation), and concludes with detailed case studies of the 1970s and 1980s oil price shocks, showing how they affected inflation, output, and unemployment.

📝 Lecture Summary

SHOCKS: exogenous changes in aggregate supply or demand

Shocks are exogenous changes in aggregate supply or demand that temporarily push the economy away from full-employment. They are the primary source of short-run economic fluctuations.

A DEMAND SHOCK

The economy begins in long-run equilibrium at point A. An increase in aggregate demand, due to an increase in the velocity of money, moves the economy from point A to point B, where output is above its natural level. As prices rise, output gradually returns to its natural rate, and the economy moves from point B to point C.

🔑 Definition — Demand Shock: An exogenous change in aggregate demand (e.g., a change in velocity of money) that temporarily pushes output away from its natural level.

📌 Example: A positive demand shock (increase in V) shifts AD right → output rises above Yn in the short run, then prices rise and output returns to Yn in the long run.

THE EFFECTS OF A NEGATIVE DEMAND SHOCK

An exogenous decrease in velocity: If the money supply is held constant, then a decrease in V means people will be using their money in fewer transactions, causing a decrease in demand for goods and services. The shock shifts AD left, causing output and employment to fall in the short run. Over time, prices fall and the economy moves down its demand curve toward full-employment.

📌 Example: A negative demand shock (decrease in V) shifts AD left → output and employment fall in the short run; eventually, falling prices restore full-employment output.

💡 Why this matters: The self-correcting mechanism of the economy works through price adjustments, but it can take a long time—justifying the need for stabilization policy.

SUPPLY SHOCKS

A supply shock alters production costs, affects the prices that firms charge (also called price shocks). Examples of adverse supply shocks:

• Bad weather reduces crop yields, pushing up food prices.
• Workers unionize, negotiate wage increases.
• New environmental regulations require firms to reduce emissions. Firms charge higher prices to help cover the costs of compliance. (Favorable supply shocks lower costs and prices)

🔑 Definition — Supply Shock: An exogenous change in production costs that affects the prices firms charge, shifting the short-run aggregate supply curve.

📌 Example: An adverse supply shock shifts SRAS up (or left) → output falls (stagflation: higher prices + lower output).

STABILIZATION POLICY

Stabilization policy refers to policy actions aimed at reducing the severity of short-run economic fluctuations. Example: Using monetary policy to combat the effects of adverse supply shocks. When a central bank accommodates the shock by raising aggregate demand, the result is that P is permanently higher, but Y remains at its full-employment level.

🔑 Definition — Stabilization Policy: Policy actions (monetary or fiscal) aimed at reducing the severity of short-run economic fluctuations.

📌 Example: After an adverse supply shock, the central bank can increase AD to prevent a recession, but with the trade-off of permanently higher prices.

THE 1970s OIL SHOCKS

Early 1970s: OPEC coordinates a reduction in the supply of oil. Oil prices rose 11% in 1973, 68% in 1974, and 16% in 1975. Such sharp oil price increases are supply shocks because they significantly impact production costs and prices. The oil price shock shifts SRAS up, causing output and employment to fall. In absence of further price shocks, prices will fall over time and economy moves back toward full employment. Predicted effects of the oil price shock: Inflation ↑, Output ↓, Unemployment ↑ and then a gradual recovery.

📌 Example: The 1973-1975 oil price shock caused stagflation—high inflation and high unemployment simultaneously—exactly as the AD-AS model predicts for an adverse supply shock.

LATE 1970s: As economy was recovering, oil prices shot up again, causing another huge supply shock!!!

📌 Example: The 1979 oil shock (second OPEC crisis) repeated the pattern: oil prices surged, inflation and unemployment rose again.

THE 1980s OIL SHOCKS

1980s: A favorable supply shock—a significant fall in oil prices. As the model would predict, inflation and unemployment fell.

📌 Example: The 1986 oil price collapse (oil prices fell ~50%) reduced production costs, shifting SRAS down → both inflation and unemployment decreased, confirming the model's predictions for a favorable supply shock.

⭐ Key Takeaways

Shocks are exogenous changes that temporarily push the economy away from full-employment. Demand shocks (changes in velocity, e.g.) shift the AD curve: positive shocks cause short-run output booms followed by price increases, while negative shocks cause recessions followed by falling prices. Supply shocks shift the SRAS curve: adverse shocks cause stagflation (higher prices + lower output), while favorable shocks reduce both inflation and unemployment. The economy is self-correcting in the long run through price adjustments, but stabilization policy (especially monetary accommodation) can be used to mitigate short-run fluctuations, though often with trade-offs like permanently higher prices. Historical oil price shocks from the 1970s and 1980s perfectly illustrate these dynamics: the 1973-74 and 1979 oil price increases caused stagflation, while the 1986 oil price collapse led to falling inflation and unemployment.

🧠 Quick Revision Questions

1. What is the key difference between a demand shock and a supply shock in terms of which curve they shift (AD vs. SRAS)?
2. In the AD-AS model, what happens to output, prices, and employment in the short run and long run after a negative demand shock?
3. What is "stagflation" and which type of shock typically causes it?
4. When a central bank "accommodates" an adverse supply shock, what is the trade-off in terms of output and prices?
5. Using the oil price shocks of the 1970s and 1980s, explain how the data confirmed the AD-AS model's predictions for both adverse and favorable supply shocks.

📘 Lecture 26 — KEYNESIAN THEORY OF INCOME & EMPLOYMENT

📖 Overview: This lecture presents the Keynesian theory of income and employment, focusing on the short run where prices are fixed and output is determined by aggregate demand. The Keynesian Cross model is introduced as a framework for understanding how planned expenditure determines equilibrium income, and the concepts of government purchases and tax multipliers are derived.

🗂️ Topics Covered

The lecture distinguishes between long-run and short-run macroeconomic conditions, introduces the Keynesian Cross model with its components including consumption function, planned expenditure, and equilibrium condition, graphs planned expenditure and equilibrium, derives the government purchases multiplier showing why it exceeds one, analyzes the effects of tax increases, derives the tax multiplier and its properties, and finally introduces the IS curve as representing goods market equilibrium across different interest rates and output levels.

📝 Lecture Summary

KEYNESIAN THEORY OF INCOME & EMPLOYMENT

In the long run, prices are flexible, output is determined by factors of production and technology, and unemployment equals its natural rate. In the short run, prices are fixed, output is determined by aggregate demand, and unemployment is negatively related to output.

THE KEYNESIAN CROSS

The Keynesian Cross is the simple closed economy model in which income is determined by expenditure, presented by J.M. Keynes.

Notations:

• I = planned investment
• E = C + I + G = planned expenditure
• Y = real GDP = actual expenditure

Actual expenditure is the amount that households, firms, and the government spend on goods and services; it equals the economy's gross domestic product (GDP). Planned expenditure is the amount households, firms, and the government would like to spend on goods and services.

ELEMENTS OF THE KEYNESIAN CROSS

Consumption function: C = C(Y - T) Govt policy variables: G = G, T = T For now, investment is exogenous: I = I

Planned expenditure: E = C(Y - T) + I + G Equilibrium condition: Actual expenditure = Planned expenditure → Y = E

GRAPHING PLANNED EXPENDITURE

The planned expenditure line (E = C + I + G) is plotted with income/output (Y) on the horizontal axis and planned expenditure on the vertical axis. The slope of this line equals the MPC (Marginal Propensity to Consume).

GRAPHING THE EQUILIBRIUM CONDITION

The equilibrium condition Y = E is represented by a 45-degree line from the origin, where actual expenditure equals planned expenditure at every point.

THE EQUILIBRIUM VALUE OF INCOME

Equilibrium income occurs at the intersection of the planned expenditure line (E = C + I + G) and the 45-degree line (Y = E).

AN INCREASE IN GOVERNMENT PURCHASES

An increase in government purchases (ΔG) shifts the planned expenditure line upward by ΔG. At the initial income level Y₁, there is now an unplanned drop in inventory, so firms increase output, and income rises toward a new equilibrium.

SOLVING FOR ΔY

Equilibrium condition: Y = C + I + G In changes form: ΔY = ΔC + ΔI + ΔG Since I is exogenous: ΔY = ΔC + ΔG Because ΔC = MPC × ΔY: ΔY = MPC × ΔY + ΔG

Collect terms with ΔY on the left side: (1 - MPC) × ΔY = ΔG

Finally, solve for ΔY: ΔY = [1/(1 - MPC)] × ΔG

THE GOVERNMENT PURCHASES MULTIPLIER

The increase in income resulting from Rs.1 increase in G is known as the government purchases multiplier.

📐 Formula: ΔY/ΔG = 1/(1 - MPC)

📌 Example: If MPC = 0.8, then ΔY/ΔG = 1/(1 - 0.8) = 1/0.2 = 5. The increase in G causes income to increase by 5 times as much!

WHY THE MULTIPLIER IS GREATER THAN 1

Initially, the increase in G causes an equal increase in Y: ΔY = ΔG. But ↑Y ⇒ ↑C ⇒ further ↑Y ⇒ further ↑C ⇒ further ↑Y. So the final impact on income is much bigger than the initial ΔG.

💡 Why this matters: This explains why government spending can have a powerful effect on the economy—each rupee spent generates additional rounds of consumption spending.

AN INCREASE IN TAXES

A tax increase reduces consumption: ΔC = -MPC × ΔT. This shifts the planned expenditure line downward. At the initial income level Y₁, there is now an unplanned inventory buildup, so firms reduce output, and income falls toward a new equilibrium.

SOLVING FOR ΔY

Equilibrium condition in changes: ΔY = ΔC + ΔI + ΔG I and G are exogenous: ΔY = ΔC ΔC = MPC × (ΔY - ΔT)

Solving for ΔY: (1 - MPC) × ΔY = -MPC × ΔT

Final result: ΔY = [-MPC/(1 - MPC)] × ΔT

THE TAX MULTIPLIER

The change in income resulting from a $1 increase in T is known as the tax multiplier.

📐 Formula: ΔY/ΔT = -MPC/(1 - MPC)

📌 Example: If MPC = 0.8, then ΔY/ΔT = -0.8/(1 - 0.8) = -0.8/0.2 = -4

PROPERTIES OF TAX MULTIPLIER

• Tax multiplier is negative: A tax hike reduces consumer spending, which reduces income.
• Tax multiplier is greater than one (in absolute value): A change in taxes has a multiplier effect on income.
• Tax multiplier is smaller than the govt. spending multiplier: Consumers save the fraction (1-MPC) of a tax cut, so the initial boost in spending from a tax cut is smaller than from an equal increase in G.

IS CURVE

A graph of all combinations of r and Y that result in goods market equilibrium is called the IS curve. Goods market equilibrium means actual expenditure (output) = planned expenditure.

The equation for the IS curve is: Y = C(Y - T) + I(r) + G

🔑 Definition — IS Curve: Shows all combinations of the interest rate (r) and income (Y) such that the goods market is in equilibrium.

DERIVING THE IS CURVE

Starting from an initial equilibrium at interest rate r₁ and output Y₁:

• A decrease in interest rates (↓r) causes an increase in planned investment (↑I)
• This shifts the planned expenditure line upward (E = C + I(r₂) + G)
• The new equilibrium occurs at a higher output level Y₂
• Plotting (r₁, Y₁) and (r₂, Y₂) gives points on the IS curve, which slopes downward

💡 Why this matters: The IS curve shows the negative relationship between interest rates and output in the goods market—lower interest rates stimulate investment, which increases output through the multiplier.

⭐ Key Takeaways

The Keynesian Cross model demonstrates that in the short run with fixed prices, output is determined by planned expenditure. The government purchases multiplier equals 1/(1-MPC) and exceeds one because initial spending increases generate successive rounds of consumption. The tax multiplier equals -MPC/(1-MPC), is negative, and has a smaller absolute value than the government spending multiplier because part of any tax cut is saved. The IS curve captures all combinations of interest rates and output where the goods market is in equilibrium, sloping downward because lower interest rates stimulate investment and thus increase equilibrium output. Understanding these multipliers is essential for analyzing fiscal policy effectiveness.

🧠 Quick Revision Questions

1. What is the equilibrium condition in the Keynesian Cross model?
2. Derive the government purchases multiplier and explain why it exceeds 1.
3. What is the tax multiplier when MPC = 0.6? Show your calculation.
4. Why is the tax multiplier smaller in absolute value than the government spending multiplier?
5. Explain why the IS curve slopes downward. What happens to planned expenditure and output when the interest rate falls?

📘 Lecture 27 — IS Curve’s Slope & IS-LM Framework

📖 Overview: This lecture introduces the IS-LM framework, a cornerstone of macroeconomic analysis that shows the interaction between the goods market (IS curve) and the money market (LM curve). It explains the slope of each curve, how fiscal and monetary policies shift them, and how the short-run equilibrium of the economy is determined.

🗂️ Topics Covered

The lecture covers the negative slope of the IS curve, its relationship with the loanable funds model, and how fiscal policy (changes in G and T) shifts the IS curve. It then introduces the Theory of Liquidity Preference to explain interest rate determination in the money market, derives the positively sloped LM curve, shows how the central bank can raise interest rates by reducing the money supply, and how changes in M shift the LM curve. Finally, it defines the short-run equilibrium where both markets clear simultaneously.

📝 Lecture Summary

IS CURVE’S SLOPE

The IS curve is negatively sloped. A fall in the interest rate motivates firms to increase investment spending, which drives up total planned spending (E). To restore equilibrium in the goods market, output (actual expenditure, Y) must increase.

IS CURVE AND THE LOANABLE FUNDS MODEL

The IS curve can be derived from the loanable funds model. In the loanable funds model, the interest rate (r) equilibrates saving (S) and investment (I). A lower interest rate increases investment, which corresponds to a higher level of income (Y) on the IS curve. The lecture shows a two-panel diagram: panel (a) shows the loanable funds market with saving and investment curves, and panel (b) shows the resulting downward-sloping IS curve plotting r against Y.

🔑 Definition — IS Curve: A graph of all combinations of r and Y that equate planned expenditure (E) and actual expenditure (Y) in the goods market.

FISCAL POLICY AND IS CURVE

Fiscal policy (changes in government spending G and taxes T) can shift the IS curve.

SHIFTING THE IS CURVE: ΔG

An increase in government spending (ΔG) shifts the IS curve to the right. The mechanism is: at any value of r, an increase in G raises planned expenditure (E), which then raises income (Y) through the multiplier effect. The lecture shows this with a Keynesian Cross diagram where the planned expenditure line shifts up from E = C + I(r₁) + G₁ to E = C + I(r₁) + G₂, increasing output from Y₁ to Y₂. The corresponding IS curve shifts right from IS₁ to IS₂.

📐 Formula: ΔY = (1/(1-MPC)) × ΔG → The change in income equals the government spending multiplier times the change in government spending.

THE THEORY OF LIQUIDITY PREFERENCE

John Maynard Keynes presented a simple theory in which the interest rate is determined by money supply and money demand. In this theory, the interest rate adjusts to equilibrate the supply and demand for real money balances.

MONEY SUPPLY

The supply of real money balances (M/P) is fixed by the central bank and is independent of the interest rate. It is represented as a vertical line in the money market diagram.

📐 Formula: (M/P)ˢ = M̄/P̄ → The real money supply is fixed at a given level.

MONEY DEMAND

The demand for real money balances is a function of the interest rate: (M/P)ᵈ = L(r). As the interest rate rises, the opportunity cost of holding money increases, so the quantity of money demanded falls. The money demand curve is downward sloping.

📐 Formula: (M/P)ᵈ = L(r) → Demand for real money balances is a decreasing function of the interest rate.

EQUILIBRIUM

The interest rate adjusts to equate the supply and demand for money. At the equilibrium interest rate r₁, the quantity of real money balances demanded exactly equals the fixed supply.

📐 Formula: M/P = L(r) → In equilibrium, real money supply equals real money demand.

💡 Why this matters: The Theory of Liquidity Preference explains how the interest rate is determined in the short run, which is essential for understanding monetary policy transmission.

HOW CENTRAL BANK RAISES THE INTEREST RATE

To increase the interest rate, the Central Bank reduces the money supply (M). By shifting the money supply curve to the left (from M₁/P to M₂/P), the equilibrium interest rate rises from r₁ to r₂ to eliminate the excess demand for money.

LM CURVE

The LM curve is a graph of all combinations of r and Y that equate the supply and demand for real money balances. When income (Y) is included in the money demand function, the equation for the LM curve becomes:

📐 Formula: M/P = L(r, Y) → The LM curve shows all combinations of r and Y for which the money market is in equilibrium.

DERIVING THE LM CURVE

The LM curve is derived using a two-panel diagram. Panel (a) shows the market for real money balances. An increase in income from Y₁ to Y₂ raises money demand, shifting the L(r) curve to the right. Since the money supply is fixed, the interest rate must rise from r₁ to r₂ to restore equilibrium. In panel (b), this positive relationship between income and the interest rate generates the upward-sloping LM curve.

📌 Example: If income (Y) rises, consumers and firms demand more money for transactions. This excess demand pushes up the interest rate until money demand falls back to equal the fixed supply.

LM CURVE’S SLOPE

The LM curve is positively sloped. An increase in income raises money demand. Since the supply of real balances is fixed, there is now excess demand in the money market at the initial interest rate. The interest rate must rise to restore equilibrium in the money market.

