The Simple Short-Run Macroeconomic Model with Demand-Determined Output

Chapter 6: The Simple Short-Run Macroeconomic Model

Introduction

This chapter introduces the Keynesian short-run macroeconomic model, focusing on how aggregate demand determines output in a closed economy without a government sector. The model is foundational for understanding the relationship between aggregate expenditures and national income.

Aggregate Expenditures (AE) in a Closed Economy

Definition and Components

• Aggregate Expenditures (AE): The total amount that households and businesses plan to spend on goods and services at each level of income.

• In a closed economy without government or foreign trade, the AE equation is: $AE = C + I$

• C: Consumption Expenditures

• I: Investment Expenditures

Determinants of Household Consumption Expenditures (C)

Key Factors

• Personal Disposable Income ($Y_D$ or $DI$): Income available to households after taxes.

• Households' Wealth (W): The value of assets owned by households.

• Expectations/Consumer Confidence (HEc): Households' outlook on future economic conditions.

• Real Interest Rates (r): The cost of borrowing and the return on savings.

• Household Debt (D): The total amount owed by households.

• Taxes (T): Affect disposable income and thus consumption.

The Relationship between Consumption (C), Saving (S), and Disposable Income ($Y_D$)

Key Equations and Concepts

• Disposable Income Identity: $Y_D = C + S$

• Average Propensity to Consume (APC): Fraction of disposable income spent. $APC = \frac{C}{Y_D}$

• Average Propensity to Save (APS): Fraction of disposable income saved. $APS = \frac{S}{Y_D}$

• APC + APS = 1

• Marginal Propensity to Consume (MPC): Fraction of each additional dollar of disposable income spent. $MPC = \frac{\Delta C}{\Delta Y_D}$

• Marginal Propensity to Save (MPS): Fraction of each additional dollar of disposable income saved. $MPS = \frac{\Delta S}{\Delta Y_D}$

• MPC + MPS = 1

Example Calculation

• If $Y_D$ increases from $154,897$ to $161,580$ and $C$ increases from $128,600$ to $132,745$:

• $APC_{Year 1} = \frac{128,600}{154,897} = 0.8302$

• $APC_{Year 2} = \frac{132,745}{161,580} = 0.8215$

• $MPC = \frac{132,745 - 128,600}{161,580 - 154,897} = 0.6202$

• $MPS = 1 - MPC = 0.3798$

The Consumption Function

Linear Consumption Equation

• The consumption function is typically linear: $C = C_0 + mpc(Y_D)$

• $C_0$: Autonomous consumption (spending not related to current income)

• $mpc$: Marginal propensity to consume (slope of the consumption curve)

• Example: $C = 668 + 0.62Y_D$

Graphical Representation

• As $Y_D$ increases, $C$ increases along the consumption curve.

• Shifts in the curve occur due to changes in $C_0$ (e.g., changes in wealth, confidence, interest rates, or debt).

Shifts in the Consumption Curve

Factors Causing Shifts

• Increase in Wealth: Shifts curve up.

• Increase in Consumer Confidence: Shifts curve up.

• Decrease in Real Interest Rates: Shifts curve up.

• Increase in Household Debt: Shifts curve down.

The Private-Sector Saving Equation

Saving Function

• $S = S_0 + mps(Y_D)$

• $S_0 = -C_0$ and $mps = (1 - mpc)$

• Example: Given $C = 668 + 0.62Y_D$, $S = -668 + 0.38Y_D$

Break-Even Disposable Income ($Y_{BE}$)

Definition and Calculation

• Level of disposable income where households spend exactly their disposable income ($C = Y_D$ and $S = 0$).

• Example: For $C = 668 + 0.62Y_D$, solve $C = Y_D$ for $Y_D$.

Business Investment Expenditures (I)

Determinants

• Interest Rates: Inversely related to investment.

• Expected Rate of Profit: Positively related.

• Government Policy: Taxes and regulations can affect investment.

• Technological Change: Positively related.

• Rate of Capacity Utilization: Positively related.

• Expectations (Business Confidence): Positively related.

Investment Demand Curve

• Shows inverse relationship between real interest rate and investment demand.

• Investment schedule is typically horizontal, indicating investment is autonomous with respect to current income.

Aggregate Expenditures Equation

Formulation

• $AE = a_0 + zY$

• $a_0$: Autonomous expenditures ($C_0 + I$)

• $z$: Marginal propensity to spend (same as $mpc$ in this model)

• Example: If $C = 668 + 0.62Y_D$ and $I = 478$, then $AE = 1146 + 0.62Y$

Graphical Representation

• AE curve is linear with slope $z$ and vertical intercept $a_0$.

• Shifts in $a_0$ move the AE curve up or down; changes in $z$ rotate the curve.

Macroeconomic Equilibrium

Equilibrium Condition

• Occurs when $AE = Y$ (Aggregate Expenditures equal Real GDP).

• Unplanned Inventory Change (UIC) is zero: $UIC = Y - AE = 0$

• Total Injections equal Total Leakages: $I = S$

Methods to Determine Equilibrium Output ($Y^*$)

1. Solve a Model: Substitute $C$ and $I$ into $AE = C + I$, set $AE = Y$, and solve for $Y$.

2. Use a Formula: $Y^* = \frac{a_0}{1 - z}$

3. Read from a Table: Compare $AE$ and $Y$ values to find equilibrium.

When the Economy is Not in Equilibrium

Cases

• When $Y > Y^*$: Output exceeds AE, inventories accumulate, businesses reduce output.

• When $Y < Y^*$: Output is less than AE, inventories fall, businesses increase output.

Changing Equilibrium Output

Methods

• Change the marginal propensity to spend ($z$): Reflects cultural and behavioral changes in spending habits.

• Change autonomous expenditures ($a_0$): E.g., through fiscal or monetary policy.

The Multiplier Effect

Definition and Formulas

• The multiplier shows how a change in autonomous expenditures ($\Delta a_0$) leads to a larger change in equilibrium output ($\Delta Y$).

• Formula 1: $\text{Expenditures Multiplier} = \frac{\Delta Y}{\Delta a_0}$

• Formula 2: $\text{Expenditures Multiplier} = \frac{1}{1 - z}$

• Example: If $z = 0.62$, multiplier $= \frac{1}{1 - 0.62} = 2.63$

Multiplier Process Table

The following table illustrates the cumulative effect of successive rounds of spending after an initial increase in investment:

Round of Spending	Expenditure Created	Cumulative Effect
1	100.00	100.00
2	62.00	162.00
3	38.44	200.44
4	23.83	224.27
5	14.77	239.04
10	1.62	258.62
All others	6.38	264.99

Summary

• The simple short-run macroeconomic model demonstrates how aggregate demand determines output in the absence of government and foreign trade.

• Key concepts include the consumption function, saving function, investment determinants, aggregate expenditures, equilibrium output, and the multiplier effect.

• Understanding these relationships is essential for analyzing short-run fluctuations in national income and output.