Chapter 6: The Simplest Short-Run Macro Model – Study Notes

Chapter 6: The Simplest Short-Run Macro Model

Chapter Outline and Learning Objectives

This chapter introduces the basic short-run macroeconomic model, focusing on aggregate expenditure, equilibrium national income, and the effects of changes in expenditure. The main learning objectives are:

• Explain the difference between desired and actual expenditure.

• Identify the determinants of desired consumption and desired investment.

• Understand the meaning of equilibrium national income.

• Explain how changes in desired expenditure affect equilibrium income through the simple multiplier.

6.1 Desired Aggregate Expenditure

Definition and Components

Aggregate expenditure (AE) refers to the total planned or desired spending in an economy. Economists distinguish between actual and desired values for each category:

• Actual consumption: $C_a$

• Actual investment: $I_a$

• Actual government purchases: $G_a$

• Actual net exports: $(X_a - IM_a)$

For desired/planned values, subscripts are omitted:

• Desired consumption: $C$

• Desired investment: $I$

• Desired government purchases: $G$

• Desired net exports: $(X - IM)$

The sum of these is desired aggregate expenditure:

• $AE = C + I + G + (X - IM)$

Meaning of "Desired" Expenditure

• Desired expenditure is what consumers and firms would like to purchase, given their real-world constraints of income and market prices.

• It is more realistic than assuming unlimited spending.

Autonomous vs. Induced Expenditure

• Autonomous expenditure: Aggregate expenditure that does not change systematically with national income.

• Induced expenditure: Aggregate expenditure that does change systematically with national income.

Simplest Short-Run Macro Model Assumptions

• No government (no taxes).

• No foreign sector (closed economy).

• Constant price level.

These assumptions simplify the model, making its structure easier to understand before introducing more complexity.

6.1 Desired Consumption Expenditure

Disposable Income and Saving

• Disposable income: Household income minus taxes.

• Saving: Disposable income minus consumption.

Formulas:

• $\text{Disposable income} = \text{Household income} - \text{Taxes}$

• $\text{Saving} = \text{Disposable income} - \text{Consumption}$

The Consumption Function

The consumption function describes the relationship between desired consumption expenditure and its determinants:

• Disposable income

• Wealth

• Interest rates

• Expectations about the future

Average and Marginal Propensity to Consume

• Average Propensity to Consume (APC): The percentage of disposable income spent on consumption.

• Formula: $APC = \frac{C}{Y_D}$

• As disposable income rises, APC falls toward the marginal propensity to consume (MPC).

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

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

• MPC is the constant slope of the consumption function.

Example: Consumption Function

• If the consumption function is $C = 30 + 0.8Y$, then $30$is autonomous consumption and $0.8$ is the MPC.

• For every additional dollar of income, $0.80$ is spent on consumption.

6.1 Desired Saving Function

Average and Marginal Propensity to Save

• Average Propensity to Save (APS): The percentage of disposable income saved.

• Formula: $APS = \frac{S}{Y_D}$

• APS starts infinitely negative and rises toward the marginal propensity to save (MPS) as disposable income rises.

• Marginal Propensity to Save (MPS): The constant fraction of an additional dollar of disposable income that is saved.

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

• MPS is the constant slope of the saving function.

Relationship Between Consumption and Saving

• All disposable income is either spent or saved: $APC + APS = 1$

• For any increment to disposable income: $MPC + MPS = 1$

6.1 Shifts in the Consumption and Saving Functions

The consumption function shifts upward (and the saving function downward) with:

• Increase in wealth

• Decrease in interest rates

• Increase in optimism about the future

6.1 Extensions: Theories of Consumption

Different theories explain household consumption behavior:

• Keynesian Theory: Households are not fully forward-looking; they respond to current income.

• Life-Cycle Theory (Franco Modigliani): Households plan consumption over their lifetime, smoothing spending.

• Permanent-Income Theory (Milton Friedman): Consumption depends on long-term expected income, not just current income.

Most households fall somewhere between shortsighted and forward-looking behavior.

6.1 Desired Investment Expenditure

Categories and Determinants

• Categories: Inventory accumulation, residential construction, new plant and equipment.

• Investment is the most volatile component of GDP and strongly associated with economic fluctuations.

• Main determinants: Real interest rate, changes in sales, business confidence.

• Current real GDP is not a major determinant of current desired investment (investment is considered autonomous).

6.1 The Aggregate Expenditure Function

The aggregate expenditure (AE) function relates the level of desired aggregate expenditure to the level of actual national income. In the absence of government and international trade:

• $AE = C + I$

Example:

• If $C = 30 + 0.8Y$ and $I = 75$, then $AE = 30 + 0.8Y + 75 = 105 + 0.8Y$

The slope of the AE function is the marginal propensity to spend, which in the simple model is just the MPC.

6.2 Equilibrium National Income

Definition and Adjustment Mechanism

• If desired aggregate expenditure exceeds actual income, inventories fall and there is pressure for national income to rise.

• If desired aggregate expenditure is less than actual income, inventories rise and there is pressure for national income to fall.

• Equilibrium national income occurs when desired aggregate expenditure equals actual national income.

Table: Equilibrium National Income

Actual National Income	Desired Aggregate Expenditure (AE = C + I)	Effect
0	105	Inventories are falling; firms increase output
150	165	Inventories are falling; firms increase output
525	525	Equilibrium income
600	585	Inventories are rising; firms reduce output
900	825	Inventories are rising; firms reduce output

6.3 Changes in Equilibrium National Income

Shifts and Rotations of the AE Function

• A shift occurs when the AE function moves up or down in parallel fashion (e.g., due to changes in autonomous expenditure).

• A rotation occurs when the AE curve gets steeper or flatter (e.g., due to changes in the marginal propensity to consume).

The Simple Multiplier

• The simple multiplier measures the ratio of the change in equilibrium national income ($\Delta Y$) to the change in autonomous expenditure ($\Delta A$) that caused it.

• If $z$ is the marginal propensity to spend out of national income, then:

$\text{Simple Multiplier} = \frac{1}{1 - z}$

• The larger the marginal propensity to spend, the steeper the AE function and the larger the simple multiplier.

Economic Fluctuations as Self-Fulfilling Prophecies

Expectations play a crucial role in macroeconomic fluctuations:

• Households' and firms' expectations about the future influence desired consumption and investment.

• Changes in desired AE, through the multiplier process, lead to changes in national income.

• Optimism can lead to increased investment, shifting the AE function upward and raising national income—a self-fulfilling prophecy.

Additional info: Some formulas and examples have been expanded for clarity and completeness.