HOW ΔM SHIFTS THE LM CURVE

A decrease in the money supply (ΔM↓) shifts the LM curve to the left. In panel (a), reducing the money supply from M₁/P to M₂/P raises the interest rate from r₁ to r₂ at the initial income level Y₁. In panel (b), this means every level of income is now associated with a higher interest rate, so the LM curve shifts left from LM₁ to LM₂.

💡 Why this matters: Contractionary monetary policy (reducing M) shifts the LM curve up/left, raising interest rates and reducing output. Expansionary monetary policy (increasing M) shifts the LM curve down/right, lowering interest rates and raising output.

SHIFTING THE LM CURVE

Exercise Question: Suppose a wave of credit card fraud causes consumers to use cash more frequently in transactions. Use the Liquidity Preference model to show how these events shift the LM curve. Answer hint: Increased cash usage raises money demand (L(r, Y) shifts right). At the fixed money supply, this creates excess demand, pushing up the interest rate. This causes the LM curve to shift left/upward.

THE SHORT-RUN EQUILIBRIUM

The short-run equilibrium is the combination of r and Y that simultaneously satisfies the equilibrium conditions in both the goods market and the money market. This is found at the intersection of the IS curve and the LM curve.

📐 Formulas:

• Goods market: Y = C(Y - T) + I(r) + G
• Money market: M/P = L(r, Y)

At the intersection, the equilibrium interest rate and the equilibrium level of income are determined. The IS curve represents all points where the goods market is in balance, and the LM curve represents all points where the money market is in balance. Only at their intersection are both markets in simultaneous equilibrium.

⭐ Key Takeaways

The IS-LM model shows the short-run interaction between the goods market (IS curve) and the money market (LM curve). The IS curve is negatively sloped because lower interest rates boost investment and output. The LM curve is positively sloped because higher income raises money demand, requiring higher interest rates to maintain equilibrium. Fiscal policy (changes in G and T) shifts the IS curve, while monetary policy (changes in M) shifts the LM curve. The goods market equilibrium condition is Y = C(Y-T) + I(r) + G, and the money market equilibrium is M/P = L(r, Y), and the short-run equilibrium is where both hold simultaneously.

🧠 Quick Revision Questions

1. Why is the IS curve negatively sloped?
2. How does an increase in government spending (G) shift the IS curve, and what is the mechanism?
3. According to the Theory of Liquidity Preference, how is the interest rate determined?
4. Why is the LM curve positively sloped?
5. What happens to the LM curve if the central bank reduces the money supply?

📘 Lecture 28 — IS-LM Framework (Continued) The Big Picture

📖 Overview: This lecture completes the IS-LM framework by showing how the goods market (IS curve) and money market (LM curve) intersect to determine equilibrium output and interest rates. It then analyzes how fiscal and monetary policies affect the economy, including the interaction between these policies and the central bank's choice of policy instrument.

🗂️ Topics Covered

The lecture covers equilibrium in the IS-LM model where IS and LM curves intersect; policy analysis showing effects of increased government purchases, tax cuts, and monetary expansion; interaction between monetary and fiscal policy including three central bank responses to fiscal expansion; IS and LM shocks from exogenous changes; and the central bank's decision to target interest rates rather than the money supply.

📝 Lecture Summary

Equilibrium in the IS-LM Model

The IS curve represents equilibrium in the goods market, while the LM curve represents money market equilibrium where M/P = L(r, Y). The intersection of these two curves determines the unique combination of Y (output) and r (interest rate) that satisfies equilibrium in both markets simultaneously.

🔑 Definition — Money Market Equilibrium: M/P = L(r, Y) → Real money supply equals real money demand, where demand depends on the interest rate and income.

Policy Analysis with the IS-LM Model

Policymakers can affect macroeconomic variables using fiscal policy (government spending G and/or taxes T) and monetary policy (money supply M). The IS-LM model analyzes the effects of these policies on output and interest rates.

An Increase in Government Purchases

When government purchases increase, the IS curve shifts right by 1/(1-MPC) × ΔG, causing output and income to rise. This raises money demand, causing the interest rate to rise. The higher interest rate reduces investment, so the final increase in Y is smaller than 1/(1-MPC) × ΔG.

📐 Formula: IS shift = [1/(1-MPC)] × ΔG → The multiplier effect of government spending on output

📌 Example: If MPC = 0.8, then 1/(1-0.8) = 5. A $100 billion increase in G shifts IS right by $500 billion, but the final Y increase will be less than $500 billion due to crowding out of investment.

A Tax Cut

Because consumers save (1-MPC) of the tax cut, the initial boost in spending is smaller for ΔT than for an equal ΔG. The IS curve shifts by [1/(1-MPC)] × (1-MPC) × ΔT = MPC/(1-MPC) × ΔT. The effects on r and Y are smaller for a ΔT than for an equal ΔG.

📐 Formula: IS shift from tax cut = [MPC/(1-MPC)] × ΔT → The tax multiplier, smaller than the government spending multiplier

Monetary Policy: An Increase in M

An increase in money supply (ΔM > 0) shifts the LM curve down (or to the right). This causes the interest rate to fall, which increases investment, causing output and income to rise.

💡 Why this matters: Expansionary monetary policy lowers interest rates to stimulate investment and output, while expansionary fiscal policy raises interest rates and crowds out some investment.

Interaction Between Monetary & Fiscal Policy

In the model, M, G, and T are exogenous. In the real world, monetary policymakers may adjust M in response to changes in fiscal policy, or vice versa. Such interaction may alter the impact of the original policy change.

Central Bank’s Response to ΔG > 0

When the government increases G, there are three possible central bank responses with different outcomes:

Response 1: Hold M constant — IS shifts right, LM unchanged. Results: ΔY = Y₂ - Y₁, Δr = r₂ - r₁ (both positive).

Response 2: Hold r constant — IS shifts right, central bank increases M to shift LM right. Results: ΔY = Y₃ - Y₁ (larger than response 1), Δr = 0.

Response 3: Hold Y constant — IS shifts right, central bank reduces M to shift LM left. Results: ΔY = 0, Δr = r₃ - r₁ (largest increase in r).

🔑 Definition — Crowding Out: The reduction in investment that occurs when increased government spending raises interest rates

💡 Why this matters: The central bank's response determines whether fiscal expansion affects output, interest rates, or both. Holding r constant maximizes the output effect; holding Y constant eliminates it entirely.

Shocks in the IS-LM Model

IS shocks are exogenous changes in the demand for goods and services. Examples include stock market boom/crash changing households' wealth (affecting C), or changes in business/consumer confidence affecting I and/or C.

LM shocks are exogenous changes in the demand for money. Examples include a wave of credit card fraud increasing money demand, or more ATMs/the Internet reducing money demand.

📌 Example: A stock market boom makes consumers wealthier, increasing C, shifting IS right → higher Y and r. This raises C and lowers I (due to higher r), reducing unemployment.

📌 Example: After credit card fraud, consumers use more cash, increasing money demand, shifting LM left → higher r and lower Y. This lowers C and I (both fall with Y), increasing unemployment.

What is the Central Bank’s Policy Instrument?

The central bank targets the discount rate: it announces a target value and uses monetary policy to shift the LM curve as needed to attain its target rate. The central bank targets interest rates instead of the money supply for two reasons: (a) interest rates are easier to measure than the money supply, and (b) the central bank might believe that LM shocks are more prevalent than IS shocks. If so, targeting the interest rate stabilizes income better than targeting the money supply.

🔑 Definition — Policy Instrument: The variable (typically the interest rate) that the central bank directly targets and adjusts to achieve its macroeconomic objectives

⭐ Key Takeaways

The IS-LM model's intersection determines equilibrium output and interest rates where both goods and money markets clear. Fiscal policy shifts the IS curve, while monetary policy shifts the LM curve, but their effects are interdependent — expansionary fiscal policy raises interest rates and crowds out investment, reducing the multiplier effect. The central bank's response to fiscal policy dramatically changes outcomes: holding M constant allows partial crowding out, holding r constant maximizes output expansion, and holding Y constant neutralizes fiscal policy entirely. IS shocks come from changes in goods demand (wealth, confidence) while LM shocks come from money demand changes (financial technology, payment methods). Central banks target interest rates rather than money supply because rates are easier to measure and targeting rates better stabilizes income when LM shocks are prevalent.

🧠 Quick Revision Questions

1. What determines the unique combination of Y and r in the IS-LM model?
2. Why is the final increase in Y smaller than 1/(1-MPC) × ΔG when government purchases increase?
3. Compare the effects of a tax cut versus an equal increase in government spending on output and interest rates.
4. What are the three possible central bank responses to an increase in government spending, and how do they affect the final change in output?
5. Why does the central bank choose to target interest rates rather than the money supply?

📘 Lecture 29 — IS-LM Framework and Aggregate Demand

📖 Overview: This lecture bridges the IS-LM model (which assumes a fixed price level) with the Aggregate Demand (AD) curve, showing how changes in the price level shift the LM curve and affect output. It explains how monetary and fiscal policies shift the AD curve, and analyzes the short-run and long-run effects of IS shocks and monetary policy changes.

🗂️ Topics Covered

Deriving the AD curve from the IS-LM model, showing the inverse relationship between price level and output; monetary policy effects on the AD curve; fiscal policy effects on the AD curve; short-run and long-run equilibrium in the IS-LM and AD-AS frameworks; analyzing short-run and long-run effects of an IS shock; analyzing short-run and long-run effects of a change in the money supply (ΔM).

📝 Lecture Summary

DERIVING THE AD CURVE

The Aggregate Demand (AD) curve captures the relationship between the price level (P) and output (Y). When the price level changes, it shifts the LM curve, affecting the interest rate (r) and therefore investment (I) and output (Y).

🔑 Definition — Aggregate Demand (AD) curve: A curve that shows the relationship between the price level and the quantity of output demanded.

📐 Intuition for slope of AD curve: P ↑ → (M/P) ↓ → LM shifts left → r ↑ → I ↓ → Y ↓. This inverse relationship gives the AD curve its downward slope.

📌 Example: When the price level rises from P₁ to P₂, real money balances (M/P) fall. This shifts the LM curve leftward from LM(P₁) to LM(P₂), increasing the interest rate from r₁ to r₂. Since investment is inversely related to the interest rate, output falls from Y₁ to Y₂, tracing out the downward-sloping AD curve.

MONETARY POLICY AND THE AD CURVE

The central bank can increase aggregate demand through expansionary monetary policy. An increase in the money supply (M) shifts the LM curve to the right at each price level, lowering the interest rate and increasing investment and output.

🔑 Definition — Monetary policy: Actions by the central bank that affect the money supply and interest rates.

📐 Effect: M ↑ → LM shifts right → r ↓ → I ↑ → Y ↑ at each value of P. This shifts the AD curve to the right (from AD₁ to AD₂).

📌 Example: Starting at equilibrium with LM(M₁/P₁), an increase in the money supply to M₂ shifts LM to LM(M₂/P₁). The interest rate falls from r₁ to r₂, investment rises, and output increases from Y₁ to Y₂ at the same price level P₁. The AD curve therefore shifts rightward.

FISCAL POLICY AND THE AD CURVE

Expansionary fiscal policy (increasing government spending G or decreasing taxes T) increases aggregate demand. A tax cut increases consumption (C), shifting the IS curve to the right, which increases output at each price level.

🔑 Definition — Fiscal policy: Government decisions about spending and taxation.

📐 Effect: T ↓ → C ↑ → IS shifts right → Y ↑ at each value of P. This shifts the AD curve to the right.

📌 Example: A tax cut increases disposable income, raising consumption. The IS curve shifts rightward, causing the interest rate to rise from r₁ to r₂ and output to increase from Y₁ to Y₂ at the same price level P₁. The AD curve shifts rightward.

IS-LM AND AD-AS IN THE SHORT RUN & LONG RUN

The force that moves the economy from the short run to the long run is the gradual adjustment of prices. In short-run equilibrium, if output (Y) differs from the natural rate (Ȳ), the price level will adjust over time.

🔑 Definition — Natural rate of output (Ȳ): The level of output the economy produces when all prices are fully flexible and resources are fully employed.

📐 Price adjustment rule:

• If Y > Ȳ → Price level will rise over time
• If Y < Y̅ → Price level will fall over time
• If Y = Y̅ → Price level remains constant

THE SR AND LR EFFECTS OF AN IS SHOCK

A negative IS shock (such as a decrease in consumer confidence or investment) shifts the IS curve leftward and the AD curve leftward, causing output to fall below its natural rate in the short run.

Short Run Impacts:

• Y ↑ (positive because Y moved)
• P 0 (prices are sticky in the SR)
• r ↑ (positive ΔY leads to a rise in r as IS slides along the LM curve)
• C ↑ (positive ΔY increases consumption: C = C(Y-T))
• I ↓ (since r increased, investment decreased)

Long Run Impacts:

• Y 0 (rising P shifts LM left, returning Y to Y* as required by long-run LRAS)
• P ↑ (to eliminate excess demand at P₀)
• r ↑ (reflecting leftward shift in LM due to +ΔP)
• C 0 (since both Y and T are back to initial levels)
• I ↓↓ (since r has risen even more due to +ΔP)

📌 Example: A negative IS shock shifts IS₁ to IS₂ and AD₁ to AD₂. In the new short-run equilibrium, Y < Y̅. Over time, P gradually falls, which causes the Short-Run Aggregate Supply (SRAS) curve to move down. The fall in P increases real money balances (M/P), which causes the LM curve to shift down. This process continues until the economy reaches a long-run equilibrium with Y = Y̅.

ANALYZE SR & LR EFFECTS OF ΔM

When the central bank increases the money supply (M), it has different effects in the short run and long run.

Short Run Impacts:

• Y ↑ (positive because Y moved)
• P 0 (prices are sticky in the SR)
• r ↓ (positive ΔY leads to a decrease in r as LM slides along the IS curve)
• C ↑ (positive ΔY increases consumption: C = C(Y-T))
• I ↑ (since r decreased, investment increased)

Long Run Impacts:

• Y 0 (rising P shifts LM left, returning Y to Y* as required by long-run LRAS)
• P ↑ (to eliminate excess demand at P₀)
• r 0 (leftward shift in LM due to +ΔP restores r to its original level)
• C 0 (since both Y and T are back to initial levels)
• I 0 (since Y or r has not changed)

💡 Why this matters: The only long-run impact of an increase in the money supply is an increase in the price level. This demonstrates the principle of monetary neutrality — in the long run, changes in the money supply only affect nominal variables (like the price level), not real variables (like output or the real interest rate).

⭐ Key Takeaways

The AD curve is derived from the IS-LM model and shows an inverse relationship between the price level and output — a higher price level reduces real money balances, raising interest rates and lowering investment and output. Both expansionary monetary policy (increasing M) and expansionary fiscal policy (increasing G or decreasing T) shift the AD curve to the right, increasing output at every price level. The key difference between short-run and long-run analysis is price flexibility: in the short run, prices are sticky, so changes in policy affect real output; in the long run, prices adjust fully, returning output to its natural rate. For an IS shock, output eventually returns to Ȳ, but the interest rate changes permanently. For a monetary policy shock, all real variables return to their original levels in the long run, with only the price level increasing — demonstrating monetary neutrality.

🧠 Quick Revision Questions

1. Explain the intuition for why the AD curve is downward sloping. What happens to the interest rate and investment when the price level rises?
2. How does expansionary monetary policy shift the AD curve? What happens to the LM curve and the interest rate?
3. How does expansionary fiscal policy shift the AD curve? What happens to the IS curve and the interest rate?
4. What are the short-run and long-run effects of a negative IS shock on output, the price level, the interest rate, consumption, and investment?
5. What are the short-run and long-run effects of an increase in the money supply on output, the price level, the interest rate, consumption, and investment? Why is money said to be neutral in the long run?

📘 Lecture 30 — The Mundell-Fleming Model

📖 Overview: This lecture introduces the Mundell-Fleming model, which extends the IS-LM framework to a small open economy with perfect capital mobility. It explains how fiscal, monetary, and trade policies affect output and exchange rates under both floating and fixed exchange rate systems, highlighting key differences from closed economy analysis.

🗂️ Topics Covered

The lecture covers the derivation and intuition of the IS* curve for goods market equilibrium and the LM* curve for money market equilibrium in a small open economy. It then presents equilibrium in the Mundell-Fleming model, distinguishes between floating and fixed exchange rate systems, and analyzes the effects of fiscal policy and monetary policy under floating exchange rates, including the crowding out mechanisms.

📝 Lecture Summary

THE MUNDELL-FLEMING MODEL

The Mundell-Fleming model portrays the relationship between the nominal exchange rate and the economy’s output. It is an extension of the IS-LM model. The key assumption of this model is the small open economy with perfect capital mobility, which implies that the domestic interest rate equals the world interest rate: r = r* (given).

IS* CURVE: GOODS MARKET EQUILIBRIUM

Goods market equilibrium is represented by the IS curve*. The equation is: Y = C(Y - T) + I(r*) + G + NX(e) Where e = nominal exchange rate = foreign currency per unit of domestic currency (e.g., 110 yen per dollar). The IS* curve is drawn for a given value of r*.

🔑 Definition — Nominal Exchange Rate (e): The price of domestic currency in terms of foreign currency (e.g., 110 yen per dollar).

💡 Why this matters: The IS* curve slopes downward because an increase in e (appreciation) causes a decrease in net exports (NX), which leads to a decrease in output (Y).

