Aggregate Expenditure and Output in the Short Run: Study Notes

Aggregate Expenditure and Output in the Short Run

Introduction

This chapter explores the aggregate expenditure model, a foundational concept in macroeconomics that explains how total spending in the economy determines output and income in the short run. The model is essential for understanding fluctuations in real GDP and the business cycle.

The Aggregate Expenditure Model

Definition and Purpose

• Aggregate expenditure model: A macroeconomic model focusing on the short-run relationship between total spending (aggregate expenditure) and real GDP, assuming a constant price level.

• The model determines the short-run equilibrium level of output in the economy.

Components of Aggregate Expenditure

• Consumption (C): Household spending on goods and services.

• Planned Investment (I): Firm spending on capital goods and household spending on new homes (excludes unplanned inventory changes).

• Government Purchases (G): Government spending on goods and services at all levels.

• Net Exports (NX): Exports minus imports.

• Aggregate Expenditure (AE): The sum of the above components: $AE = C + I + G + NX$

Planned vs. Actual Investment

• Planned investment excludes unplanned changes in inventories, while actual investment includes them.

• Macroeconomic equilibrium occurs when planned investment equals actual investment (no unplanned inventory changes).

Determinants of Aggregate Expenditure Components

Consumption

• Largest component of aggregate expenditure.

• Determinants include:

  • Current disposable income

  • Household wealth

  • Expected future income

  • Price level

  • Interest rate

Volatility of Durable Goods Consumption

• Spending on durable goods (e.g., cars, RVs) is more volatile than overall consumption due to postponable purchases, substitutes, and sensitivity to interest rates.

The Consumption Function and Marginal Propensity to Consume (MPC)

• Consumption function: Relationship between consumption and disposable income.

• Marginal propensity to consume (MPC): The change in consumption from a change in disposable income.

• Formula: $MPC = \frac{\Delta C}{\Delta Y}$

Marginal Propensity to Save (MPS)

• Marginal propensity to save (MPS): The change in saving from a change in disposable income.

• Relationship: $MPC + MPS = 1$

Planned Investment

• More volatile than consumption.

• Determinants include:

  • Expectations of future profitability

  • Interest rate

  • Taxes

  • Cash flow

Government Purchases

• Includes all levels of government spending on goods and services (excludes transfer payments).

Net Exports

• Typically negative for the U.S. in recent decades.

• Determinants include:

  • Relative price levels

  • Relative growth rates

  • Exchange rates

Macroeconomic Equilibrium

Graphical Representation: The 45-Degree Line Diagram

• Equilibrium occurs where aggregate expenditure equals real GDP.

• The 45-degree line shows all points where output equals spending.

Finding Equilibrium

• Equilibrium is found where the aggregate expenditure function intersects the 45-degree line.

• At this point, there are no unplanned changes in inventories.

Recessionary Gaps

• If equilibrium occurs below potential GDP, the economy experiences a recessionary gap (unemployment above the natural rate).

The Multiplier Effect

Definition and Mechanism

• Multiplier effect: A small change in autonomous expenditure leads to a larger change in equilibrium real GDP.

• Occurs because each round of spending induces further rounds of consumption.

• Formula: $\text{Multiplier} = \frac{1}{1 - MPC}$

Calculation Example

• If $MPC = 0.75$, then $\text{Multiplier} = \frac{1}{1 - 0.75} = 4$.

• A $200$billion increase in investment leads to an $800$ billion increase in equilibrium GDP.

Reverse Multiplier

• The multiplier works in reverse: decreases in autonomous expenditure cause larger decreases in GDP (e.g., during the Great Depression).

Limitations

• Real-world factors (imports, taxes, inflation, interest rates) reduce the actual size of the multiplier compared to the simple model.

The Paradox of Thrift

• In the short run, increased saving can reduce consumption, lowering incomes and potentially causing a recession.

• Known as the paradox of thrift: what is beneficial for individuals (saving) can be harmful for the economy in the short run.

The Aggregate Demand Curve

Relationship to Aggregate Expenditure

• The aggregate demand (AD) curve shows the inverse relationship between the price level and the quantity of real GDP demanded.

• As the price level rises, aggregate expenditure falls due to:

  • Decreased real wealth (reducing consumption)

  • Reduced net exports (as U.S. goods become relatively more expensive)

  • Higher interest rates (reducing investment)

Appendix: The Algebra of Macroeconomic Equilibrium

Aggregate Expenditure Equations

• Consumption function: $C = a + bY$

• Planned investment: $I = I_0$

• Government purchases: $G = G_0$

• Net exports: $NX = NX_0$

• Equilibrium condition: $Y = C + I + G + NX$

Solving for Equilibrium Output

• Substitute the first four equations into the equilibrium condition and solve for $Y$:

$Y = a + bY + I_0 + G_0 + NX_0$

$Y - bY = a + I_0 + G_0 + NX_0$

$Y(1 - b) = a + I_0 + G_0 + NX_0$

$Y = \frac{a + I_0 + G_0 + NX_0}{1 - b}$

Summary Table: Key Concepts

Concept	Definition
Aggregate Expenditure (AE)	Total spending in the economy: $C + I + G + NX$
Marginal Propensity to Consume (MPC)	Fraction of additional income spent on consumption
Multiplier	Effect of a change in autonomous expenditure on equilibrium GDP: $\frac{1}{1 - MPC}$
Macroeconomic Equilibrium	Occurs when AE = Real GDP
Aggregate Demand Curve	Shows relationship between price level and real GDP demanded