Aggregate Expenditure and Output in the Short Run (Chapter 12 Study Notes)

Aggregate Expenditure and Output in the Short Run

The Aggregate Expenditure Model

The aggregate expenditure model is a macroeconomic model that examines the short-run relationship between total spending (aggregate expenditure) and real GDP, under the assumption that the price level is constant. This model is used to determine the total output produced in an economy in the short run.

• Aggregate expenditure (AE): The total amount of spending in the economy, consisting of consumption, planned investment, government purchases, and net exports.

• Short-run focus: The model assumes prices are fixed, so changes in output are driven by changes in spending.

Four Components of Aggregate Expenditure

Aggregate expenditure is composed of the same four components as GDP:

• 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.

Formula: $AE = C + I + G + NX$

The Difference between Planned Investment and Actual Investment

The aggregate expenditure model uses planned investment rather than actual investment. The key difference is that planned investment does not include unplanned changes in inventories (goods produced but not yet sold).

• Planned investment = Actual investment – Unplanned change in inventories

• Unplanned inventory changes occur when actual sales differ from what firms expected.

Example: If a publisher prints 1.5 million books but sells only 1.2 million, the 0.3 million unsold books represent an unplanned increase in inventories.

Macroeconomic Equilibrium

Equilibrium in the economy occurs when total spending on output equals the value of output produced:

• Equilibrium condition: $AE = GDP$

• In the AE model, $I$ is planned investment; in GDP accounting, $I$ is actual investment.

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

Relationship between Aggregate Expenditure and GDP

If ...	Then ...	And ...
Aggregate expenditure is equal to GDP	Inventories are unchanged	The economy is in macroeconomic equilibrium
Aggregate expenditure is less than GDP	Inventories rise	GDP and employment decrease
Aggregate expenditure is greater than GDP	Inventories fall	GDP and employment increase

Just as individual markets may not always be in equilibrium, the overall economy may not be in macroeconomic equilibrium at all times.

Determinants of Consumption

Key Factors Influencing Consumption

Consumption is primarily determined by the following factors:

1. Current Disposable Income: The income households have after taxes and transfer payments. Higher disposable income leads to higher consumption.

2. Household Wealth: The value of assets (homes, stocks, bonds, bank accounts) minus liabilities (mortgages, loans). Greater wealth increases consumption.

3. Expected Future Income: Households tend to smooth consumption over time, basing spending on both current and expected future income.

4. The Price Level: Higher prices reduce the real value of wealth, leading to lower consumption.

5. The Interest Rate: Higher real interest rates encourage saving and discourage consumption, especially of durable goods.

The Consumption Function and Marginal Propensity to Consume (MPC)

The consumption function shows the relationship between consumption spending and disposable income. Households typically spend a consistent fraction of each extra dollar of income on consumption.

• Marginal Propensity to Consume (MPC): The fraction of an additional dollar of disposable income that is spent on consumption.

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

Example: If consumption increases by $364$billion when disposable income increases by $530$ billion, $MPC = \frac{364}{530} = 0.69$.

Consumption and National Income

For simplicity, national income and GDP are often treated as equal in this model. Disposable income is defined as:

• Disposable income = National income – Net taxes

• Net taxes = Taxes – Transfer payments

If net taxes do not change as national income changes, then any change in disposable income equals the change in national income.

Income, Consumption, and Saving

National income can be decomposed as:

• $Y = C + S + T$

• Any change in national income: $\Delta Y = \Delta C + \Delta S + \Delta T$

• If taxes do not change, $\Delta T = 0$, so $\Delta Y = \Delta C + \Delta S$

Marginal Propensity to Save (MPS)

The marginal propensity to save (MPS) is the fraction of an additional dollar of income that is saved.

• Formula: $MPS = \frac{\Delta S}{\Delta Y}$

• Relationship: $MPC + MPS = 1$

Any increase in income is either consumed or saved.

Determinants of Planned Investment

Key Factors Influencing Planned Investment

1. Expectations of Future Profitability: Firms invest more when they are optimistic about future profits. Purchases of new housing are also included in planned investment.

2. The Interest Rate: Higher real interest rates increase the cost of borrowing, reducing investment spending. Lower rates encourage investment.

3. Taxes: Higher corporate income taxes reduce funds available for investment and decrease incentives. Investment tax incentives can increase investment.

4. Cash Flow: Firms often finance investment from their own profits (cash flow). During recessions, lower profits reduce investment.