📐 Formula: IS* equation: Y = C(Y - T) + I(r*) + G + NX(e) → This equation shows that in a small open economy, output depends on consumption, investment at the world interest rate, government spending, and net exports which are a function of the exchange rate.

📌 Example: If e rises from 110 to 120 yen per dollar, domestic goods become more expensive for foreigners. This reduces NX, which in turn reduces Y. This relationship gives the IS* curve its negative slope.

LM* CURVE: MONEY MARKET EQUILIBRIUM

The LM curve* equation is: M/P = L(r*, Y). The LM* curve is drawn for a given value of r*. It is vertical because given r*, there is only one value of Y that equates money demand with supply, regardless of e.

🔑 Definition — LM* Curve: The set of combinations of e and Y where money supply equals money demand at the world interest rate.

📌 Example: Since r is fixed at r*, the level of output Y is uniquely determined by the money market equilibrium condition. A change in e does not affect money demand or supply, so the LM* curve is vertical at that Y.

EQUILIBRIUM IN THE MUNDELL-FLEMING MODEL

Equilibrium occurs at the intersection of the IS* and LM* curves. This determines the equilibrium exchange rate and the equilibrium level of income. At this point, both the goods market and the money market are in simultaneous equilibrium.

FLOATING & FIXED EXCHANGE RATES

In a system of floating exchange rates, e is allowed to fluctuate in response to changing economic conditions. In contrast, under fixed exchange rates, the central bank trades domestic for foreign currency at a predetermined price. The lecture analyzes fiscal and monetary policy under both systems.

🔑 Definition — Floating Exchange Rate: A system where the exchange rate is determined by market forces without central bank intervention.

🔑 Definition — Fixed Exchange Rate: A system where the central bank commits to buying or selling domestic currency at a predetermined price to maintain a specific exchange rate.

FISCAL POLICY UNDER FLOATING EXCHANGE RATES

The model equations are: Y = C(Y - T) + I(r*) + G + NX(e) M/P = L(r*, Y)

At any given value of e, a fiscal expansion (increase in G or decrease in T) increases Y, shifting the IS* curve to the right.

📌 Example: Suppose the government increases G. At the initial exchange rate e₁, this raises Y, shifting IS* right from IS₁ to IS₂. The new equilibrium is at e₂ > e₁, but Y remains at Y₁.

Results: Δe > 0 (appreciation), ΔY = 0.

LESSONS ABOUT FISCAL POLICY

In a small open economy with perfect capital mobility, fiscal policy is utterly incapable of affecting real GDP. The “crowding out effect” works differently here than in a closed economy.

In a closed economy, fiscal policy crowds out investment by causing the interest rate to rise. In a small open economy, fiscal policy crowds out net exports by causing the exchange rate to appreciate.

MONETARY POLICY UNDER FLOATING EXCHANGE RATES

An increase in M shifts the LM* curve right because Y must rise to restore equilibrium in the money market.

📌 Example: Suppose the central bank increases the money supply M. The LM* curve shifts right from LM₁ to LM₂. The new equilibrium is at e₂ < e₁ (depreciation) and Y₂ > Y₁.

Results: Δe < 0 (depreciation), ΔY > 0 (increase in output).

LESSONS ABOUT MONETARY POLICY

Monetary policy affects output by affecting one (or more) of the components of aggregate demand.

In a closed economy: ↑M → ↓r → ↑I → ↑Y In a small open economy: ↑M → ↓e → ↑NX → ↑Y

💡 Why this matters: Expansionary monetary policy does not raise world aggregate demand; it shifts demand from foreign to domestic products. Thus, the increases in income and employment at home come at the expense of losses abroad.

⭐ Key Takeaways

The Mundell-Fleming model is the essential framework for understanding how macroeconomic policies affect small open economies with perfect capital mobility. Under floating exchange rates, fiscal policy is completely ineffective at changing output because it only appreciates the exchange rate and crowds out net exports. Monetary policy, by contrast, is highly effective because it depreciates the exchange rate and boosts net exports. The model clearly demonstrates that the transmission mechanisms of policy differ fundamentally between closed and open economies due to the interest rate parity condition (r = r*). Crucially, expansionary monetary policy in a small open economy is a "beggar-thy-neighbor" policy that boosts domestic output at the expense of foreign economies.

🧠 Quick Revision Questions

1. What is the key assumption of the Mundell-Fleming model regarding capital mobility and interest rates?
2. Why is the LM* curve vertical in the Mundell-Fleming model?
3. Under floating exchange rates, what happens to output and the exchange rate when a government increases its spending?
4. In a small open economy with floating exchange rates, what is the transmission mechanism of expansionary monetary policy? (Start with ↑M)
5. How does the "crowding out" effect of fiscal policy differ between a closed economy and a small open economy?

📘 Lecture 31 — The Mundell-Fleming Model (Continued)

📖 Overview: This lecture continues the analysis of the Mundell-Fleming model by examining trade policy under floating exchange rates, then introduces fixed exchange rate systems. It compares how fiscal, monetary, and trade policies affect output and exchange rates under both regimes, and concludes by incorporating interest-rate differentials into the model.

🗂️ Topics Covered

The lecture covers trade policy under floating exchange rates and its lessons, fixed exchange rate systems with equilibrium comparisons, fiscal and monetary policy effectiveness under fixed rates, trade policy under fixed rates, a summary table of policy effects across regimes, and an extension of the model to include interest-rate differentials from country risk and expected exchange rate changes.

📝 Lecture Summary

Trade Policy Under Floating Exchange Rates

At any given value of e (exchange rate), a tariff or quota reduces imports, increases NX (net exports), and shifts the IS* curve to the right. This causes the exchange rate to appreciate (from e₁ to e₂), but output remains unchanged at Y₁.

🔑 Definition — IS* curve: The relationship between the exchange rate and income in an open economy under the Mundell-Fleming model, where goods market equilibrium holds.

Lessons About Trade Policy

Import restrictions cannot reduce a trade deficit. Even though NX is unchanged, there is less trade: the trade restriction reduces imports, but exchange rate appreciation reduces exports. Less trade means fewer gains from trade. Import restrictions on specific products save jobs in domestic industries that produce those products, but destroy jobs in export-producing sectors. Hence, import restrictions fail to increase total employment. Worse yet, import restrictions create "sectoral shifts," which cause frictional unemployment.

Fixed Exchange Rates

Under a system of fixed exchange rates, the country's central bank stands ready to buy or sell the domestic currency for foreign currency at a predetermined rate. The central bank shifts the LM* curve as required to keep e at its pre-announced rate. This system fixes the nominal exchange rate. In the long run, when prices are flexible, the real exchange rate can move even if the nominal rate is fixed.

The lecture presents two cases: a. The Equilibrium exchange rate is greater than the fixed exchange rate b. The Equilibrium exchange rate is less than the fixed exchange rate

Fiscal Policy Under Fixed Exchange Rates

Under fixed exchange rates, a fiscal expansion would raise e. To keep e from rising, the central bank must sell domestic currency, which increases M (money supply) and shifts LM* right. Results: Δe = 0, ΔY > 0. Under floating rates, fiscal policy is ineffective at changing output. Under fixed rates, fiscal policy is very effective at changing output. LM shifts out!

📐 Formula: Fiscal expansion → e↑ → Central bank sells domestic currency → M↑ → LM* shifts right → Y↑

Monetary Policy Under Fixed Exchange Rates

An increase in M would shift LM* right and reduce e. To prevent the fall in e, the central bank must buy domestic currency, which reduces M and shifts LM* back left. Results: Δe = 0, ΔY = 0. Under floating rates, monetary policy is very effective at changing output. Under fixed rates, monetary policy cannot be used to affect output.

Trade Policy Under Fixed Exchange Rates

A restriction on imports puts upward pressure on e. To keep e from rising, the central bank must sell domestic currency, which increases M and shifts LM* right. Results: Δe = 0, ΔY > 0. Under floating rates, import restrictions do not affect Y or NX. Under fixed rates, import restrictions increase Y and NX. But these gains come at the expense of other countries, as the policy merely shifts demand from foreign to domestic goods.

M-F: Summary of Policy Effects

Interest-Rate Differentials

There are two reasons why r (domestic interest rate) may differ from r* (world interest rate):

1. Country risk: The risk that the country's borrowers will default on their loan repayments because of political or economic turmoil. Lenders require a higher interest rate to compensate them for this risk.
2. Expected exchange rate changes: If a country's exchange rate is expected to fall, then its borrowers must pay a higher interest rate to compensate lenders for the expected currency depreciation.

Differentials in the M-F Model

The model is modified as: r = r* + θ Where θ (theta) is a risk premium. Substitute the expression for r into the IS* and LM* equations:

• Y = C(Y - T) + I(r* + θ) + G + NX(e)
• M/P = L(r* + θ, Y)

🔑 Definition — θ (risk premium): The additional interest rate above the world rate required to compensate lenders for country risk or expected depreciation.

The Effects of an Increase in θ

An increase in θ causes:

• IS* shifts left, because θ↑ → r↑ → I↓ (investment falls)
• LM* shifts right, because θ↑ → r↑ → (M/P)ᵈ↓ (money demand falls), so Y must rise to restore money market equilibrium

The exchange rate falls (depreciates). The fall in e is intuitive: An increase in country risk or an expected depreciation makes holding the country's currency less attractive.

📌 Example: If investors believe a country's currency will depreciate by 5% next year, they will demand a higher interest rate (r = r* + 5%) to compensate. This expected depreciation becomes a self-fulfilling prophecy as the actual exchange rate falls. The increase in Y occurs because the boost in NX (from the depreciation) is even greater than the fall in I (from the rise in r).

💡 Why this matters: Expected depreciation is a self-fulfilling prophecy — if investors believe a currency will fall, their actions cause it to actually fall.

⭐ Key Takeaways

Under floating exchange rates, fiscal policy has no effect on output (crowded out by exchange rate appreciation), while monetary policy is very effective. Under fixed exchange rates, the opposite holds: fiscal policy is very effective (because the central bank must increase money supply to maintain the peg), while monetary policy cannot affect output (any attempt is offset by interventions to maintain the fixed rate). Trade policy under floating rates cannot reduce a trade deficit or increase output, but under fixed rates, import restrictions do increase Y and NX, though at the expense of other countries. The Mundell-Fleming model can be extended to include interest-rate differentials through a risk premium θ, where increased country risk or expected depreciation shifts IS* left and LM* right, causing currency depreciation but potentially increasing output if the boost from NX outweighs the fall in investment.

🧠 Quick Revision Questions

1. Why does fiscal policy have zero effect on output under floating exchange rates but increase output under fixed exchange rates?
2. What is the mechanism by which a central bank maintains a fixed exchange rate when there is upward pressure on the currency?
3. What are the two reasons why a country's interest rate might differ from the world interest rate?
4. Under which exchange rate regime can monetary policy effectively change output, and why?
5. What happens to IS* and LM* curves when the risk premium θ increases, and what is the net effect on output and the exchange rate?

📘 Lecture 32 — The Mundell-Fleming Model (Continued) & The Three Models of Aggregate Supply

📖 Overview: This lecture completes the study of the Mundell-Fleming (M-F) model by examining why income might not rise after depreciation, analyzing the South East Asian crisis, and comparing floating vs. fixed exchange rates. It then derives the Aggregate Demand (AD) curve from the M-F model and introduces the three models of Aggregate Supply — the sticky-wage, imperfect-information, and sticky-price models — all of which yield the same short-run supply equation.

🗂️ Topics Covered

The lecture first explores reasons income may not rise after a currency depreciation, including central bank intervention and import price effects. It presents data on the South East Asian crisis and compares floating vs. fixed exchange rate arguments. The M-F model is extended to derive the AD curve by allowing price level changes, then shows the transition from short run to long run. The concept of a large open economy is introduced as a middle ground. Finally, three models of aggregate supply are presented: the sticky-wage model, imperfect-information model, and sticky-price model, all implying the same relationship between output, the natural rate, and unexpected price level changes.

📝 Lecture Summary

WHY INCOME MIGHT NOT RISE?

After a depreciation of the domestic currency (which should boost net exports and income), income might not rise because of three possible shifts. The central bank may try to prevent the depreciation by reducing the money supply. The depreciation might boost the price of imports enough to increase the price level (which would reduce the real money supply). Consumers might respond to the increased risk by holding more money. Each of these would shift LM* leftward, reducing income instead of increasing it.

🔑 Definition — LM*: The LM* curve represents equilibrium in the money market in the Mundell-Fleming model under a floating exchange rate, showing combinations of income and the exchange rate where money supply equals money demand.

THE SOUTH EAST ASIAN CRISIS

The lecture presents data showing the severity of the 1997-98 Asian financial crisis. For example, Indonesia experienced a -59.4% exchange rate change (depreciation against the U.S. dollar) from July 1997 to January 1998, a -32.6% stock market change, and a -16.2% change in nominal GDP from 1997-98. Thailand saw a -48.3% exchange rate change, -25.6% stock market change, and -1.2% GDP change. In contrast, the U.S. had a 2.7% stock market increase and 2.3% GDP growth, with no exchange rate change listed.

FLOATING VS. FIXED EXCHANGE RATES

Arguments for floating rates include that they allow monetary policy to be used to pursue other goals such as stable growth and low inflation. Arguments for fixed rates include that they avoid uncertainty and volatility, making international transactions easier, and they discipline monetary policy to prevent excessive money growth and hyperinflation.

MUNDELL-FLEMING AND THE AD CURVE

Previously, the M-F model assumed a fixed price level. To derive the AD curve, we now consider the impact of a change in P (the price level). The M-F equations are rewritten as: (IS*) Y = C(Y − T) + I(r*) + G + NX(ε) (LM*) M/P = L(r*, Y) Earlier, NX could be written as a function of e (the nominal exchange rate) because e and ε (the real exchange rate) move in the same direction when P is fixed.

📐 Formula: ε = e × (P/P*), where P* is the foreign price level. The real exchange rate measures the price of domestic goods relative to foreign goods.

DERIVING THE AD CURVE

The AD curve has a negative slope because: As P increases, M/P (real money balances) decreases, causing LM* to shift left. This increases ε (the real exchange rate), which reduces NX (net exports), and thus reduces Y (income). This is shown graphically: LM*(P₂) lies to the left of LM*(P₁), at a higher ε₂ and lower Y₂, and the corresponding AD curve slopes downward from (P₁, Y₁) to (P₂, Y₂).

FROM SHORT RUN TO THE LONG RUN

If Y₁ < Y̅ (the natural rate of output), there is downward pressure on prices. Over time, P will move down, causing M/P to increase, which reduces ε, increases NX, and increases Y until the economy returns to Y̅ at the long-run equilibrium. This transition is shown graphically: as P falls from P₁ to P₂, the SRAS curve shifts from SRAS₁ to SRAS₂, and output moves from Y₁ back toward Y̅ along the AD curve.

💡 Why this matters: This mechanism explains how an economy self-corrects from short-run fluctuations to long-run equilibrium through price adjustment.

LARGE: BETWEEN SMALL AND CLOSED

Many countries — including the U.S. — are neither closed nor small open economies. A large open economy is in between the polar cases of closed and small open. Consider a monetary expansion: Like in a closed economy, ΔM > 0 reduces r (the interest rate), which increases I (investment) — though not as much. Like in a small open economy, ΔM > 0 reduces ε (the real exchange rate), which increases NX — though not as much. The IS* curve shows the new equilibrium at a higher Y₂.

THREE MODELS OF AGGREGATE SUPPLY

All three models imply the same equation: Y = Y̅ + α(P − Pᵉ) Where: Y is aggregate output, Y̅ is the natural rate of output, α is a positive parameter, P is the actual price level, and Pᵉ is the expected price level.

1- THE STICKY-WAGE MODEL

Assumes that firms and workers negotiate contracts and fix the nominal wage before they know what the price level will turn out to be. The nominal wage, W, they set is the product of a target real wage, ω, and the expected price level: W = ω × Pᵉ.

• If P = Pᵉ: The real wage (W/P) equals ω, unemployment and output are at their natural rates.
• If P > Pᵉ: Real wage is less than its target, so firms hire more workers and output rises above its natural rate.
• If P < Pᵉ: Real wage exceeds its target, so firms hire fewer workers and output falls below its natural rate.

🔑 Definition — Real wage: W/P, the purchasing power of nominal wages in terms of goods and services.

This model implies that the real wage should be counter-cyclical — it should move in the opposite direction as output over the course of business cycles. In booms, when P typically rises, the real wage should fall. In recessions, when P typically falls, the real wage should rise. This prediction does not come true in the real world.

💡 Why this matters: The failure of the counter-cyclical real wage prediction is a weakness of the sticky-wage model, motivating alternative models of aggregate supply.

⭐ Key Takeaways

The AD curve derived from the Mundell-Fleming model slopes downward because a higher price level reduces real money balances, appreciates the real exchange rate, reduces net exports, and lowers income. The transition from short run to long run involves price adjustment that restores output to its natural rate. All three aggregate supply models — sticky-wage, imperfect-information, and sticky-price — imply the same short-run relationship: output deviates from the natural rate only when the actual price level differs from the expected price level. The sticky-wage model specifically predicts a counter-cyclical real wage, which is not empirically observed. Understanding the distinction between small open, large open, and closed economies is essential for applying macroeconomic models to different countries.

