PROBLEM SET 1
- THE GOODS MARKET AND MULTIPLIERS - QUESTIONS
ANSWERS
1. True, False or Uncertain - "In national income accounting, the value
of inventories must be added to the value of final goods and services sold
to determine GDP."
2. Suppose that the economy is characterized by the following behavioral
equations:
C = 400 + .75 YD
I = 450
G = 300
T = 400
a. What is equilibrium GDP (Y) in this economy?
b. What is disposable income (YD) in this economy?
c. What is private savings in this economy?
3. Find the change in equilibrium income in the economy described in question
1 if the following changes occur (treat each change separately):
a. Investment is increased by 100 (i.e. from 450 to 550).
b. Government is increased by 100 (i.e. from 300 to 400).
c. Government and taxes are both increased by 100 (i.e. if G becomes
400 and T becomes 500).
4. Suppose that the model described in question 1 is changed in such a
way that taxes were given by: T = 100 + .2 Y.
a. What is the equilibrium GDP (Y) in this economy?
b. What is the change in equilibrium income in this economy if Investment
is increased by 100 (i.e. from 450 to 550)?
c. Explain in words why the change in income computed in part b is
smaller than the change in income in the model discussed in question 3
part a.
5. Suppose that the model described in question 2 is changed in such a
way that the consumption function becomes C = 300 + .75 YD.
a. What is the new level of equilibrium income?
b. Compare the level of private savings in the original model and the
new model?
c. Explain the result from part b.
6. Suppose that the economy is characterized by the following behavioral
equations:
C= c0 + c1 YD
I = I0
G = G0
T = T0
a. What is the formula for equilibrium GDP (Y) in this model?
b. Suppose that Investment becomes I = I0 + D
I. What is the formula for the new equilibrium GDP (Y) in this model?
c. What is the formula for the difference in income between the economy
described in part b and the economy described in part a?
7. Start with the same model described in question 6.
a. Suppose that the original model is changed such that G becomes
G + D G and that T becomes T + D
T where D G = D T,
(i.e. both government expenditures and taxes are changed an equal amount).
What is formula for the equilibrium GDP (Y) in this model?
b. What formula for the change in equilibrium income comparing this
model with the original model?
8. Demonstrate graphically the type of total expenditure function one would
have to have such that the multiplier in the model would be equal to one.
9. Suppose that we complicate the model in question 6 by adding X, exports,
and Q, imports. The model would become:
C= c0 + c1 YD
I = I0
G = G0
T = T0
X = X0
Q = q0 + m Y
a. What is the formula for equilibrium GDP (Y) in this model income?
b. What would you call m in this model?
c. What is the multiplier in this model?
10. How does the multiplier in the model with exports and imports compare
with the multiplier in the original model (i.e. compare the formulae and
tell which is bigger and why)?
11. Suppose that investment depends upon interest rates and is
given by the formula
I = I0 – d r, where d is a positive constant and r is the
real interest rate. What is the formula for equilibrium GDP (Y) in
an economy otherwise described by the model presented in question 6?
What would happen to equilibrium income if the real interest rate increased?
Is there any change in the multiplier in this model?
12. In your answer to question 7 you should have proved what is called
the “balanced budget multiplier result.” This result demonstrates
that if DT = DG,
then DY = DG.
Draw a graph that proves this same result. Be careful to measure
things correctly and include a commentary explaining the lines on your
graph.
ANSWERS