Aggregate Expenditure and Keynesian Equilibrium

Introduction

This chapter explores the Aggregate Expenditure (AE) Model, a foundational concept in macroeconomics that explains how total spending in an economy determines output and income. Developed by John Maynard Keynes, this model is crucial for understanding why economies sometimes operate below their potential and how policy can address such gaps.

Components of Aggregate Expenditure

GDP and the Expenditure Approach

Gross Domestic Product (GDP) measures the total value of all final goods and services produced within a country. The expenditure approach sums all spending by different participants in the economy:

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

• Investment (I): Spending by firms on capital goods.

• Government Spending (G): Expenditures by the government on goods and services (excluding transfer payments).

• Net Exports (NX): Exports (X) minus Imports (M).

The GDP identity is given by:

$ Y = C + I + G + NX $

Consumption (C)

Consumption is the largest component of GDP, typically accounting for about two-thirds of total spending. It is determined by disposable income (YD), which is income after taxes. Households allocate disposable income to either consumption or saving:

$ Y_D = C + S $

• Autonomous Consumption: Consumption that occurs even when income is zero, influenced by factors such as expectations, wealth, and interest rates.

• Income-dependent Consumption: Consumption that varies with disposable income.

The consumption function is:

$ C = a + bY_D $

• a: Autonomous consumption

• b: Marginal Propensity to Consume (MPC)

Marginal Propensity to Consume (MPC)

The MPC is the fraction of an additional dollar of disposable income that is spent on consumption:

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

MPC ranges between 0 and 1. For example, if MPC = 0.8, then 80% of extra income is spent, and 20% is saved.

Investment (I)

Investment spending is determined by:

• Expected profitability: Optimism about future returns increases investment.

• Interest rates: Higher rates discourage investment due to increased borrowing costs.

• Business taxes: Higher taxes reduce after-tax profits and investment.

Government Spending (G)

Government spending is determined by fiscal policy decisions and is considered exogenous (fixed) in the AE model. Transfer payments are not included in G.

Net Exports (NX)

Net exports are affected by:

• Domestic income: Higher income increases imports, reducing NX.

• Foreign income: Higher foreign income increases exports, raising NX.

• Exchange rates: Appreciation reduces NX; depreciation increases NX.

• Tastes and trade policies: Can have positive or negative effects.

Planned Aggregate Expenditure (PAE)

Definition and Formula

Planned Aggregate Expenditure (PAE) is the total amount of spending that households, firms, government, and foreign buyers plan to make on domestic goods and services at each level of income:

$ PAE = C_P + I_P + G_P + NX_P $

With the consumption function, this becomes:

$ PAE = a + bY + I_P + G_P + NX_P $

Or, grouping autonomous expenditures:

$ PAE = A + bY $

Where $A = a + I_P + G_P + NX_P$ is autonomous expenditure (not affected by income), and $b$ is the MPC.

Keynesian Equilibrium

Equilibrium occurs when planned aggregate expenditure equals actual output (GDP):

$ PAE = Y $

At this point, there is no unplanned inventory accumulation, and firms have no incentive to change production.

Output Gaps

Recessionary Output Gap

A recessionary gap exists when equilibrium output is below full employment output ($Y_1 < Y_{FE}$). This indicates underutilized resources and unemployment.

Inflationary Output Gap

An inflationary gap occurs when equilibrium output exceeds full employment output ($Y_1 > Y_{FE}$), leading to upward pressure on prices.

The Multiplier Process

Concept and Formula

The Keynesian multiplier measures how an initial change in autonomous spending leads to a larger change in equilibrium output:

$ \text{Expenditure multiplier} = \frac{1}{1 - MPC} $

For example, if MPC = 0.75, the multiplier is 4. An initial $100 billion increase in investment would ultimately increase total output by $400 billion.

Multiplier in Action

When investment declines, the reduction in spending leads to a chain reaction of lower income, lower consumption, and further reductions in output. The total impact is a multiple of the initial change.

Worked Examples

Example: Calculating PAE and Equilibrium Output

• Suppose planned consumption is $50 + 0.8Y$, planned investment is $100$, government spending is $200$, and net exports are $50$.

• PAE function: $PAE = 50 + 0.8Y + 100 + 200 + 50 = 400 + 0.8Y$

• Equilibrium: Set $PAE = Y$ to solve for $Y$.

• $Y = 400 + 0.8Y \implies 0.2Y = 400 \implies Y = 2000$

Example: The Multiplier Effect

• If MPC = 0.8, multiplier = $\frac{1}{1-0.8} = 5$.

• If investment increases by $100$, total output increases by $500$.

Summary Table: Determinants of Aggregate Expenditure Components

Key Formulas

• GDP (Expenditure Approach): $ Y = C + I + G + NX $

• Consumption Function: $ C = a + bY_D $

• Marginal Propensity to Consume: $ MPC = \frac{\Delta C}{\Delta Y_D} $

• Planned Aggregate Expenditure: $ PAE = A + bY $

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