🧠 Quick Revision Questions

1. What three factors can prevent income from rising after a currency depreciation in the Mundell-Fleming model, and how does each shift the LM* curve?
2. How does an increase in the price level (P) affect the real exchange rate (ε), net exports (NX), and income (Y) when deriving the AD curve from the M-F model?
3. In the sticky-wage model, what is the formula for the nominal wage (W) set by firms and workers, and what happens to output when P > Pᵉ?
4. What is the common equation implied by all three models of aggregate supply, and what does each variable represent?
5. Why does the prediction of a counter-cyclical real wage in the sticky-wage model fail to match real-world data?

📘 Lecture 33 — Three Models of Aggregate Supply (Continued)

📖 Overview: This lecture continues the examination of models explaining the short-run aggregate supply curve, focusing on the imperfect-information model and the sticky-price model. Understanding these models is crucial for grasping why output can deviate from its natural rate in the short run when the actual price level differs from the expected price level.

🗂️ Topics Covered

The lecture covers the second and third models of aggregate supply: the imperfect-information model, which is based on supplier confusion between relative and overall price changes, and the sticky-price model, which is based on firms setting prices in advance due to menu costs and contracts. For the sticky-price model, the lecture details the derivation of the overall price level and the aggregate supply curve, concluding with a note on the pro-cyclical real wage implication.

📝 Lecture Summary

2- THE IMPERFECT-INFORMATION MODEL

This model assumes all wages and prices are perfectly flexible and all markets clear. Each supplier produces one good but consumes many goods. The key assumption is that each supplier knows the nominal price of the good she produces but does not know the overall price level. The supply of each good depends on its relative price: the nominal price of the good divided by the overall price level. Since the supplier doesn't know the price level at the time of her production decision, she uses the expected price level, Pᵉ.

Suppose P rises but Pᵉ does not. The supplier thinks her relative price has risen (her good is now more valuable compared to others), so she produces more. With many producers thinking this way, output (Y) will rise whenever the actual price level (P) rises above the expected price level (Pᵉ).

🔑 Definition — Relative price: The nominal price of a good divided by the overall price level; what the good is truly worth in terms of purchasing power. 📐 Formula: Y = Y̅ + α (P - Pᵉ) → This is the short-run aggregate supply curve, showing output deviates from its natural rate when actual prices differ from expected prices.

3- THE STICKY-PRICE MODEL

Reasons for sticky prices include long-term contracts between firms and customers, menu costs (the costs of changing prices, like printing new menus), and firms not wishing to annoy customers with frequent price changes. The model assumes firms set their own prices (e.g., as in monopolistic competition). An individual firm’s desired price is:

p = P + a(Y - Y̅) where a > 0

This means a firm wants to set a higher nominal price when the overall price level (P) is higher or when aggregate output (Y) is above its natural rate (Y̅), as demand for its product is higher.

Suppose two types of firms:

• Firms with flexible prices set prices as above: p = P + a(Y - Y̅).
• Firms with sticky prices must set their price before they know how P and Y will turn out: p = Pᵉ + a(Yᵉ - Y̅ᵉ).

Assuming firms with sticky prices expect that output will equal its natural rate (Yᵉ = Y̅ᵉ), their formula simplifies to: p = Pᵉ.

To derive the aggregate supply curve, we first find an expression for the overall price level. Let s denote the fraction of firms with sticky prices. Then, the overall price level (P) is a weighted average:

P = s × Pᵉ + (1 - s) × [P + a(Y - Y̅)]

The price set by sticky price firms + The price set by flexible price firms

Now, solve for P:

1. Subtract (1 - s)P from both sides: sP = sPᵉ + (1 - s)[a(Y - Y̅)]
2. Divide both sides by s: P = Pᵉ + [(1 - s)a / s] × (Y - Y̅)

This equation shows:

• High Pᵉ ⇒ High P: If firms expect high prices, firms who must set prices in advance will set them high. Other firms respond by setting high prices.
• High Y ⇒ High P: When income is high, the demand for goods is high. Firms with flexible prices set high prices. The greater the fraction of flexible price firms (smaller s), the bigger the effect of a change in Y on P.

Finally, derive the AS equation by solving for Y:

Y = Y̅ + α (P - Pᵉ) , where α = s / [(1 - s)a]

💡 Why this matters: In contrast to the sticky-wage model, the sticky-price model implies a pro-cyclical real wage. Suppose aggregate output/income falls. Firms see a fall in demand for their products. Firms with sticky prices reduce production, and hence reduce their demand for labor. The leftward shift in labor demand causes the real wage to fall (a fall in the real wage accompanies a fall in output, hence pro-cyclical).

⭐ Key Takeaways

Both the imperfect-information and sticky-price models lead to the same short-run aggregate supply equation: Y = Y̅ + α(P - Pᵉ), showing output deviates from its natural rate when actual prices differ from expected prices. The imperfect-information model relies on suppliers misperceiving changes in the overall price level as changes in their relative price. The sticky-price model explains price stickiness through menu costs and contracts, where a fraction of firms set prices in advance based on expectations. The derived price level equation shows that higher expected prices or higher output leads to a higher actual price level. A key difference between models is the implication for the real wage: the sticky-wage model implies a counter-cyclical real wage, while the sticky-price model implies a pro-cyclical real wage.

🧠 Quick Revision Questions

1. In the imperfect-information model, what key information does a supplier lack when making a production decision?
2. In the sticky-price model, what are two reasons given for why firms might have "sticky" prices?
3. In the derivation of the sticky-price model, what does the variable "s" represent?
4. Write down the final formula for the short-run aggregate supply curve derived from the sticky-price model.
5. How does the sticky-price model's implication for the cyclical behavior of the real wage differ from that of the sticky-wage model?

📘 Lecture 34 — Inflation, Unemployment, and the Phillips Curve

📖 Overview: This lecture explores the relationship between inflation and unemployment through the Phillips Curve framework. It derives the modern Phillips Curve from the aggregate supply model, explains how expectations and supply shocks affect this relationship, and examines the policy trade-offs between inflation and unemployment in the short run versus long run.

🗂️ Topics Covered

The lecture covers deriving the Phillips Curve from the SRAS model, the relationship between the Phillips Curve and SRAS, adaptive expectations and inflation inertia, two causes of inflation (cost-push and demand-pull), graphing and shifting the Phillips Curve, the sacrifice ratio for disinflation, rational expectations theory, the natural rate hypothesis, and the alternative hypothesis of hysteresis.

📝 Lecture Summary

Inflation, Unemployment, and the Phillips Curve

The Phillips curve states that inflation (π) depends on expected inflation (πᵉ), cyclical unemployment (the deviation of the actual unemployment rate from the natural rate), and supply shocks (ν). The equation is: π = πᵉ – β(u – uⁿ) + ν, where β > 0 is an exogenous constant.

🔑 Definition — Phillips Curve: A curve that shows the short-run trade-off between inflation and unemployment. 📐 Formula: π = πᵉ – β(u – uⁿ) + ν → Inflation equals expected inflation minus β times cyclical unemployment plus supply shocks. 💡 Why this matters: This relationship is central to macroeconomic policy, showing that policymakers face a trade-off between inflation and unemployment in the short run.

Deriving the Phillips Curve from SRAS

Starting from the aggregate supply equation (1) Y = Ȳ + α(P – Pᵉ), we can derive the Phillips Curve. First, rewrite as (2) P = Pᵉ + (1/α)(Y – Ȳ). Then add a supply shock ν: (3) P = Pᵉ + (1/α)(Y – Ȳ) + ν. Subtract last year's price level P₋₁ from both sides: (4) (P – P₋₁) = (Pᵉ – P₋₁) + (1/α)(Y – Ȳ) + ν. The left side is inflation π, and the right side has expected inflation πᵉ: (5) π = πᵉ + (1/α)(Y – Ȳ) + ν.

Using Okun's law, which relates output and unemployment, we can write (6) (1/α)(Y – Ȳ) = –β(u – uⁿ). Substituting into equation 5 gives (7) π = πᵉ – β(u – uⁿ) + ν.

🔑 Definition — Okun's Law: The empirical relationship stating that for every 1% increase in the unemployment rate above the natural rate, real GDP falls by approximately 2%. 📐 Formula: (1/α)(Y – Ȳ) = –β(u – uⁿ) → Output gap is proportional to cyclical unemployment. 💡 Why this matters: This derivation shows how the Phillips Curve is directly linked to the aggregate supply model, connecting price level movements to unemployment fluctuations.

The Phillips Curve and SRAS

The SRAS curve states that output is related to unexpected movements in the price level: Y = Ȳ + α(P – Pᵉ). The Phillips curve states that unemployment is related to unexpected movements in the inflation rate: π = πᵉ – β(u – uⁿ) + ν. Both represent the same economic relationship from different perspectives—one focusing on output and price level, the other on unemployment and inflation.

Adaptive Expectations

Adaptive expectations is an approach that assumes people form their expectations of future inflation based on recently observed inflation. A simple example: πᵉ = π₋₁ (expected inflation equals last year's actual inflation). Then the Phillips curve becomes: π = π₋₁ – β(u – uⁿ) + ν.

Inflation Inertia

In this form, the Phillips curve implies that inflation has inertia. In the absence of supply shocks or cyclical unemployment, inflation will continue indefinitely at its current rate. Past inflation influences expectations of current inflation, which in turn influences the wages and prices that people set.

Two Causes of Rising and Falling Inflation

Cost-push inflation is inflation resulting from supply shocks. Adverse supply shocks typically raise production costs and induce firms to raise prices, "pushing" inflation up. Demand-pull inflation is inflation resulting from demand shocks. Positive shocks to aggregate demand cause unemployment to fall below its natural rate, which "pulls" the inflation rate up.

🔑 Definition — Cost-push inflation: Inflation caused by negative supply shocks that raise production costs. 🔑 Definition — Demand-pull inflation: Inflation caused by positive demand shocks that pull unemployment below its natural rate.

Graphing the Phillips Curve

In the short run, policymakers face a trade-off between π and u. The short-run Phillips Curve shows this inverse relationship. The curve crosses the natural rate of unemployment (uⁿ) at the level of expected inflation plus supply shocks (πᵉ + ν).

Shifting the Phillips Curve

People adjust their expectations over time, so the trade-off only holds in the short run. An increase in πᵉ shifts the short-run Phillips Curve upward, meaning that at any given unemployment rate, inflation will be higher.

The Sacrifice Ratio

To reduce inflation, policymakers can contract aggregate demand, causing unemployment to rise above the natural rate. The sacrifice ratio measures the percentage of a year's real GDP that must be foregone to reduce inflation by 1 percentage point. A typical estimate is 5.

If policymakers wish to reduce inflation from 6 to 2 percent (a 4-point reduction) and the sacrifice ratio is 5, then reducing inflation requires a loss of 4 × 5 = 20 percent of one year's GDP. This could be achieved as a 20% GDP reduction for one year, 10% for each of two years, or 5% for each of four years. The cost of disinflation is lost GDP, which can be translated into unemployment using Okun's law.

🔑 Definition — Sacrifice Ratio: The percentage of annual GDP lost to reduce inflation by 1 percentage point. 📐 Formula: GDP loss = (inflation reduction) × (sacrifice ratio) → For a 4-point reduction with ratio 5: loss = 20% of one year's GDP. 📌 Example: Reducing inflation from 6% to 2% with sacrifice ratio 5 means losing 20% of one year's GDP, achievable by reducing GDP by 5% for four consecutive years.

Rational Expectations

Rational expectations is an alternative way of modeling expectations where people base their expectations on all available information, including information about current and prospective future policies. This contrasts with adaptive expectations which rely only on past inflation.

Painless Disinflation?

Proponents of rational expectations believe that the sacrifice ratio may be very small. Suppose u = uⁿ and π = πᵉ = 6%, and the central bank credibly announces it will reduce inflation from 6 to 2 percent as soon as possible. If the announcement is credible, then πᵉ will fall, perhaps by the full 4 points. Then, π can fall without an increase in u.

🔑 Definition — Rational Expectations: The theory that people optimally use all available information, including information about current and future policies, to form their expectations.

The Natural Rate Hypothesis

Our analysis is based on the natural rate hypothesis: Changes in aggregate demand affect output and employment only in the short run. In the long run, the economy returns to the levels of output, employment, and unemployment described by the classical model.

An Alternative Hypothesis: Hysteresis

Hysteresis is the long-lasting influence of history on variables such as the natural rate of unemployment. Negative shocks may increase uⁿ, so the economy may not fully recover. The skills of cyclically unemployed workers deteriorate while unemployed, and they cannot find a job when the recession ends. Cyclically unemployed workers may lose their influence on wage-setting; insiders (employed workers) may then bargain for higher wages. The cyclically unemployed "outsiders" may become structurally unemployed when the recession ends.

🔑 Definition — Hysteresis: The theory that the natural rate of unemployment depends on the history of actual unemployment, so temporary shocks can permanently affect the natural rate.

⭐ Key Takeaways

The Phillips Curve—π = πᵉ – β(u – uⁿ) + ν—is derived directly from the SRAS model and shows the short-run trade-off between inflation and unemployment. This trade-off can shift due to changes in expected inflation and supply shocks, meaning the Phillips Curve is not stable in the long run. The sacrifice ratio quantifies the GDP cost of reducing inflation, typically estimated around 5% of GDP per percentage point reduction. Rational expectations theory suggests that if disinflation policy is credible, inflation expectations can adjust quickly, potentially achieving painless disinflation. The natural rate hypothesis states that in the long run, the economy returns to its natural rate of unemployment regardless of demand-side policies, though hysteresis challenges this by suggesting that cyclical unemployment can become structural.

🧠 Quick Revision Questions

1. What are the three forces that determine inflation according to the modern Phillips Curve?
2. How is the Phillips Curve derived from the aggregate supply equation?
3. What is the difference between cost-push inflation and demand-pull inflation?
4. If the sacrifice ratio is 5, what GDP loss is required to reduce inflation from 8% to 3%?
5. How do adaptive expectations and rational expectations differ in their implications for disinflation policy?

📘 Lecture 35 — Government Debt

📖 Overview: This lecture examines government debt, its components, and the measurement of budget deficits. It explores the distinction between permanent, floating, and unfunded debt, and critically analyzes problems in accurately measuring budget deficits, including the effects of inflation, capital assets, uncounted liabilities, and the business cycle.

🗂️ Topics Covered

The lecture begins by defining government debt and the annual budget deficit, then details the three components of domestic debt: permanent debt (market loans, bonds, prize bonds), floating debt (treasury bills), and unfunded debts (savings certificates, accounts). It presents data on domestic debt outstanding and trends in public debt from 1990 to 2004 as a percentage of GDP. The lecture then discusses serious problems in measurement, including the overstatement of deficits due to inflation, the need for capital budgeting to account for government assets, the exclusion of uncounted liabilities like pensions, and the automatic impact of the business cycle on deficit figures.

📝 Lecture Summary

Government Debt and the Annual Budget Deficit

When a government spends more than it collects in taxes, it borrows from the private sector to finance the budget deficit. The government debt is an accumulation of all past annual deficits.

Components of Domestic Debt

Domestic debt is categorized into three main components:

• Permanent Debt: This includes Market Loans, Federal Government Bonds, Income tax Bonds, National Funds Bonds, Federal investment Bonds, and Prize Bonds.
• Floating Debt: This consists of Treasury Bills and Market Treasury Bills.
• Unfunded Debts: This category includes Savings or Deposit Certificates, Savings Account, Postal Life insurance, and GP Fund.

Domestic Debt Outstanding

The lecture provides a data table showing the stock and flow of domestic debt in Million Rupees up to 31-Jan-05. The total domestic debt outstanding was 2,015,078 Million Rupees, with a net flow of 36,120. Floating debt saw the largest increase (68,704), while permanent and unfunded debt decreased.

Trends in Public Debt

A table shows the trend of public debt from 1990 to 2004. Key observations include that total public debt increased from Rs. 801.2 billion in 1990 to Rs. 3848.5 billion in 2004. However, as a percentage of GDP, total net public debt fell significantly from 91.7% in 1990 to 69.7% in 2004. Debt payable in rupees and foreign exchange both declined as a percentage of GDP over this period.

Budget Deficit of Pakistan

A graph illustrates the budget deficit of Pakistan as a percentage of GDP over time, showing a generally declining trend from a high near 10% of GDP to near zero.

Problems in Measurement

The standard formula states: Govt. Budget Deficit = Govt. Spending – Govt. Revenue = Amount of new debt. However, this measure has significant flaws. A meaningful deficit measurement should:

• Modify the real value of outstanding public debt to reflect current inflation.
• Subtract government assets from government debt.
• Include hidden liabilities that currently escape detection.
• Calculate a cyclically-adjusted budget deficit.

Inflation

Almost all economists agree the government’s indebtness should be measured in real terms, not nominal terms. The commonly measured budget deficit does not correct for inflation. If the real government debt is not changing, the nominal debt must be rising at the rate of inflation: ΔD / D = π, where π is the inflation rate and D is the stock of government debt. This means ΔD = πD, so the reported budget deficit is overstated by the amount πD.

Another perspective: For correct measurement, government expenditure should include only the real interest paid on the debt (rD), not the nominal interest paid (iD). Since i – r = π, the budget deficit is overstated by πD.

