University of California, Santa Cruz
Fall Quarter 2008
Econ 100B
INTERMEDIATE MACROECONOMICS
Problem set 1 Answer Key
1. Suppose that the following behavioral equations characterize an economy (in billions of dollars):
C = 2000 + 0.9 Y
d
I = 1800
G = 1800
T = (1/3) Y
(a) Solve for equilibrium real GDP, Y.
Y
=
C
+
I
+
G
Y =
2000
+ 0.9 Y d + 1800 +1800
Y = 5600 + 0.9 Y d
Y = 5600 + 0.9 (Y – 1/3 Y)
Y = 5600 + 0.9 * 2/3 Y
Y = 5600 + 0.6Y
Y – 0.6 Y = 5600
Y = [1 / (10.6) ] 5600
Y = $14,000
Thus the equilibrium real GDP is $11000.
(b) Solve for equilibrium disposable income, Y
d
We get the disposable income by subtracting taxes (net of transfers) from the equilibrium real
income.
Y d = Y  T
Y d = (Y – 1/3 Y)
Y d = 2/3 * 14,000
Y d = $ 9,333.33
(c) Solve for consumption expenditures.
The total consumption expenditure is given as
C = 2000 + 0.9 Y d
C = 2000 + 0.9 * 9,333.33
C = $ 10,400
2. Calculate the multiplier for the economy of problem 1.
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As shown in the above question the multiplier is [1 / (10.6)] or 2.5. For a given $100 increase in
government expenditure, the real GDP increases by $250 billion.
(b) How much do taxes rise with this increase in real GDP?
Given
T
= (1/ 3)
*Y
we have
(c) What is the net change in the government deficit (GT)?
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 Spring '07
 YiSun
 Economics, Macroeconomics, Public Finance, gross domestic product

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