Answer Key - Problem Set 3

EC132.01(02)
Serge Kasyanenko
Principles of Macroeconomics Fall 2005
Answer Key - Problem Set 3
1. (Consumption Function with nonconstant MPC) C
a. Fill the table and use it to build consumption
and saving functions. Assume that 3000
consumption function is linear (has constant
marginal propensity to consume) between 2500
two consecutive points.
Disposable Consumption
Income Expenditure
Savings
A
B
C
D
E
1000
1500
2000
2500
3000
1250
1725
2150
2500
2800
-250
-225
-150
0
200
F 3500 3050 450
What is the break-even disposable income?
2000
1500
1000
S
D
C
B
A
1000 1500 2000 2500
E
3000
F
3500
DI
b.
Find the marginal propensity to consume
(MPC) and marginal propensity to save (MPS)
for every line segment.
400
300
200
F
ΔDI ΔC ΔS MPC
A-B 500 475 25 0.95
B-C 500 425 75 0.85
C-D 500 350 150 0.70
D-E 500 300 200 0.60
E-F 500 250 250 0.50
MPS
0.05
0.15
0.30
0.40
0.50
100
0
-100
-200
-300
A
B
C
D
E
1000 1500 2000 2500
3000 3500
DI
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2.
If f(x) is a linear function of x then it can be mathematical represented in the following form:
f(x)=a+b*x, where a (intercept) and b (slope) are two arbitrary constants. Thus, we can
represent consumption and saving function with the same analytical expression. For a linear
function it is sufficient to know two arbitrary point on the line to find the values of both a and b.
For example, took two points form table 6-3 (page 109) in your text:
Disposable
Income
24000
25000
Consumption
Saving
First, let find a and b for the consumption function. We know that the slope of the consumption
function b is equal to the MPC, thus we can find b by dividing a change in consumption (800)
with a change in income (1000):
thus our consumption function is:
C = 5 000 + 0.8*DI (1)
You may use point B to check that it is actually true:
A
B
24200
25000
b=MPC=ΔC/ΔDI=800/1000=0.8
To find a simply use either point A or B in the following way: since C=a+b*DI, consumption at
point A is equal to:
C(B) = 5 000 + 0.8*25 000 = 5 000 + 20 000 = 25 000
The same logic applied to the savings function: S=a+b*DI, where b is the slope of the saving
function which is equal to the marginal propensity to save (0.2 in this table). To find a for this
function use same steps as with consumption function:
-200
24 200 = a+0.8*24 000 or a = 24 200 - 0.8*24 000 = 24 200 - 19 200 = 5 000
-200 = a+0.2*24 000 or a = -200 - 0.2*24 000 =- 200 - 4 800 = - 5 000
as a result, the saving function is
S = - 5 000 + 0.2*DI (2)
Alternatively, you can use your consumption function to derive the savings function:
S = DI-C, S = DI - 5000 - 0.8*DI = - 5000 + 0.2*DI
0
i.
ii.
Using data from the problem 1 fill the following table:
Consumption
function
Saving function
intercept a slope b intercept a slope b
A-B
B-C
300
450
0.95
0.85
-300
-450
0.05
0.15
C-D
D-E
E-F
750
1000
1300
0.70
0.60
0.50
-750
-1000
-1300
0.30
0.40
0.50
What is the economic meaning of the intercepts a of savings and consumption functions?
ANSWER: The value of intercept shows the consumption (savings) when disposable income is
equal to zero. That is in case of consumption function a represents the amount household
needs to consume in order to survive.
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05
iii.
How will you use equations 1 and 2 to find the break-even disposable income? (You may either
show it in a general case or for any given a and b from the table.)
ANSWER: To find break even income you have either to equate savings to zero or
consumption to disposable income:
using savings function:
S=0, aS+bS*DI=0 thus DI=-aS/bS
using consumption function:
C=DI, aC+bC*DI=DI thus DI=aC/(1-bC)
for example for the segment A-B aS=-300, bS=0.05, and aC=300, bC=0.95
then S=0 implies that DI=-(-300)/0.05=6000
and C=DI implies that DI=300/(1-0.95)=6000
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3. (Fiscal Policy and the Multiplier Model)
a. Fill the table and find the marginal propensities to consume and save.
A
B
C
D
E
GDP Taxes
Disposable Consumption Planned Government Total Planned
Income Expenditure Investment Purchases Expenditure
Q
T DI
C
I
G C+I+G=TE
7000 350 6650 6400 250 150 6800
6500 350 6150 6000 250 150 6400
6000 350 5650 5600 250 150 6000
5500 350 5150 5200 250 150 5600
5000 350 4650 4800 250 150 5200
What is the equilibrium level of GDP?
6000
b. What is the value of the government expenditure multiplier?
What is the value of the tax multiplier?
5.00
4.00
c.
If the government wants to increase GDP with 1000 how should it use each of the fiscal policy instrum
(Discuss each of the instruments separately)
(indicate both the direction and the magnitude of the change)
1) increase government purchases by:
200
2) decrease taxes by:
250
d. Illustrate question c with a multiplier model (Keynesian cross) diagram.
TE
TE=C+I+G+ΔG+X
TE
TE=C+I+G+X+ΔT*MPC
↑
TE=C+I+G+X
↑
TE=C+I+G+X
ΔG=200
ΔT*MPC=
250*0.8=200
ΔQ=1000
ΔQ=1000
Q0
→
Q1
GDP
Q0
→
Q1
GDP
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