🔑 Definition — Overstated Deficit: The amount by which the reported budget deficit exceeds the true change in the government's real debt due to the erosion of the nominal debt's real value by inflation. 📐 Formula: Overstated Amount = πD → The nominal budget deficit is inflated by the inflation rate times the total stock of government debt. 📌 Example: In 1979, the reported budget deficit was $28 billion, with an inflation rate of 8.6% and government debt of $495 billion. The overstatement was πD = 0.086 x $495 = $43 billion. So, the true budget position was a surplus of $28 - $43 = $15 billion.

Capital Assets

An accurate assessment requires accounting for the government's assets as well as liabilities. The Govt. budget deficit = change in debt – change in assets. A budget procedure that accounts for assets as well as liabilities is called capital budgeting.

For example, if the government sells some of its land or buildings to reduce the deficit: under current procedure, the reported deficit is lower. Under capital budgeting, the reduction in debt is offset by a reduction in assets. Similarly, borrowing to finance the purchase of capital assets would not raise the deficit. 💡 Why this matters: Capital budgeting provides a more accurate picture of the government's net worth but is difficult to implement because it is hard to decide which expenditures count as capital expenditures.

Uncounted Liabilities

Measuring the budget deficit may be misleading because it excludes some government liabilities. These include pensions of government workers and the social security system. Although social security liabilities can be differentiated from government debt, the government can always choose not to repay all of its debt.

The Business Cycle

Changes in the deficit occur automatically in response to a fluctuating economy. For example, during a recession: falling incomes reduce personal taxes, falling profits reduce corporate taxes, and a higher number of needy persons increases government spending (G), causing the budget deficit to increase. These automatic changes are not errors in measurement, but they make it difficult to use the deficit to monitor changes in fiscal policy. A cyclically adjusted (full employment) budget deficit reflects policy changes but not the current stage of the business cycle.

⭐ Key Takeaways

The government debt is the accumulation of past budget deficits and is categorized into permanent, floating, and unfunded debt. A critical lesson is that the commonly reported budget deficit is a flawed measure because it does not correct for inflation, which significantly overstates the deficit (by πD). Accurately measuring the deficit requires capital budgeting to account for government assets and liabilities, as well as including uncounted liabilities like future pension obligations. Finally, the budget deficit automatically fluctuates with the business cycle, making it difficult to assess active fiscal policy changes unless a cyclically-adjusted measure is used.

🧠 Quick Revision Questions

1. What is the difference between permanent debt, floating debt, and unfunded debt? Give one example of each.
2. How does inflation cause the reported budget deficit to be overstated? Provide the formula and explain.
3. Explain what capital budgeting is and how it would change the assessment of a government's budget deficit compared to the standard method.
4. List two types of uncounted liabilities that can make the measured budget deficit misleading.
5. Why does a recession automatically increase the budget deficit, and why does this make it difficult to use the deficit to monitor fiscal policy?

📘 Lecture 36 — Government Debt (Continued)

📖 Overview: This lecture continues the analysis of government debt by comparing two competing views: the traditional view and the Ricardian view. It explains how tax cuts and budget deficits affect the economy through saving, investment, interest rates, and international trade, and then contrasts this with the Ricardian perspective that consumers anticipate future taxes.

🗂️ Topics Covered

The lecture covers the traditional view of government debt using the Solow growth model to show long-run effects of reduced saving and investment, followed by short-run analysis using IS-LM and Mundell-Fleming models to show output and exchange rate impacts. It then introduces the Ricardian view of government debt, explaining why forward-looking consumers might not change consumption in response to tax cuts, and discusses three reasons consumers may not be fully Ricardian: myopia, borrowing constraints, and concern for future generations.

📝 Lecture Summary

TRADITIONAL VIEW OF GOVT. DEBT

A tax cut stimulates consumer spending and reduces national saving. The reduction in saving raises the interest rate, which crowds out investment. The Solow growth model shows that lower investment leads to a lower steady-state capital stock and lower output.

SOLOW GROWTH MODEL

The change in capital stock equals investment minus depreciation: Δk = i – δk. Since i = s f(k), this becomes: Δk = s f(k) – δk.

📐 Formula: Δk = s f(k) – δk → The change in capital per worker equals saving (investment) minus depreciation.

The economy will then have less capital than the Golden Rule steady-state, which will mean lower consumption and lower economic well-being.

STARTING WITH TOO LITTLE CAPITAL

If K < K gold**, then increasing c* requires an increase in s. Future generations enjoy higher consumption, but the current one experiences an initial drop in consumption.

💡 Why this matters: There is a trade-off between current and future consumption when the economy starts with too little capital.

A TAX CUT

We have C = C(Y - T), at any value of r, ↓T ⇒ ↑C ⇒ ↑E ⇒ ↑Y. So the IS curve shifts to the right. The horizontal distance of the IS shift equals ΔY = MPC/(1 – MPC) ΔT.

📐 Formula: ΔY = MPC/(1 – MPC) × ΔT → The change in output equals the multiplier times the change in taxes.

INTERNATIONAL TRADE

When national saving falls, people borrow from abroad, causing a trade deficit. It also causes the local currency to appreciate.

MUNDELL-FLEMING MODEL

The model shows that the appreciation and resulting fall in net exports reduce the short-run expansionary effect of the fiscal change.

Equations: Y = C(Y – T) + I(r*) + G + NX(e) and M/P = L(r*, Y). At any given value of e, a fiscal expansion increases Y, shifting IS* to the right. Results: Δe > 0, ΔY = 0.

💡 Why this matters: Under floating exchange rates with perfect capital mobility, fiscal expansion has no effect on output—it only appreciates the currency.

THE RICARDIAN VIEW OF GOVERNMENT DEBT

Forward-looking consumers perceive that lower taxes now mean higher taxes later, leaving consumption unchanged. "Tax cuts are simply tax postponements." When the government borrows to pay for its current spending (higher G), rational consumers look ahead to the future taxes required to support this debt.

Another view:

• Govt. borrows Rs. 1,000 from a citizen to give him a Rs. 1,000 tax cut (similar to giving him a Rs. 1,000 govt. bond as a gift)
• On one side the government owes him Rs. 1,000 plus interest. On the other side, he owes Rs. 1,000 plus interest.
• Overall no change in citizen's wealth because the value of the bond is offset by the value of the future tax liability

🔑 Definition — Ricardian equivalence: Government Debt is equivalent to future taxes. If consumers are forward looking, future taxes are equivalent to current taxes. So, financing government by debt is equivalent to financing it by taxes.

CONSUMERS AND FUTURE TAXES

The essence of the Ricardian view is that when people choose their consumption, they rationally look ahead to the future taxes implied by government debt. But, how forward-looking are consumers? Defenders of the traditional view believe that the prospect of future taxes does not have as large an influence on current consumption as the Ricardian view assumes.

MYOPIA

The Ricardian view assumes that people are rational when making decisions. When the government borrows to pay for current spending, rational consumers look ahead to anticipate the future taxes required to support this debt.

The traditional view is that people are myopic, meaning that they see a decrease in taxes in such a way that their current consumption increases because of this new "wealth." They don't see that when expansionary fiscal policy is financed through bonds, they will just have to pay more taxes in the future since bonds are just tax-postponements.

BORROWING CONSTRAINTS

The Ricardian view assumes that consumers base their spending not only on current but on their lifetime income, which includes both current and expected future income. Advocates of the traditional view argue that current consumption is more important than lifetime income for those consumers who face borrowing constraints, which are limits on how much an individual can borrow from financial institutions.

A person who wants to consume more than his current income must borrow. If he can't borrow to finance his current consumption, his current income determines what he can consume, regardless of his future income. So, a debt-financed tax cut raises current income and thus consumption, even though future income is lower. In essence, when a government cuts current taxes and raises future taxes, it is giving tax payers a loan.

FUTURE GENERATIONS

According to the traditional view of government debt, consumers expect the implied future taxes to fall not on them but on future generations. This behavior raises the lifetime resources of the current generation as well as their consumption. In essence, the debt-financed tax cut stimulates consumption because it gives the current generation the opportunity to consume at the expense of the next generation.

⭐ Key Takeaways

The traditional view argues that tax cuts reduce national saving, raise interest rates, crowd out investment, and lower long-run output in the Solow model, while in the short run, they shift IS right and, under floating exchange rates, appreciate the currency with no output effect in the Mundell-Fleming model. The Ricardian view challenges this by arguing that forward-looking consumers see tax cuts as tax postponements, so they save the tax cut to pay future taxes, leaving consumption unchanged. The three main reasons consumers may not be fully Ricardian are myopia (they don't see future tax implications), borrowing constraints (they cannot borrow against future income), and concern for future generations (they expect future taxes to fall on others, not themselves). Ricardian equivalence implies that debt financing and tax financing are equivalent, while the traditional view holds that debt-financed tax cuts stimulate current consumption at the expense of future generations.

🧠 Quick Revision Questions

1. According to the Solow growth model, what happens to the steady-state capital stock and output when a tax cut reduces national saving?
2. Using the Mundell-Fleming model, what are the effects of a fiscal expansion on output and the exchange rate under floating exchange rates with perfect capital mobility?
3. What is the core proposition of Ricardian equivalence regarding government debt and future taxes?
4. List and explain the three reasons given in the lecture why consumers may not behave according to the Ricardian view.
5. According to the traditional view, why might a debt-financed tax cut increase consumption even though future taxes will be higher?

📘 Lecture 37 — Consumption Theories

📖 Overview: This lecture examines the evolution of consumption theory in macroeconomics, beginning with Keynes's conjectures about the consumption function and the empirical puzzles they generated. It then introduces Irving Fisher's intertemporal choice model, which provides a framework for understanding how rational, forward-looking consumers make consumption and saving decisions across different time periods.

🗂️ Topics Covered

The lecture covers Keynes's three conjectures about the consumption function including marginal and average propensities to consume, the secular stagnation hypothesis and Simon Kuznets's empirical findings that created the consumption puzzle, Fisher's intertemporal choice model showing how consumers allocate consumption across two periods, and the derivation and interpretation of the intertemporal budget constraint with saving and borrowing scenarios.

📝 Lecture Summary

JOHN MAYNARD KEYNES AND THE CONSUMPTION FUNCTION

The consumption function was central to Keynes's theory of economic fluctuations presented in The General Theory in 1936. Keynes made three specific conjectures about consumption behavior. First, he conjectured that the marginal propensity to consume—the amount consumed out of an additional dollar of income—is between zero and one. He claimed that out of every dollar of earned income, people will consume part of it and save the rest. Second, Keynes proposed the average propensity to consume—the ratio of consumption to income—falls as income rises. Third, Keynes held that income is the primary determinant of consumption and that the interest rate does not have an important role.

THE CONSUMPTION FUNCTION

The consumption function is expressed as C = C̅ + c Y, where C is consumption spending by households, C̅ is autonomous consumption, c is the marginal propensity to consume, and Y is income. This function exhibits three properties that Keynes conjectured: the marginal propensity to consume is between zero and one, the average propensity to consume falls as income rises, and consumption is determined by current income.

🔑 Definition — Marginal Propensity to Consume (MPC): The amount consumed out of an additional dollar of income, measuring the sensitivity of change in consumption with respect to a change in income.

🔑 Definition — Average Propensity to Consume (APC): The ratio of consumption to income, calculated as APC = C/Y = C̅/Y + c. As Y rises, C/Y falls, so the APC falls.

📌 Example: Consider a person who loves to shop with a large MPC of 0.99. This means that for every extra rupee earned after tax deductions, they spend 99 paisas of it.

AVERAGE PROPENSITY TO CONSUME

The APC is calculated as APC = C/Y = C̅/Y + c. As Y rises, C̅/Y falls, and so the average propensity to consume falls. Notice that the interest rate is not included in this function.

MARGINAL PROPENSITY TO CONSUME

To understand the MPC, consider a shopping scenario. A person who loves to shop probably has a large MPC, let's say 0.99. This means that for every extra rupee earned after tax deductions, they spend 99 paisas of it. The MPC measures the sensitivity of the change in one variable (C) with respect to a change in the other variable (Y).

SECULAR STAGNATION AND SIMON KUZNETS

During World War II, based on Keynes's consumption function, economists predicted that the economy would experience what they called secular stagnation—a long depression of infinite duration—unless fiscal policy was used to stimulate aggregate demand. However, the end of the war did not throw the U.S. into another depression, suggesting Keynes's conjecture that the APC would fall as income rose appeared not to hold. Simon Kuznets constructed new aggregate data on consumption and investment dating back to 1869, discovering that the ratio of consumption to income was stable over time despite large increases in income. This called Keynes's conjecture into question and created what became known as the consumption puzzle.

💡 Why this matters: This historical episode demonstrates that Keynes's short-run consumption function did not hold over long time periods, creating a major puzzle in macroeconomics that required new theoretical approaches.

CONSUMPTION PUZZLE

The failure of the secular-stagnation hypothesis and Kuznets's findings indicated that the APC is fairly constant over time. This presented a puzzle: why did Keynes's conjectures hold up well in studies of household data and in short time-series, but fail when long time-series were examined? Studies of household data and short time-series found a relationship between consumption and income similar to what Keynes conjectured—called the short-run consumption function (with falling APC). But studies using long time-series found that the APC did not vary systematically with income—called the long-run consumption function (with constant APC).

IRVING FISHER AND INTERTEMPORAL CHOICE

The economist Irving Fisher developed the model with which economists analyze how rational, forward-looking consumers make intertemporal choices—choices involving different periods of time. The model illuminates the constraints consumers face, the preferences they have, and how these constraints and preferences together determine their choices about consumption and saving. When consumers are deciding how much to consume today versus how much to consume in the future, they face an intertemporal budget constraint, which measures the total resources available for consumption today and in the future.

CONSUMER'S BUDGET CONSTRAINT

Consider a consumer who lives for two periods (representing youth and age). The consumer earns income Y₁ in period 1 and Y₂ in period 2, and consumes C₁ and C₂ in both periods respectively (adjusted for inflation). The savings in the first period will be S = Y₁ – C₁. In the second period, C₂ = (1 + r)S + Y₂, where r is the real interest rate. S can represent either saving or borrowing.

If C₁ < Y₁, the consumer is saving (S > 0). If C₁ > Y₁, the consumer is borrowing (S < 0). The model assumes the borrowing rate equals the saving rate.

Combining the two equations: C₂ = (1 + r)(Y₁ – C₁) + Y₂. Rearranging: (1 + r)C₁ + C₂ = (1 + r)Y₁ + Y₂. Dividing both sides by (1 + r): C₁ + C₂/(1+r) = Y₁ + Y₂/(1+r)

🔑 Formula: C₁ + C₂/(1+r) = Y₁ + Y₂/(1+r) — This is the intertemporal budget constraint, which states that the present value of consumption must equal the present value of income.

Key implications:

• If the interest rate is zero, total consumption in the two periods equals total income in the two periods
• In the usual case where r > 0, future consumption and future income are discounted by a factor of (1+r)
• This discounting arises from the interest earned on savings—future income is worth less than current income
• Because future consumption is paid for out of savings that have earned interest, future consumption costs less than current consumption
• The factor 1/(1+r) is the price of second-period consumption measured in terms of first-period consumption—the amount of first-period consumption the consumer must forgo to obtain 1 unit of second-period consumption

📌 Example: The budget constraint shows combinations of first-period and second-period consumption the consumer can choose. If a consumer chooses a point between A and B on the budget line, they consume less than their income in the first period and save the rest. If they choose between A and C, they consume more than their income in the first period and borrow to make up the difference. The vertical intercept is (1+r)Y₁ + Y₂, and the horizontal intercept is Y₁ + Y₂/(1+r).

⭐ Key Takeaways

The consumption puzzle arose because Keynes's short-run consumption function (with falling APC) held for household data and short time-series, while Kuznets found a long-run consumption function (with constant APC) over long time-series. Fisher's intertemporal choice model resolves this by showing consumers are forward-looking and consider both present and future income when making consumption decisions, unlike Keynes's assumption that only current income matters. The intertemporal budget constraint, C₁ + C₂/(1+r) = Y₁ + Y₂/(1+r), is the fundamental relationship showing that the present value of lifetime consumption equals the present value of lifetime income. The real interest rate determines the price of future consumption relative to present consumption, with higher rates making future consumption cheaper. Understanding both the static Keynesian consumption function and Fisher's dynamic intertemporal framework is essential for analyzing how consumers respond to income changes across different time horizons.

🧠 Quick Revision Questions

1. What were Keynes's three conjectures about the consumption function, and which one was contradicted by Kuznets's long-run data?
2. Why did economists predict secular stagnation after World War II, and why did this prediction fail?
3. What is the consumption puzzle, and how does it relate to the difference between short-run and long-run consumption functions?
4. Derive the intertemporal budget constraint for a two-period consumer and explain what happens to it when the interest rate increases.
5. If a consumer has Y₁ = 100, Y₂ = 50, and r = 0.1, what is the maximum amount they can consume in the first period?

📘 Lecture 38 — Consumption Theories (Continued)

📖 Overview: This lecture continues the exploration of consumption theories by examining how consumers make intertemporal choices. It introduces Irving Fisher's model of consumer preferences and optimization, analyzes how changes in income and real interest rates affect consumption, and discusses the implications of borrowing constraints. The lecture concludes with a case study on Japan's high savings rate.

🗂️ Topics Covered

This lecture covers consumer preferences and indifference curves for two-period consumption, the optimization process where consumers maximize satisfaction subject to budget constraints, the effects of income changes on consumption when goods are normal, the decomposition of interest rate changes into income and substitution effects, the empirical relationship between savings and interest rates, the concept of borrowing constraints and their impact on consumption functions, and a case study analyzing Japan's high savings rate and its economic implications.

