Answers to Problem Set #2: Keynesian Model
1.
Income
$0
10,000
20,000
30,000
40,000
Consumption
$4000
12,000
20,000
28,000
36,000
Savings
- $4000
- 2000
0
2,000
4,000
APC
--1.20
1.00
0.93
0.90
APS
---0.20
0.00
0.07
0.10
MPC
MPS
0.80
0.80
0.80
0.80
0.20
0.20
0.20
0.20
(b) The consumption function graphically will have a vertical intercept of 4,000 (i.e., when Y = 0,
C = 4000) and a slope of 0.80 (= MPC). It will intersect the 45 degree line at an income level of
20,000 (i.e., where all available income is spent on Consumers goods).
The Savings function will have a vertical intercept of –4000 (i.e., when income is 0, savings = 4000) and a horizontal intercept of Y = 20,000 (i.e., savings = 0 when Y = 20,000). The slope of
the Savings function will be 0.20 (+MPS)
(c) If I = 2000 and G= 0 and net exports (X – M) = 0 then AE = C + I
Income
Consumption
Investment
0
4,000
2,000
10,000
12,000
2,000
20,000
20,000
2,000
30,000
28,000
2,000
40,000
36,000
2,000
AE = C + I
6,000
14,000
22,000
30,000
38,000
Therefore equilibrium GDP is where Y (GDP) or Income = AE. This occurs at an income level of
$30,000.
(d) In an Aggregate Expenditure (AE) - GDP (Y) diagram, the AE curve has a vertical intercept
of 6,000 (i.e., AE = 6,000 when Y = 0). The slope of the AE curve is 0.80 (i.e., AE increases
by a total of $8000 each time that Y increases by $10,000). The AE curve will intersect the
45 degree line at an income level of $30,000 (equilibrium GDP).
2.
Given
C = 200 + 0.75 Y
I = 200
by assumption G = 0 and (X – M) = 0 then AE = C + I (only).
(a) The value of MPC = 0.75 (the coefficient on Y in the C equation). The definition of MPC is
the change in C divided by the change in Y.
(b) If C = 200 + 0.75 Y then the savings function is:
S = -200 + 0.25 Y
(i.e., if C>0 when Y = 0, then S = -1(C) and MPC + MPS = 1 so MPS (the slope of the savings
function) is 0.25.
(c) By definition, AE = 200 + 0.75 Y + 200
AE = 400 + 0.75 Y
The equilibrium condition is AE = Y
so 400 + 0.75 Y = Y
subtracting 0.75 Y from each side of the equation yields,
400 = 0.25 Y
therefore, Y = 1600.
Consumption in equilibrium is:
C = 200 + 0.75 (1600) = 1400
S = -200 + 0.25 (1600) = 200.