Chapter 8

Aggregate Expenditure and Output in the Short Run

Introduction

This chapter focuses on the aggregate expenditure model, a fundamental concept in macroeconomics that explains the short-run relationship between total spending and real GDP, assuming a constant price level. Understanding this model is essential for analyzing business cycles, economic equilibrium, and the effects of fiscal policy.

The Aggregate Expenditure Model

Definition and Purpose

• Aggregate Expenditure Model: A macroeconomic model that examines the short-run relationship between total spending (aggregate expenditure) and real GDP, assuming the price level is constant.

• Aggregate Expenditure (AE): The total spending in the economy, calculated as the sum of consumption, planned investment, government purchases, and net exports.

• Formula:

$AE = C + I + G + NX$

• The model is used to determine the short-run level of output in the economy.

Components of Aggregate Expenditure

The Four Components

• Consumption (C): Spending by households on goods and services.

• Planned Investment (I): Planned spending by firms on capital goods and by households on new homes.

• Government Purchases (G): Spending by all levels of government on goods and services.

• Net Exports (NX): The value of exports minus the value of imports.

Key Equation: $AE = C + I + G + NX$

Planned vs. Actual Investment

• The model uses planned investment rather than actual investment.

• Actual investment includes unplanned changes in inventories (goods produced but not yet sold).

• Planned investment excludes these inventory changes.

• Formula:

$\text{Planned investment} = \text{Actual investment} - \text{Unplanned change in inventories}$

Macroeconomic Equilibrium

Equilibrium Condition

• Equilibrium occurs when total spending equals total output produced:

$\text{Planned aggregate expenditure} = \text{GDP}$

• In equilibrium, there are no unplanned changes in inventories.

Relationship Between AE and GDP

• If planned AE > GDP: Inventories fall, firms increase production, GDP and employment rise.

• If planned AE < GDP: Inventories rise, firms decrease production, GDP and employment fall.

Determinants of Aggregate Expenditure Components

Consumption (C)

• Current Disposable Income: Income after taxes and transfers; higher disposable income leads to higher consumption.

• Household Wealth: Assets minus liabilities; greater wealth increases consumption.

• Expected Future Income: Households smooth consumption based on expectations.

• Price Level: Higher prices reduce real wealth and consumption.

• Interest Rate: Higher real interest rates encourage saving, reducing consumption, especially of durable goods.

Marginal Propensity to Consume (MPC)

• MPC: The fraction of additional disposable income that is spent on consumption.

• Formula:

$MPC = \frac{\Delta C}{\Delta Y_D}$

• Example: If disposable income rises by $10,000 and consumption rises by $7,640, then$MPC = 0.764$.

Marginal Propensity to Save (MPS)

• MPS: The fraction of additional disposable income that is saved.

• Relationship:

$MPC + MPS = 1$

Investment (I)

• Expectations of Future Profits: Optimism increases investment; recessions decrease it.

• Interest Rate: Higher rates reduce investment; lower rates increase it.

• Corporate Taxes and Tax Incentives: Lower taxes and incentives increase investment.

• Cash Flow: Firms invest more when profits (cash flow) are high.

Government Purchases (G)

• Includes spending on goods and services at all government levels.

• Does not include transfer payments.

Net Exports (NX)

• Price Level: Higher domestic prices reduce exports and increase imports.

• Relative Growth Rates: Faster domestic growth increases imports.

• Exchange Rate: A stronger domestic currency makes exports more expensive and imports cheaper.

Graphing Macroeconomic Equilibrium

The 45°-Line Diagram

• Plots real national income (GDP) on the x-axis and aggregate expenditure on the y-axis.

• Points on the 45° line represent equilibrium where income equals expenditure.

• If AE is above the 45° line, inventories fall and GDP rises; if below, inventories rise and GDP falls.

The Multiplier Effect

Definition and Mechanism

• A change in autonomous expenditure (e.g., investment, government purchases) leads to a larger change in equilibrium GDP.

• Multiplier: The ratio of the change in equilibrium GDP to the initial change in autonomous expenditure.

• Formula:

$\text{Multiplier} = \frac{1}{1 - MPC}$

• Example: If $MPC = 0.8$, then $\text{Multiplier} = 5$.

• A $80$billion increase in investment leads to a $400$ billion increase in GDP.

Summary of the Multiplier Effect

• Works for both increases and decreases in autonomous expenditure.

• The higher the MPC, the larger the multiplier.

• Real-world factors (taxes, imports, inflation) can reduce the actual multiplier.

Paradox of Thrift

Short-Run vs. Long-Run Effects

• Increased saving reduces consumption, lowering aggregate expenditure and potentially causing a recession in the short run.

• In the long run, higher savings can lead to more investment and growth.

• This is known as the paradox of thrift.

The Aggregate Demand Curve

Relationship to Aggregate Expenditure

• The aggregate demand (AD) curve shows the relationship between the price level and the level of planned aggregate expenditure (real GDP).

• As the price level rises, aggregate expenditure falls; as the price level falls, aggregate expenditure rises.

• Aggregate Demand (AD): A curve showing the relationship between the price level and the level of planned aggregate expenditure, holding other factors constant.

Effects of Price Level on Aggregate Expenditure

• Higher price levels reduce real wealth, decreasing consumption.

• Higher domestic prices reduce net exports.

• Higher prices increase the demand for money, raising interest rates and reducing investment.

Appendix: The Algebra of Macroeconomic Equilibrium

Numerical and General Models

• Economists use equations to estimate relationships and predict outcomes.

• Example Model:

C = 100 + 0.8Y I = 125 G = 125 NX = -30 Y = C + I + G + NX

• Solving for equilibrium:

Y = 100 + 0.8Y + 125 + 125 - 30 Y - 0.8Y = 320 0.2Y = 320 Y = 1600

• General Model:

C = \overline{C} + MPC \cdot Y I = \overline{I} G = \overline{G} NX = \overline{NX} Y = C + I + G + NX

• Equilibrium condition:

Y(1 - MPC) = \overline{C} + \overline{I} + \overline{G} + \overline{NX}

• Equilibrium GDP equals autonomous expenditure times the multiplier.

Tables

Table: Components of Aggregate Expenditure (2021, Canada)

Component	Value (billions, 2012 dollars)
Consumption	1,227.4
Investment	358
Government Spending	500.7
Net Exports	-58

Additional info: Values inferred from context; actual table may have more detail.

Table: Macroeconomic Equilibrium (Hypothetical)

Real GDP	Consumption	Planned Investment	Government Purchases	Net Exports	Aggregate Expenditure
1000	800	200	150	-50	1100
1200	950	200	150	-50	1250
1400	1100	200	150	-50	1400
1600	1250	200	150	-50	1550

Additional info: Table structure inferred; values are illustrative.