📝 Lecture Summary

CONSUMER PREFERENCES

The consumer's preferences regarding consumption in two periods (first-period and second-period) can be represented by indifference curves. An indifference curve shows the combination of first-period and second-period consumption that makes the consumer equally happy. The slope at any point on the indifference curve shows how much second-period consumption the consumer requires to be compensated for a 1-unit reduction in first-period consumption. This slope is the marginal rate of substitution (MRS) between first-period and second-period consumption. It tells us the rate at which the consumer is willing to substitute second-period consumption for first-period consumption.

Higher indifference curves (such as IC2) are preferred to lower ones (such as IC1). The consumer is equally happy at points W, X, and Y on IC1, but prefers point Z on IC2 to all the others — Point Z is on a higher indifference curve and is therefore not equally preferred to W, X, and Y.

🔑 Definition — Marginal Rate of Substitution (MRS): The rate at which a consumer is willing to substitute second-period consumption for first-period consumption, shown by the slope of the indifference curve.

OPTIMIZATION

The consumer achieves his highest (or optimal) level of satisfaction by choosing the point on the budget constraint that is on the highest indifference curve. At the optimum, the indifference curve is tangent to the budget constraint.

🔑 Definition — Optimization: The consumer chooses the point on the budget constraint that lies on the highest attainable indifference curve, where the indifference curve is tangent to the budget constraint.

HOW CHANGES IN INCOME AFFECT CONSUMPTION?

An increase in either first- or second-period income shifts the budget constraint outward. If consumption in period one and consumption in period two are both normal goods — those that are demanded more as income rises — this increase in income raises consumption in both periods. The new budget constraint shows higher possible consumption in both periods.

📐 Formula: New budget constraint after income increase → Allows higher consumption in both periods if both are normal goods.

HOW CHANGES IN REAL INTEREST RATE AFFECT CONSUMPTION?

Economists decompose the impact of an increase in the real interest rate on consumption into two effects: an income effect and a substitution effect.

1. The income effect is the change in consumption that results from the movement to a higher indifference curve.
2. The substitution effect is the change in consumption that results from the change in the relative price of consumption in the two periods.

An increase in the interest rate rotates the budget constraint around the point C, where C is (Y1, Y2). The higher interest rate reduces first period consumption (move to point A) and raises second-period consumption (move to point B). Irving Fisher's Model shows that depending on consumer preferences, changes in real interest rate could either raise or lower consumption. So, economic theory alone cannot predict how interest rate influences consumption. Therefore, economists have studied the empirics of interest rate affecting consumption and saving.

💡 Why this matters: The net effect of an interest rate change on consumption is ambiguous because the income and substitution effects work in opposite directions. The substitution effect encourages saving (less current consumption), while the income effect can increase or decrease current consumption depending on whether the consumer is a saver or borrower.

SAVINGS AND THE REAL INTEREST RATE

Data shows that there is no apparent relationship between the two variables. Or, savings does not depend on interest rate. Economists claim that income and substitution effects of higher interest rates approximately cancel each other out.

CONSTRAINTS ON BORROWINGS

The inability to borrow prevents current consumption from exceeding current income. A constraint on borrowing can therefore be expressed as C1 ≤ Y1. This inequality states that consumption in period one must be less than or equal to income in period one. This additional constraint on the consumer is called a borrowing constraint, or sometimes, a liquidity constraint.

Conclusions: The analysis of borrowing leads us to conclude that there are two consumption functions:

• For some consumers, the borrowing constraint is not binding, and consumption in both periods depends on the present value of lifetime income.
• For other consumers, the borrowing constraint binds. Hence, for those consumers who would like to borrow but cannot, consumption depends only on current income.
• If the consumer cannot borrow, he faces the additional constraint that 1st period consumption cannot exceed 1st period income.

🔑 Definition — Borrowing Constraint (Liquidity Constraint): The restriction that a consumer cannot borrow, so first-period consumption cannot exceed first-period income (C1 ≤ Y1).

HIGH JAPANESE SAVINGS RATE

Japan has one of the world's highest savings rates. On one hand, many economists believe that this is a key to the rapid growth Japan experienced in the decades after World War II. The Solow growth model also shows that saving rate is a primary determinant of a country's steady state level of income. An increase in the saving rate raises investment, causing the capital stock to grow toward a new steady state.

On the other hand, some economists say that high savings rate has contributed to Japan's slump during the 1990s. High savings means lower consumption which, according to the IS-LM model, translates into low aggregate demand and reduced income.

Why Do Japanese consume so little or save so much?

• It is harder for households to borrow in Japan.
• In case of borrowing to purchase a house (the most common cause of borrowing), down payment rates are very high (up to 40%).
• Japanese Tax system encourages saving by taxing capital income very lightly.
• Japanese are more risk averse and patient.

⭐ Key Takeaways

The most critical concepts from this lecture are: (1) Consumer preferences for two-period consumption are represented by indifference curves, and optimization occurs where the highest indifference curve is tangent to the budget constraint. (2) Changes in real interest rates have both income and substitution effects on consumption; these effects work in opposite directions, making the overall impact ambiguous. (3) Borrowing constraints create a bifurcation in consumption functions — for consumers who are not constrained, consumption depends on lifetime income; for those who are constrained, consumption depends only on current income. (4) Japan's high savings rate has been both praised for fueling post-war growth and criticized for contributing to the 1990s slump, influenced by borrowing difficulties, tax policy, and cultural factors. (5) Empirical evidence suggests there is no clear relationship between savings and the real interest rate, as income and substitution effects approximately cancel out.

🧠 Quick Revision Questions

1. How does the marginal rate of substitution relate to the slope of an indifference curve, and what does it measure?
2. In Fisher's two-period model, what is the condition for consumer optimization?
3. When the real interest rate rises, explain how the income effect and substitution effect on first-period consumption differ.
4. What is a borrowing constraint, and how does it change the consumption function for consumers who are bound by it?
5. According to the lecture, what are the four reasons given for Japan's exceptionally high savings rate?

📘 Lecture 39 — Consumption Theories (Continued)

📖 Overview: This lecture continues the exploration of consumption theories, addressing the puzzle posed by Simon Kuznets regarding why Keynes' consumption function held true in short-term data but failed over long periods. It presents major theoretical resolutions including Fisher's intertemporal choice model, Modigliani's life-cycle hypothesis, Friedman's permanent-income hypothesis, and Hall's random-walk hypothesis, which collectively explain how forward-looking consumers make consumption decisions over time.

🗂️ Topics Covered

The lecture revisits Keynes' consumption function properties and Kuznets' consumption puzzle, then introduces Fisher's model of intertemporal choice to analyze how rational consumers make decisions across time periods. It develops Modigliani's life-cycle hypothesis showing how consumers smooth consumption over their lifetimes, presents the life-cycle consumption function and its solution to the consumption puzzle, examines consumption and saving behavior of the elderly, explains Friedman's permanent-income hypothesis distinguishing permanent from transitory income, and concludes with Hall's random-walk hypothesis incorporating rational expectations.

📝 Lecture Summary

JOHN MAYNARD KEYNES AND THE CONSUMPTION FUNCTION

The consumption function exhibits three properties that Keynes conjectured: the marginal propensity to consume c is between zero and one, the average propensity to consume falls as income rises, and consumption is determined by current income.

🔑 Definition — Marginal Propensity to Consume (MPC): The fraction of an additional unit of income that is spent on consumption, with value between 0 and 1.

🔑 Definition — Average Propensity to Consume (APC): Total consumption divided by total income (C/Y), which Keynes believed falls as income increases.

SIMON KUZNETS AND THE CONSUMPTION PUZZLE

The failure of the secular-stagnation hypothesis and Kuznets' findings both indicated that the average propensity to consume is fairly constant over time. This presented a puzzle: why did Keynes' conjectures hold up well in household data and short time-series studies, but fail when long time series were examined?

🔑 Definition — Consumption Puzzle: The empirical observation that Keynes' prediction of a falling APC with rising income held in cross-sectional household data but not in long-term time series data, where APC remained constant.

IRVING FISHER AND INTERTEMPORAL CHOICE

The economist Irving Fisher developed the model with which economists analyze how rational, forward-looking consumers make intertemporal choices—choices involving different periods of time. The model illuminates the constraints consumers face, the preferences they have, and how these constraints and preferences together determine their choices about consumption and saving. When consumers decide how much to consume today versus the future, they face an intertemporal budget constraint, which measures the total resources available for consumption today and in the future.

🔑 Definition — Intertemporal Choice: Decisions involving trade-offs between consumption in different time periods, analyzed through Fisher's model of rational, forward-looking consumer behavior.

💡 Why this matters: Fisher's model provides the theoretical foundation for all modern consumption theories by recognizing that consumers look beyond their current income when making spending decisions.

FRANCO MODIGLIANI AND THE LIFE-CYCLE HYPOTHESIS

In the 1950s, Franco Modigliani, Ando and Brumberg used Fisher's model to study the consumption function aiming to resolve the consumption puzzle. According to Fisher's model, consumption depends on a person's lifetime income. Modigliani emphasized that income varies systematically over people's lives and that saving allows consumers to move income from high-income periods to low-income periods, forming the basis of his life-cycle hypothesis.

THE HYPOTHESIS

Most people plan to stop working at about age 65, expecting their incomes to fall when they retire, but they don't want a drop in their standard of living characterized by consumption. Suppose a consumer expects to live another T years, has wealth of W, and expects to earn income Y until she retires R years from now.

THE LIFE-CYCLE CONSUMPTION FUNCTION

The lifetime resources of a consumer for T years are wealth W and lifetime earnings of R × Y (assuming interest rate to be zero). To have smoothest consumption over her lifetime, she divides such that:

📐 Formula: C = (W + RY) / T → Consumption equals total lifetime resources (wealth plus lifetime earnings) divided by remaining years of life.

Alternatively: C = (1/T)W + (R/T)Y

📌 Example: If the consumer expects T = 50 years and R = 30 years of work, then: C = 1/50 W + 30/50 Y C = 0.02W + 0.6Y

Generalizing for the aggregate consumption function of the economy: 📐 Formula: C = αW + βY Where α = MPC out of Wealth, β = MPC out of Income

The graph shows the consumption function with intercept αW and slope β, indicating that consumption increases with both wealth and income.

SOLVING THE CONSUMPTION PUZZLE

According to the life-cycle consumption function: 📐 Formula: APC = C/Y = α(W/Y) + β

Because in short periods, wealth does not vary proportionately with income. High incomes correspond to low APC. But over longer periods, wealth and incomes grow together, resulting in a constant W/Y ratio and hence a constant APC.

The upward shift in the consumption function over time (as wealth accumulates with income growth) prevents the APC from falling as income increases, thus solving Keynes's puzzle.

📐 Formula: Consumption, Income and Wealth Over Life-Cycle During working years, income exceeds consumption, generating savings and accumulating wealth. After retirement, consumption exceeds income (pension), leading to dissavings and declining wealth until death.

CONSUMPTION AND SAVING OF ELDERLY

Research findings show that elderly people do not dissave as much as the life-cycle model predicts. In other words, the elderly do not run down their wealth as quickly as expected if they were trying to smooth consumption over their remaining years.

Reasons include:

• They are concerned about unpredictable expenses. Additional saving from uncertainty is called precautionary saving, possibly due to expecting a long life and planning for a longer retirement period.
• The precautionary saving explanation is not completely persuasive considering the availability of annuity schemes from insurance companies and public health insurance plans.
• They may want to leave bequests to their children.

🔑 Definition — Precautionary Saving: Additional saving motivated by uncertainty about future expenses, particularly relevant for elderly individuals concerned about longevity risk.

🔑 Definition — Bequests: Assets or wealth left to heirs, representing an alternative motive for elderly individuals to maintain wealth rather than consuming it.

MILTON FRIEDMAN AND THE PERMANENT-INCOME HYPOTHESIS

In 1957, Milton Friedman proposed the permanent-income hypothesis to explain consumer behavior. Its essence is that current consumption is proportional to permanent income. Friedman's hypothesis complements Modigliani's life-cycle hypothesis: both use Fisher's theory to argue that consumption should not depend on current income alone.

Unlike the life-cycle hypothesis which emphasizes that income follows a regular pattern over a person's lifetime, the permanent-income hypothesis emphasizes that people experience random and temporary changes in their incomes from year to year.

Friedman suggested viewing current income Y as the sum of two components:

📐 Formula: Y = YP + YT

• Permanent Income (YP): The part of income that people expect to persist in the future.
• Transitory Income (YT): The part of income that people do not expect to persist.

Friedman reasoned that consumption should depend primarily on permanent income because consumers use savings and borrowings to smooth consumption in response to transitory income changes.

📐 Formula: C = αYP Consumption is proportional to permanent income.

📐 Formula: APC = C/Y = αYP / Y

• When Y > YP, APC falls
• When Y < YP, APC rises

🔑 Definition — Permanent Income Hypothesis: The theory that consumption is proportional to permanent (expected long-run) income, not current income, with transitory income changes being saved or borrowed against.

ROBERT HALL AND THE RANDOM-WALK HYPOTHESIS

Robert Hall was the first to derive the implications of rational expectations for consumption. He showed that if the permanent-income hypothesis is correct and if consumers have rational expectations, then changes in consumption over time should be unpredictable. When changes in a variable are unpredictable, the variable is said to follow a random walk. According to Hall, the combination of the permanent-income hypothesis and rational expectations implies that consumption follows a random walk.

🔑 Definition — Random Walk Hypothesis: The theory that changes in consumption are unpredictable because consumers incorporate all available information about their permanent income into current consumption decisions, so only unexpected news (surprises) can change consumption.

💡 Why this matters: The random-walk hypothesis has strong implications for policy—if consumption follows a random walk, anticipated changes in income (like a pre-announced tax cut) will not affect consumption because consumers already incorporated that information into their permanent income estimates.

⭐ Key Takeaways

The lecture resolves the consumption puzzle by showing that Keynes' short-run consumption function fails in the long run because it ignores wealth and future expectations. The life-cycle hypothesis demonstrates that consumption depends on lifetime resources (wealth plus lifetime earnings), not just current income, explaining why APC remains constant over time as wealth and income grow together. The permanent-income hypothesis distinguishes between permanent and transitory income, with consumption responding primarily to permanent changes. The random-walk hypothesis incorporates rational expectations, suggesting that only unexpected changes affect consumption. All these theories share the insight that forward-looking consumers smooth consumption over time, making current consumption a poor indicator of current income.

🧠 Quick Revision Questions

1. What three properties did Keynes conjecture about the consumption function, and which one created the consumption puzzle when tested with long-term data?
2. How does the life-cycle consumption function (C = αW + βY) solve the puzzle of constant APC over long periods while falling APC in short periods?
3. According to Modigliani's life-cycle hypothesis, how does consumption, income, savings, and wealth behave before and after retirement?
4. What is the difference between permanent income and transitory income in Friedman's hypothesis, and why does consumption depend primarily on permanent income?
5. What does Robert Hall's random-walk hypothesis imply about the predictability of consumption changes and the effectiveness of anticipated policy changes?

📘 Lecture 40 — Investment Theories

📖 Overview: This lecture explores why investment is the most volatile component of GDP and examines the theoretical foundations behind investment behavior. It introduces three types of investment spending, with a primary focus on business fixed investment through the neoclassical model, explaining how firms make capital investment decisions based on the rental price and cost of capital.

🗂️ Topics Covered

The lecture covers three types of investment spending (business fixed investment, residential investment, and inventory investment), with detailed focus on business fixed investment. It introduces the neoclassical model of investment, explaining the rental price of capital and its determination through supply and demand, the Cobb-Douglas production function and MPK, the cost of capital including interest, depreciation, and capital gains/losses, and tax rules affecting investment decisions.

📝 Lecture Summary

Three Types of Investment Spending

Investment is the most volatile component of GDP, and much of the decline during recessions comes from drops in investment spending. The lecture explains that standard macroeconomic models like IS-LM use a simple investment function I = I(r) stating that investment decreases when the real interest rate increases. This lecture examines the deeper theory behind this relationship by building models of each type of investment to explain fluctuations in the economy.

The three key questions addressed are: why investment is negatively related to the interest rate, what causes the investment function to shift, and why investment rises during booms and falls during recessions.

Business Fixed Investment

Business fixed investment is the largest component of investment spending, accounting for about three-quarters of total investment. The term "business" means these investment goods are bought by firms for future production, and "fixed" means the capital will stay in place for a while, as opposed to inventory investment. This includes everything from fax machines to factories and computers to company cars.

The standard model is called the neoclassical model of investment, which examines the benefits and costs of owning capital goods. Three variables shift investment: the marginal product of capital, the interest rate, and tax rules.

The model imagines two kinds of firms: production firms that produce goods and services using rented capital, and rental firms that make all the investments in the economy. In reality, most firms perform both functions.

The Rental Price of Capital

A typical production firm decides how much capital to rent by comparing the cost and benefit of each unit of capital. The firm rents capital at a rental rate R and sells output at price P. The real cost of a unit of capital is R/P, and the real benefit is the marginal product of capital (MPK) —the extra output produced with one more unit of capital. MPK falls as the amount of capital rises.