Determinants of Net Exports

Key Factors Influencing Net Exports

If ...	U.S. Net Exports will ...	Because ...
U.S. price level rises faster than foreign price levels	Decrease	U.S. goods become more expensive relative to foreign goods, so imports rise and exports fall.
U.S. GDP grows faster than foreign GDP	Decrease	U.S. demand for imports rises faster than foreign demand for U.S. exports.
U.S. dollar rises in value relative to other currencies	Decrease	Imports are cheaper, exports are more expensive.
U.S. price level, GDP, or dollar value rises more slowly	Increase	The opposite effects occur.

Graphing Macroeconomic Equilibrium: The 45°-Line Diagram

The 45°-Line Diagram (Keynesian Cross)

The 45°-line diagram is a graphical tool for analyzing macroeconomic equilibrium. Real national income (GDP) is on the x-axis, and real aggregate expenditure is on the y-axis.

• Any point on the 45° line represents a situation where aggregate expenditure equals GDP (potential equilibrium).

• Points above the 45° line: Aggregate expenditure exceeds GDP, inventories fall, and firms increase production.

• Points below the 45° line: Aggregate expenditure is less than GDP, inventories rise, and firms decrease production.

• The actual macroeconomic equilibrium occurs where the aggregate expenditure function crosses the 45° line.

Macroeconomic Equilibrium and Recession

Macroeconomic equilibrium can occur at any point on the 45° line, but ideally, it should occur at the level of potential GDP (full employment). If equilibrium occurs below potential GDP, the economy is in a recession.

Table: Macroeconomic Equilibrium Example

Real GDP ($B)	Consumption (C)	Planned Investment (I)	Government Purchases (G)	Net Exports (NX)	Planned Aggregate Expenditure (AE)	Unplanned Change in Inventories	Real GDP Will...
18,000	14,500	2,500	2,500	-1,000	18,500	-500	Increase
20,000	16,000	2,500	2,500	-1,000	20,000	0	Be in equilibrium
22,000	17,500	2,500	2,500	-1,000	21,500	+500	Decrease

As real GDP changes, only consumption changes; planned investment, government purchases, and net exports are assumed constant in the short run.

The Multiplier Effect

Definition and Mechanism

The multiplier effect refers to the process by which an initial change in autonomous expenditure leads to a larger change in equilibrium real GDP. Autonomous expenditures are those that do not depend on the level of GDP (e.g., planned investment, government purchases, net exports).

• Consumption has both autonomous and induced components; induced consumption depends on GDP.

• The upward-sloping AE line is due to induced consumption.

Calculating the Multiplier

The multiplier is the ratio of the change in equilibrium real GDP to the initial change in autonomous expenditure.

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

• 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.

Summary of the Multiplier Effect

• The multiplier effect works for both increases and decreases in planned aggregate expenditure.

• The larger the MPC, the larger the multiplier.

• Real-world factors (imports, inflation, interest rates, taxes) can reduce the actual multiplier below the theoretical value.

The Paradox of Thrift

The paradox of thrift suggests that while saving is beneficial for long-term growth, an increase in saving in the short run can reduce consumption, aggregate expenditure, and real GDP, potentially pushing the economy into recession. This paradox highlights the difference between individual and aggregate outcomes in macroeconomics.

The Aggregate Demand Curve

Price Level and Aggregate Expenditure

As the price level changes, it affects aggregate expenditure through several channels:

• Higher price levels reduce the real value of household wealth, decreasing consumption.

• If U.S. prices rise faster than foreign prices, exports fall and imports rise, reducing net exports.

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

All these effects mean that higher price levels decrease aggregate expenditure, while lower price levels increase it.

The Aggregate Demand (AD) Curve

The aggregate demand curve shows the relationship between the price level and the quantity of real GDP demanded by households, firms, and the government. It is downward sloping because of the effects described above.

Aggregate Expenditure Equations

Model Equations

• Consumption function: $C = \bar{C} + MPC \times Y$

• Planned investment: $I = \bar{I}$

• Government purchases: $G = \bar{G}$

• Net exports: $NX = \bar{NX}$

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

Parameters with bars (e.g., $\bar{C}$) are autonomous (fixed) values. Researchers estimate these parameters using statistical methods and historical data.

Solving for Equilibrium GDP

To find equilibrium GDP, substitute the first four equations into the equilibrium condition and solve for $Y$:

• $Y = \bar{C} + MPC \times Y + \bar{I} + \bar{G} + \bar{NX}$

• $Y - MPC \times Y = \bar{C} + \bar{I} + \bar{G} + \bar{NX}$

• $Y (1 - MPC) = \bar{C} + \bar{I} + \bar{G} + \bar{NX}$

• $Y = \frac{\bar{C} + \bar{I} + \bar{G} + \bar{NX}}{1 - MPC}$

This shows that equilibrium GDP equals autonomous expenditure times the multiplier.