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 9.2
The 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


Changes in taxes on business




e.g., changes in the price of gasoline
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!
The AE multiplier
M = 1/(1- MPC) = 1/MPS
Chapter 9
Table 9.3
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