To maximize profit, the firm rents capital until MPK falls to: MPK = R/P

Thus, MPK determines the downward-sloping demand curve for capital. At any point in time, the amount of capital in the economy is fixed, so the supply curve is fixed. The real rental price of capital adjusts to equilibrate demand and fixed supply.

🔑 Definition — Real Rental Price of Capital (R/P): The cost of renting one unit of capital, adjusted for the price level, determined by the equilibrium between the demand for capital (MPK) and the fixed supply of capital.

The Cobb-Douglas production function serves as a good approximation of how the actual economy turns capital and labor into goods and services:

📐 Formula: Y = AK^α L^(1-α)

Where Y = output, K = capital, L = labor, A = technology parameter, α = capital's share of output (between 0 and 1)

📐 Formula — MPK for Cobb-Douglas: MPK = αA (L/K)^(1-α)

Since the real rental price (R/P) equals MPK in equilibrium: R/P = αA (L/K)^(1-α)

This expression shows three key relationships:

• The lower the stock of capital, the higher the real rental price of capital
• The greater the amount of labor employed, the higher the real rental price of capital
• The better the technology, the higher the real rental price of capital

Events that reduce the capital stock, raise employment, or improve technology raise the equilibrium real rental price of capital.

The Cost of Capital

Rental firms buy capital goods and rent them out. The benefit of owning capital is the real rental price (R/P) for each unit owned and rented out. For each period, the rental firm bears three costs:

1. Interest cost: Purchase price of capital (PK) times the interest rate (i) = iPK
2. Cost of capital loss or gain: The change in the price of capital = -ΔPK (negative sign means a capital gain reduces cost)
3. Depreciation cost: The fraction of value lost per period (δ) times PK = δPK

📐 Formula — Total Cost of Capital: Total cost = iPK - ΔPK + δPK

Or: = PK(i - ΔPK/PK + δ)

The cost of capital depends on the price of capital, the interest rate, the rate of change of capital prices, and the depreciation rate.

📌 Example: A car rental company buys cars for Rs. 1,000,000 each and rents them out.

• Interest rate (i) = 10% per year, so interest cost = iPK = Rs. 100,000 per year
• Car prices rising at 6% per year, so capital gain = ΔPK = Rs. 60,000 per year
• Cars depreciate at 20% per year, so depreciation = δPK = Rs. 200,000 per year

Total cost of capital = iPK - ΔPK + δPK = 100,000 - 60,000 + 200,000 = Rs. 240,000 per year

💡 Why this matters: The cost of capital framework shows that investment decisions depend not just on interest rates but also on capital gains, depreciation, and tax considerations. This explains why investment can fluctuate dramatically even when interest rates are stable.

⭐ Key Takeaways

Investment is the most volatile component of GDP, with business fixed investment making up about three-quarters of total investment. The neoclassical model explains investment decisions through the interaction of the rental price of capital (determined by MPK) and the cost of capital (determined by interest rates, depreciation, and capital gains/losses). The Cobb-Douglas production function shows that MPK depends on the capital stock, labor employed, and technology level. The cost of capital includes three components: interest cost, capital gains or losses, and depreciation. Understanding the difference between the rental price (benefit of owning capital) and the cost of capital is crucial for predicting how changes in interest rates, technology, or tax policy will affect investment spending.

🧠 Quick Revision Questions

1. What are the three types of investment spending and which is the largest?
2. According to the neoclassical model, what condition determines how much capital a production firm will rent?
3. What are the three variables that shift business fixed investment according to the neoclassical model?
4. What are the three components of the cost of capital faced by a rental firm?
5. Using the Cobb-Douglas production function, explain how a decrease in the capital stock affects the real rental price of capital.

📘 Lecture 41 — Investment Theories (Continued)

📖 Overview: This lecture continues the study of investment theories, focusing on the neoclassical model of investment. It explains how firms determine the cost of capital, make investment decisions based on profitability, and how taxes influence these decisions. Understanding this model is crucial for analyzing how interest rates and fiscal policy affect aggregate demand and long-run economic growth.

🗂️ Topics Covered

This lecture covers the concept of the cost of capital and its formula, the determinants of net investment based on comparing the marginal product of capital to the cost of capital, and the derivation of the neoclassical investment function. It also explains the long-run steady state condition where the marginal product of capital equals the cost of capital, and discusses the effects of corporate taxes, including the corporate income tax and the investment tax credit, with a real-world example from Sweden.

📝 Lecture Summary

THE COST OF CAPITAL

The lecture begins by defining the total cost of capital, which is the cost a firm incurs from owning and using a unit of capital. This cost includes the opportunity cost of the funds tied up in the capital, any change in the price of the capital good, and the cost of depreciation. The formula for the total cost of capital is: Total cost of capital = iPk - ΔPk + δPk, which simplifies to Pk (i - ΔPk/Pk + δ). This shows the cost depends on the price of capital (Pk), the nominal interest rate (i), the rate of change of capital prices, and the depreciation rate (δ).

Assuming capital goods prices rise with the general price level, the rate of change of capital prices (ΔPk/Pk) equals the overall inflation rate (π). Since the real interest rate (r) is defined as i - π, the cost of capital simplifies to: Cost of Capital = Pk (r + δ). To express this relative to other goods in the economy, the real cost of capital is defined as the cost measured in terms of the economy’s output. The formula for this is: 🔑 Definition — Real Cost of Capital: (PK / P) (r + δ), where P is the overall price level. This represents the cost of buying and renting out a unit of capital in terms of the economy's output.

THE DETERMINANTS OF INVESTMENT

This section explains how a rental firm decides whether to increase or decrease its capital stock. For each unit of capital, the firm earns a real revenue of R/P and bears a real cost of (PK / P) (r + δ). The real profit per unit of capital is therefore: 📐 Formula: Profit rate = Revenue - Cost = R/P - (PK / P) (r + δ). Because the real rental price (R/P) equals the marginal product of capital (MPK) in equilibrium, this can be rewritten as: 📐 Formula: Profit rate = MPK - (PK / P) (r + δ).

The change in the capital stock, called net investment (ΔK), depends on this profit incentive:

• If the MPK exceeds the cost of capital, firms will add to their capital stock (positive net investment).
• If the MPK falls short of the cost of capital, firms will let their capital stock shrink (negative net investment). Thus, net investment is a function of the gap between MPK and the cost of capital: 📐 Formula: ΔK = In [MPK - (PK / P) (r + δ)], where In() is the function showing how much net investment responds to the incentive to invest. 📌 Example: If a firm’s MPK is 15% and its real cost of capital is 10%, then the profit rate is +5%. This incentive would lead the firm to increase its capital stock. Conversely, if the MPK is 5% and the cost of capital is 10%, the profit rate is -5%, leading the firm to shrink its capital stock.

THE INVESTMENT FUNCTION

The neoclassical model of investment derives the total investment function (I). Total spending on business fixed investment is the sum of net investment and the replacement of depreciated capital (δK). The investment function is: 📐 Formula: I = In [MPK - (PK / P) (r + δ)] + δK

This model shows why investment depends negatively on the real interest rate (r).

• A decrease in the real interest rate lowers the cost of capital, raising the profit from owning capital and increasing the incentive to invest.
• An increase in the real interest rate raises the cost of capital, leading firms to reduce their investment. This relationship creates the downward-sloping investment function, where I falls as r rises. An outward shift in the investment function can be caused by an increase in the MPK, for instance, due to a technological innovation. 💡 Why this matters: This model links monetary policy (which affects real interest rates) directly to investment spending, a key component of aggregate demand.

The lecture then describes the adjustment of the capital stock over time towards a steady state. If the MPK is above the cost of capital, the capital stock rises, causing the MPK to fall. If the MPK is below the cost of capital, the capital stock falls, causing the MPK to rise. This process continues until the MPK equals the cost of capital, at which point the capital stock reaches a steady state: 📐 Formula: MPK = (PK / P) (r + δ)

TAXES AND INVESTMENT

Tax laws influence firms' incentives to accumulate capital. Two important provisions of corporate taxes are discussed:

• Corporate Income Tax: This is a tax on corporate profits. Its effect on investment depends on how profit is defined for tax purposes. If the tax law defined profit as R/P - (PK / P)(r + δ), the tax would not distort investment decisions. However, tax laws often differ, for example, by using depreciation at historical cost instead of current economic value, which can affect the cost of capital and distort investment incentives.
• Investment Tax Credit: This is a tax provision that encourages capital accumulation. It reduces a firm’s taxes by a certain amount for each monetary unit spent on capital goods. This effectively reduces the purchase price of capital (Pk), thereby lowering the cost of capital and raising investment. 🔑 Definition — Investment Tax Credit: A tax provision that reduces a firm's taxes proportionate to its spending on new capital goods, effectively lowering the purchase price of capital and stimulating investment.

SWEDISH INVESTMENT FUNDS SYSTEM

This section provides a historical example of how tax incentives were used to control aggregate demand. From the mid-1950s to the mid-1970s, the government of Sweden implemented a system called the Investment Fund system.

• During an economic slowdown, authorities offered a temporary investment subsidy to encourage investment and boost aggregate demand.
• During an economic recovery, the subsidy was revoked.
• Eventually, the subsidy became a permanent feature of Swedish tax policy.

⭐ Key Takeaways

The neoclassical model of investment explains that a firm's investment decision hinges on the profitability of capital, which is the difference between the marginal product of capital (MPK) and the real cost of capital (Pk/P times r+δ). The cost of capital is a function of the price of capital, the real interest rate, and the depreciation rate. The investment function is downward-sloping with respect to the real interest rate because a lower interest rate reduces the cost of capital, making investment more profitable. In the long run, the capital stock adjusts until the MPK equals the real cost of capital. Government policies like the investment tax credit and the corporate income tax can influence investment by altering the cost of capital.

🧠 Quick Revision Questions

1. What are the three components of the total cost of capital in the formula iPk - ΔPk + δPk?
2. What is the formula for the real cost of capital?
3. Under what condition will a firm decide to increase its capital stock (positive net investment)?
4. In the neoclassical investment function, why does a decrease in the real interest rate (r) lead to an increase in investment?
5. What is the steady-state condition for the capital stock in the long run?

📘 Lecture 42 — Investment Theories (Continued)

The Stock Market and Tobin’s q

📖 Overview: This lecture explores advanced investment theories, focusing on Tobin’s q as a key ratio linking stock market valuations to firms’ investment decisions. It also examines how stock markets serve as economic indicators, the role of financing constraints in limiting investment, and a simple model of residential investment. Understanding these concepts is crucial for analyzing real-world investment behavior and macroeconomic fluctuations.

🗂️ Topics Covered

The lecture covers Tobin’s q theory and its relationship to the neo-classical model, the stock market as an economic indicator with explanations using the AD-AS model and additional reasons for stock price movements, financing constraints that limit firms’ ability to raise funds for investment, and a two-part model of residential investment focusing on housing stock market and flow of new housing construction.

📝 Lecture Summary

THE STOCK MARKET AND TOBIN’S q

The term stock refers to the shares in the ownership of corporations. Stock market is the market in which these shares are traded. The Nobel-Prize-winning economist James Tobin proposed that firms base their investment decisions on the following ratio, now called Tobin’s q:

🔑 Definition — Tobin’s q: ( q = \frac{\text{Market Value of Installed Capital}}{\text{Replacement Cost of Installed Capital}} )

The numerator is the value of the economy’s capital as determined by the stock market. The denominator is the price of capital as if it were purchased today.

Tobin conveyed that net investment should depend on whether q is greater or less than 1:

• If q > 1, then firms can raise the value of their stock by increasing capital.
• If q < 1, the stock market values capital at less than its replacement cost and thus, firms will not replace their capital stock as it wears out.

Tobin’s q and the neo-classical model are closely related, since Tobin’s q measures the expected future profitability as well as the current profitability. If the MPK exceeds the cost of capital, firms are earning profits on their installed capital, making rental firms desirable to own, raising market value of stocks of such firms, implying a high value of q.

💡 Why this matters: Tobin’s q provides a simple, market-based measure to guide firms’ investment decisions—when stock markets value capital highly, it signals profitable investment opportunities.

📌 Example: If a company’s installed capital has a replacement cost of $10 million and its shares are valued at $12 million in the stock market, Tobin’s q = 12/10 = 1.2 > 1, indicating the firm should invest in new capital. Conversely, if the market value falls to $8 million, q = 0.8 < 1, suggesting the firm should not replace capital as it wears out.

THE STOCK MARKET AS AN ECONOMIC INDICATOR

Although the volatility of the stock market can give false signals about the future of the economy, one should not ignore the link between the two. Changes in the stock market often reflect changes in GDP. Whenever the stock market experiences a substantial decline, we should be ready for an upcoming recession.

Why do stock prices and economic activity tend to fluctuate together?

Tobin’s q and AD-AS Model: Suppose there occurs a fall in stock prices. Since replacement cost of capital is stable, this will result in a fall in Tobin’s q, reflecting investors’ pessimism about the current or future profitability of capital.

Some Additional Reasons:

• A fall in stock prices makes people poorer, depressing their spending, resulting in reduced aggregate demand.
• A fall in stock prices reflects bad news about technological progress and economic growth, resulting in slow expansion of the natural rate of output.

💡 Why this matters: Stock market movements are not just noise—they contain real information about future economic activity, making them useful early warning indicators for recessions.

FINANCING CONSTRAINTS

When a firm wants to invest in new capital, e.g., by building a new factory, it raises the funds in financial markets by:

• Obtaining loans from banks
• Selling bonds to the public
• Selling shares in future profits on the stock market

The neo-classical model assumes that if a firm is willing to pay the cost of capital, financial markets will make the funds available. But sometimes firms face financing constraints, limiting the amount of funds they can raise from financial markets. So the amount a firm can spend on new capital goods is limited to the amount it is currently earning.

🔑 Definition — Financing constraints: Limitations on the amount of funds a firm can raise from financial markets, forcing it to rely on current earnings for capital spending.

For example, a recession reduces employment, rental price of capital, and profits. If the firm expects the recession to be short-lived, it will continue investing for long-term profitability, thus having a small effect on Tobin’s q. So the firm that can raise funds in financial markets will face a small effect of recession on investment. While in the case of firms facing constraints, the fall in current profits restricts the spending on new capital goods and may prevent such firms from making profitable investment.

💡 Why this matters: Financing constraints explain why some firms—especially smaller ones—cannot take advantage of profitable investment opportunities during economic downturns, potentially deepening recessions.

RESIDENTIAL INVESTMENT

We will now consider the determinants of residential investment by looking at a simple model of the housing market. Residential investment includes the purchase of new housing both by people who plan to live in it themselves and by landlords who plan to rent it to others. To keep things simple, we shall assume that all housing is owner-occupied.

There are two parts to the model:

1. The market for the existing stock of houses determines the equilibrium housing price
2. The housing price determines the flow of residential investment

The relative price of housing (P_H/P) adjusts to equilibrate supply and demand for the existing stock of housing capital. Construction firms buy materials and hire labor to build the houses and then sell them at market price. Their costs depend on the overall price level P while their revenue depends on the price of houses P_H. The higher the P_H, the greater the incentive to build houses.

Graphical Model:

• Market for Housing: A demand curve (D) and a vertical supply curve (S) for stock of housing capital (K_H) determine the relative price of housing (P_H/P)
• Supply of New Housing: The relative price (P_H/P) determines the flow of residential investment (I_H) through an upward-sloping supply curve

This model of residential investment is much similar to the q theory of business fixed investment, which states that business fixed investment depends on the market price of installed capital relative to its replacement cost, which in turn depends on expected profits from owning installed capital. The residential investment depends on the relative price of housing, which in turn depends on demand for housing, depending on the imputed rent that individuals expect to receive from their housing.

🔑 Definition — Imputed rent: The implicit rental income that homeowners expect to receive from living in their own houses, which influences housing demand and thus the relative price of housing.

📌 Example: If the demand for housing increases (e.g., due to lower interest rates or population growth), the demand curve shifts right in the housing market, raising the equilibrium relative price P_H/P. This higher relative price then shifts along the supply curve for new housing, increasing the flow of residential investment I_H—more new houses are built.

⭐ Key Takeaways

The most critical concept from this lecture is Tobin’s q, which provides a direct link between stock market valuations and real investment decisions—firms invest when q > 1 and disinvest when q < 1. Stock market movements serve as leading indicators of economic activity because they affect spending through wealth effects and signal changes in future profitability and technological progress. Financing constraints are a crucial real-world modification to the neo-classical model, showing that firms limited in their ability to raise external funds may be forced to cut investment during recessions even when profitable opportunities exist. The residential investment model parallels Tobin’s q theory, with the relative price of housing (P_H/P) playing the same role as q—determining the flow of new construction based on the market valuation of existing housing stock. Finally, understanding that both business fixed investment and residential investment depend on market valuations relative to replacement costs provides a unified framework for analyzing all forms of investment.

🧠 Quick Revision Questions

1. If Tobin’s q equals 0.8 for a firm, should it increase or decrease its capital stock? Explain why.
2. How does a fall in stock prices affect aggregate demand according to the lecture?
3. What is the key difference between the neo-classical assumption about financing and the reality of financing constraints?
4. In the residential investment model, what determines the equilibrium relative price of housing (P_H/P)?
5. How is Tobin’s q theory similar to the model of residential investment?

