Basic Macroeconomic Relationships

Chapter 9

Chapter 9 Figure 9.1

Average and Marginal Propensities to Consume and Save

Average Propensities

APC = C/DI APS = S/DI since DI = S + C APC + APS = 1

Marginal Propensities

MPC = ∆C/∆DI MPS = ∆S/∆DI Since DI = S + C ∆DI = ∆S + ∆C MPC + MPS = 1

Chapter 9 Table 9.1

Chapter 9 Figure 9.2

The Consumption and Saving Functions

Consumption and Saving Functions I

Consumption function: C = CA + MPC(Y) Where

CA (intercept) = “Autonomous Consumption”

MPC (slope) = “Marginal Propensity to Consume” (also = 1 – MPS)

Y = GDP or “Disposable Income”

Consumption and Saving Functions II

Saving function: S = S0 + MPS(Y) Where

S0 (intercept) = “Maximum Dissaving” = - CA

MPS (slope) = “Marginal Propensity to Save” (also = 1 – MPC)

Y = GDP or “Disposable Income”

Consumption and Saving Functions III

Since CA = - S0 and MPS +MPC = 1

If the consumption function is C = 100 + .85Y The saving function must be S = -100 + .15Y

If the saving function is S = -125 + .3Y The consumption function must be C = 125 + .7Y

Chapter 9 Figure 9.3

Chapter 9 Figure 9.4(a)Shifting the Consumption

Schedule

Chapter 9 Figure 9.4(b)

Shifting the Saving Schedule

Chapter 9 Table 9.2The Investment Demand

Schedule

Chapter 9 Figure 9.5

The Investment Demand Function

Chapter 9 Figure 9.6

What Shifts the Investment Demand Function?

Changes in the cost of acquiring capital equipment, maintaining capital equipment, or operating capital equipment e.g., changes in the price of gasoline

Changes in taxes on business e.g., accelerated depreciation

Technological Improvements How much capital equipment is already installed Producer Expectations

Overoptimistic during the expansionary phase of the business cycle

Frustrating efforts to slow down the economy Overpessimistic during the contractionary phase of

the business cycle Delaying recovery

Chapter 9 Figure 9.7

Investment is highly volatile!

Chapter 9 Table 9.3The AE multiplier

M = 1/(1- MPC) = 1/MPS

The Multiplier Formula

First round, increase in Aggregate Expenditure = ∆AE0

This induces an increase in C, ∆C1 = (MPC)∆AE0

Which becomes the second round increase in income

Inducing a further increase in C, ∆C2 = (MPC)∆C1 = (MPC)2∆AE0

∆C3 = (MPC)∆C2 = (MPC)3∆AE0, etc.

Derivation of the Multiplier

∆Y = ∆AE0 + ∆AE1 + ∆AE2 + ∆AE3 + … + ∆AEn + …

∆Y = ∆AE0 + (MPC)∆AE0 + (MPC)∆AE1 + (MPC)∆AE2 + … + ∆AEn + …

∆Y = ∆AE0 + (MPC)∆AE0 + (MPC)2∆AE0 + (MPC)3∆AE0 + … + (MPC)n∆AE0 + …

∆Y = (MPC)0∆AE0 + (MPC)1∆AE0 + (MPC)2∆AE0 + (MPC)3∆AE0 + … + (MPC)n∆AE0 + …

Derivation of the Multiplier

∆Y = (MPC)0∆AE0 + (MPC)1∆AE0 + (MPC)2∆AE0 + (MPC)3∆AE0 + … + (MPC)n∆AE0 + …

∆Y = ∑i=0,∞(MPC)n∆AE0 = ∆AE0∑i=0,∞(MPC)n

for infinite convergent sums, m = ∆Y/∆AE = 1/(1 – MPC) = 1/MPS

MPC < 1 necessary for infinite sum to converge

Chapter 9 Figure 9.8

Chapter 9

Figure 9.9

How M varies with the MPC

The AE multiplier

M = 1/(1- MPC) = 1/MPS M = change in real GDP/change in

spending M = ∆GDP/∆AE = ∆Y/∆AE Change in AE can come from any

component of aggregate expenditure

AE = C + Ig + G + Xn