📘 Lecture 43 — Investment Theories (Continued)

Inventory Investment

📖 Overview: This lecture shifts focus from fixed business investment to inventory investment — the goods businesses store. Though small in magnitude, inventory investment is highly volatile and a key driver of economic fluctuations. It explains how firms decide to hold stock, why seasonal patterns contradict production smoothing theory, and how output changes and interest rates affect inventory behavior.

🗂️ Topics Covered

The lecture defines inventory investment and explains why it matters despite its small size. It examines four core motivations for holding inventory: production smoothing, inventories as a factor of production, stock-out avoidance, and work in process. It then challenges the production smoothing hypothesis using evidence from seasonal industries. Two models of inventory investment are presented: the Accelerator Model, linking inventory stock proportionally to output, and the role of the real interest rate as the opportunity cost of holding inventories.

📝 Lecture Summary

What Is Inventory Investment?

Inventory investment refers to the goods businesses put aside in storage. It is one of the smallest components of spending but its volatility makes it critical for studying economic booms and recessions. Firms may hold inventories for four reasons:

1. Production smoothing — When sales are high, the firm sells more than it currently produces by drawing down inventory (and vice versa).
2. Inventories as a factor of production — Holding inventory may allow firms to operate more efficiently.
3. Stock-out avoidance — Firms don’t want to run out of goods when sales are unexpectedly high.
4. Work in process — Partially completed products are still counted in inventory.

💡 Why this matters: In a recession, firms stop replenishing inventory as goods are sold, making inventory investment negative. This amplifies downturns.

Seasonal Fluctuation and Production Smoothing

Contrary to expectations, firms do not use inventories to smooth production over time. The clearest evidence comes from industries with seasonal fluctuations in demand (e.g., fan manufacturing). One would expect firms to build up inventories in low-sales seasons and draw them down in high-sales seasons. Yet in most industries, the seasonal pattern of production matches the seasonal pattern of sales, not the inverse.

🔑 Key Insight: The textbook theory of production smoothing is not supported by real-world seasonal data.

The Accelerator Model of Inventories

The accelerator model assumes firms hold a stock of inventories proportional to their level of output. When output rises, manufacturing firms need more materials and supplies, and retailers need more merchandise on shelves.

Let:

• N = economy’s stock of inventories
• Y = output
• β = parameter reflecting desired inventory-to-output ratio

Then:

📐 Formula:

• Stock of inventories:
  N = βY
• Inventory investment (I) is the change in stock:
  I = ΔN = βΔY

📌 Example: If β = 0.2 and output increases by $100 billion, then inventory investment = 0.2 × $100 billion = $20 billion.

Prediction:

• When output rises, firms want larger inventory stock → positive inventory investment.
• When output falls, firms let inventory run down → negative inventory investment.

💡 Why this matters: Inventory investment depends on whether the economy is speeding up or slowing down — it amplifies the business cycle.

Inventories and the Real Interest Rate

Like other forms of investment, inventory investment depends on the real interest rate. When a firm holds a good in inventory and sells it tomorrow rather than today, it gives up the interest it could have earned on the proceeds in the meantime.

🔑 Definition — Opportunity Cost of Holding Inventory: The real interest rate measures the opportunity cost of holding inventories.

📌 Example: Holding $1 million of inventory for one year when the real interest rate is 5% costs the firm $50,000 in forgone interest.

Prediction:

• When the real interest rate rises, holding inventories becomes more costly → firms reduce inventory stock → inventory investment falls.

⭐ Key Takeaways

• Inventory investment is small in magnitude but highly volatile, making it critical for understanding business cycles.
• Firms hold inventories for four reasons: production smoothing, factor of production, stock-out avoidance, and work in process.
• Real-world seasonal industries contradict the production smoothing hypothesis — production patterns match sales patterns, not the inverse.
• The accelerator model states inventory investment is proportional to the change in output: I = βΔY.
• The real interest rate represents the opportunity cost of holding inventory; higher rates depress inventory investment.

🧠 Quick Revision Questions

1. Why is inventory investment considered "negligible but significant" in macroeconomics?
2. What are the four reasons firms hold inventories? Briefly explain each.
3. How does the evidence from seasonal industries (e.g., fan manufacturing) challenge the production smoothing theory?
4. In the accelerator model, what is the relationship between inventory investment (I) and the change in output (ΔY)? Write the formula.
5. How does an increase in the real interest rate affect inventory investment? Explain the economic reasoning.

📘 Lecture 44 — Money & Banking

📖 Overview: This lecture moves beyond the simplified view of money supply controlled only by the central bank, introducing the critical role of the banking system and household behavior. It explains how different banking systems—100% reserve and fractional-reserve—affect the total money supply, and introduces the key concept that banks can actually create money.

🗂️ Topics Covered

The lecture begins by redefining money supply as currency plus demand deposits, then explores two banking models: 100% reserve banking (where all deposits are held as reserves, not affecting money supply) and fractional-reserve banking (where banks lend out a portion of deposits, thereby creating new money). The concepts of reserves, reserve-deposit ratio, and excess reserves are formally introduced.

📝 Lecture Summary

MONEY SUPPLY

Earlier, we introduced the concept of money supply in a highly simplified way, defining the quantity of money as the number of rupees held by the public, and assuming the central bank controls supply through open-market operations. This definition omits the role of the banking system. Here, we see that the money supply is determined not only by the Central Bank, but also by the behavior of households (which hold money) and banks (where money is held). The Money supply includes both currency in the hand of public and deposits at banks that households use on demand for transactions.

🔑 Definition — Money Supply (M): M = C + D, where C is Currency and D is Demand Deposits. 💡 Why this matters: This formula shows that money is not just physical cash; bank deposits are a major component of the total money available in the economy.

100% RESERVE BANKING

Imagine a world without banks, where all money is currency ($1,000). A new bank accepts deposits but does not make loans. Its only purpose is to provide a safe place for depositors. The deposits that banks have received but have not lent out are called reserves. Some reserves are held in vaults of local banks but most are held at the central bank. In a 100% reserve banking system, all deposits are held in reserve, and the banking system does not affect the supply of money.

Suppose households deposit the economy’s entire $1,000 in First bank. The bank’s balance sheet shows:

• Assets: Reserves $1,000
• Liabilities: Deposits $1,000

The bank makes no loans, so it is not earning a profit, only a small fee. The money supply before and after creation of the bank remains $1,000.

🔑 Definition — Reserves: Deposits that banks have received but have not lent out. 📐 Key Principle: 100% reserve banking → M remains constant. All deposits are held as reserves, so the banking system does not affect the money supply.

FRACTIONAL RESERVE BANKING

If banks start to use some of their deposits to make loans (e.g., to households for house finance and to firms for capital finance), they can charge interest. Banks must keep some reserve on hand so that reserves are available whenever depositors want to make withdrawals. As long as new deposits approximately equal withdrawals, a bank need not keep all its deposits in reserves.

🔑 Definition — Reserve-deposit ratio: The fraction of deposits kept in reserve. 🔑 Definition — Excess reserves: Reserves above the reserve requirement. 🔑 Definition — Fractional-reserve banking: A system under which banks keep only a fraction of their deposits in reserve. In this system, banks create money.

📌 Example: In a 100% reserve system, a $1,000 deposit stays as $1,000 in money supply. In a fractional-reserve system with a 10% reserve ratio, the bank keeps $100 as reserves and lends out $900. That $900 is then deposited in another bank, which keeps $90 and lends $810, and so on. The total money supply becomes $1,000 + $900 + $810 + ... = $10,000, showing money creation. 📐 Formula: Money multiplier ≈ 1 / reserve-deposit ratio. 💡 Why this matters: This is how the banking system expands the money supply. Each loan creates new deposits, which can be lent again, multiplying the initial deposit.

⭐ Key Takeaways

The money supply is not controlled solely by the central bank; it is also influenced by household decisions to hold cash versus deposits and by banks' decisions on how much to lend. In a 100% reserve banking system, banks merely store money and do not affect the total money supply. In contrast, a fractional-reserve banking system allows banks to create money because only a fraction of deposits needs to be held in reserve, and the rest can be lent out, which eventually becomes new deposits elsewhere. The reserve-deposit ratio is the key determinant of how much money banks can create, with a lower ratio leading to a larger money multiplier. Finally, excess reserves represent any reserves held above the required minimum.

🧠 Quick Revision Questions

1. What is the formula for the money supply, and what are its two components?
2. In a 100% reserve banking system, does the creation of a bank change the money supply? Why or why not?
3. Define the “reserve-deposit ratio.”
4. In a fractional-reserve banking system, how do banks “create money”?
5. If the reserve-deposit ratio is 20%, what is the approximate money multiplier?

📘 Lecture 45 — Money & Banking (Continued)

📖 Overview: This lecture examines how central banks control the money supply through three key policy instruments. It then transitions to theories of money demand, comparing classical, Keynesian, portfolio, and transactions approaches, and concludes with a formal model of money supply determination and the process of money creation through the banking system.

🗂️ Topics Covered

The lecture covers central bank instruments for controlling money supply (open market operations, reserve requirements, discount rate), classical and Keynesian theories of money demand, portfolio theories emphasizing money as a store of value, transactions theories including the Baumol-Tobin model of cash management, the process of money creation through fractional-reserve banking, financial intermediation, and a formal model of money supply with the money multiplier.

📝 Lecture Summary

HOW DOES THE CENTRAL BANK CONTROL THE MONEY SUPPLY?

Central banks use three main instruments to influence the money supply. Open market operations are the purchase and sale of government bonds by the central bank. When the central bank buys bonds from the public, the money it pays increases the monetary base and thus increases the money supply. When it sells bonds, the money received reduces the monetary base and reduces the money supply.

Reserve requirements are regulations that impose on banks a minimum reserve-deposit ratio. An increase in reserve requirements raises this ratio, thus lowering the money multiplier and the money supply.

The discount rate is the interest rate the central bank charges when it lends to banks. Banks borrow from the central bank when they have too few reserves to meet requirements. The lower the discount rate, the cheaper borrowed reserves become, and the more banks demand such loans. Hence, a reduction in the discount rate raises the monetary base and the money supply.

💡 Why this matters: Although these instruments give the central bank substantial power to influence the money supply, it cannot do so perfectly. Bank discretion—such as holding excessive reserves or there being no limit on bank borrowings from the discount window—can cause the money supply to change in ways the central bank did not anticipate.

MONEY DEMAND

CLASSICAL THEORY OF MONEY DEMAND

The Quantity Theory of Money assumes that the demand for real money balances is directly proportional to income:

🔑 Definition — Real money balances demand (classical): (M/P)ᵈ = kY, where k is a constant measuring how much people want to hold for every dollar of income.

KEYNESIAN THEORY OF MONEY DEMAND

This presents a more realistic money demand function where the demand for real money balances depends on both the interest rate (i) and income (Y):

🔑 Definition — Keynesian money demand: (M/P)ᵈ = L(i, Y), where L is the liquidity preference function.

Money serves three functions: unit of account, store of value, and medium of exchange. The first function cannot by itself generate any demand for money, because we can quote prices in any currency without holding any of it. Theories focus on the latter two functions.

PORTFOLIO THEORIES OF MONEY DEMAND

Portfolio theories emphasize the role of money as a store of value. According to these theories, people hold money as part of their portfolio of assets. The key point is that money offers a different combination of risk and return than other assets—particularly a safe nominal return—while other assets may fall in both real and nominal terms.

These theories predict that money demand should depend on the risk and return offered by money and other assets, and also on total wealth, which measures the size of the portfolio to be allocated.

🔑 Definition — Portfolio money demand function: (M/P)ᵈ = L(rₛ, r_b, πᵉ, W), where:

• rₛ = expected real return on stocks
• r_b = expected real return on bonds
• πᵉ = expected inflation rate
• W = real wealth

If rₛ or r_b rises, money demand decreases because other assets become more attractive. A rise in πᵉ also reduces money demand because money becomes less attractive. An increase in W raises money demand because higher wealth means a larger portfolio.

Money Demand Function L(i,Y): A useful simplification:

• Uses real income Y as a proxy for real wealth W
• Nominal interest rate i = r_b + πᵉ

💡 Why this matters: Whether portfolio theories are useful depends on which measure of money we use. M1 is a dominated asset—as a store of value, it exists alongside other assets that are always better. Portfolio theories cannot explain demand for dominated forms of money like M1, but are more plausible for broader measures like M2.

TRANSACTIONS THEORIES OF MONEY DEMAND

These theories emphasize the role of money as a medium of exchange. They acknowledge that money is a dominated asset but stress that people hold money to make purchases. These theories best explain why people hold narrow measures of money, assuming that money has the cost of earning a low rate of return but makes transactions more convenient.

BAUMOL-TOBIN MODEL OF CASH MANAGEMENT

This model, developed in the 1950s, analyzes the costs and benefits of holding money:

• Benefit: Convenience (fewer trips to the bank)
• Costs: Foregone interest on money that could have been deposited in a savings account

📌 Example: A person plans to spend Y dollars over the course of a year (assuming constant price levels and real spending). If they withdraw Y dollars at the beginning of the year and gradually spend it, the average money balance is Y/2. If they withdraw Y/2 at the beginning, spend it in six months, then withdraw the rest Y/2 for the next half-year, the average balance is Y/4.

Generalizing: money holdings vary between Y/N and zero, averaging Y/(2N), where N is the number of trips to the bank.

🔑 Definition — Fixed cost effect: Any change in the fixed cost of going to the bank (F) alters the money demand function—it changes the quantity of money demanded for a given interest rate and income.

MONEY CREATION

Assume each bank maintains a reserve-deposit ratio (rr) of 20% and the initial deposit is $1000.

First Bank Balance Sheet:

Second Bank Balance Sheet:

Third Bank Balance Sheet:

Mathematically, the amount of money the original $1000 deposit creates:

• Original Deposit = $1000
• First bank lending = (1-rr) × $1000
• Second bank lending = (1-rr)² × $1000
• Third bank lending = (1-rr)³ × $1000
• And so on...

📐 Formula: Total Money Supply = [1 + (1-rr) + (1-rr)² + (1-rr)³ + ...] × $1000 = (1/rr) × $1000

📌 Example: With rr = 0.2: Total Money Supply = (1/0.2) × $1000 = $5000

The banking system's ability to create money is the primary difference between banks and other financial institutions.

Financial intermediation is the process of transferring funds from savers to borrowers. Financial markets transfer resources from households (who wish to save) to households and firms that wish to borrow to buy investment goods for future production.

A MODEL OF MONEY SUPPLY

Three exogenous variables:

🔑 Definitions:

• Monetary base (B): The total number of dollars held by the public as currency (C) and by banks as reserves (R)
• Reserve-deposit ratio (rr): The fraction of deposits (D) that banks hold in reserves (R)
• Currency-deposit ratio (cr): The amount of currency (C) people hold as a fraction of their holdings of demand deposits (D)

Definitions of money supply and monetary base:

• M = C + D
• B = C + R

Solving for M as a function of the three exogenous variables:

• M/B = (C/D + 1) / (C/D + R/D)

Making substitutions:

• M = [(cr + 1) / (cr + rr)] × B

The money multiplier (m) = (cr + 1) / (cr + rr)

So: M = m × B

Because the monetary base has a multiplied effect on the money supply, it is sometimes called high-powered money.

📌 Example: Suppose monetary base B is $500 billion, rr = 0.1, and cr = 0.6

• Money multiplier: m = (0.6 + 1) / (0.6 + 0.1) = 1.6 / 0.7 = 2.3
• Money supply: M = 2.3 × $500 billion = $1,150 billion

How changes in exogenous variables affect money supply:

1. The money supply M is proportional to the monetary base B. An increase in the monetary base increases the money supply by the same percentage.

2. The lower the reserve-deposit ratio (rr = R/D), the more loans banks make, and the more money banks create from every dollar of reserves.

3. The lower the currency-deposit ratio (cr = C/D), the fewer dollars of the monetary base the public holds as currency, the more base dollars banks hold in reserves, and the more money banks can create. A decrease in the currency-deposit ratio raises the money multiplier and the money supply.

⭐ Key Takeaways

The three central bank instruments—open market operations, reserve requirements, and the discount rate—affect the money supply through different channels, but bank behavior introduces uncertainty into monetary control. Money demand theories range from the simple classical quantity theory (M/P proportional to income) to the Keynesian function incorporating interest rates, portfolio theories emphasizing risk-return trade-offs across assets, and transactions theories like the Baumol-Tobin model explaining optimal cash management given the trade-off between convenience and foregone interest. The fractional-reserve banking system creates money through a multiplier process where an initial deposit generates loans that become new deposits at other banks, with the total money created equal to 1/rr times the original deposit. The formal money supply model shows that the money multiplier depends on both the reserve-deposit ratio and the currency-deposit ratio, making the monetary base "high-powered" because small changes in base money are multiplied into larger changes in the money supply.

🧠 Quick Revision Questions

1. What are the three instruments the central bank uses to control the money supply, and how does each affect the monetary base or money multiplier?

2. According to portfolio theories of money demand, what four factors determine the demand for real money balances, and in what direction does each affect money demand?

3. In the Baumol-Tobin model, if a person makes N trips to the bank over the year and spends Y dollars total, what is their average money balance?

4. If the reserve-deposit ratio is 0.25 and a bank receives a new deposit of $1,000, what is the total amount of money that can ultimately be created from this deposit?

5. Given a monetary base of $800 billion, a reserve-deposit ratio of 0.15, and a currency-deposit ratio of 0.5, calculate the money multiplier and the total money supply.