Economics 102
Fall 2007
Answers to Homework #5
1. Complete the following table, and answer the questions that follow.
Taxes are proportional to income, so T = tY.
Assume that there are NO TRANSFERS.
Hint: You should consider using the slope formula to calculate MPC.
Y
T
YT
C
S
60
15
45
56
11
100
25
75
80
5
175
43.75
131.25
125
6.25
400
100
300
260
40
a)
Determine the progressive tax rate t.
15 = t(60)
t = .25
b)
Determine the consumption and saving functions with respect to disposable
income, and with respect to aggregate income.
2
.
8
.
1
1
8
.
45
75
56
80
)
(
)
(
)
(
2
1
2
1
=

=

=
=


=




=

∆
∆
=
MPC
MPS
T
Y
T
Y
C
C
T
Y
C
MPC
C = 20 + .8(YT)
C = 20 + .6Y
S = 20 + .2(YT)
S = 20 + .15Y
c)
Given the consumption function you determined in part (b), the tax rate you found
in part (a), and the following information about the economy, determine the
equilibrium output:
I = 130
G = 100 + .16T
X = 250
M = 200
Y = [20 + .8(YT)] + 130 + [100 + .16T] + [250200]
Y = 300 + .8(.75Y) + .16(.25Y)
Y = 300 + .64Y
.36Y = 300
Y = 833.33
d)
Given equilibrium output, determine the equilibrium levels of consumption,
savings, taxes, and government spending.
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View Full DocumentC = 20 + .6(833.33)
C = 20 + 499.99
C = 519.99
S = 20 + .15(833.33)
S = 20 + 124.99
S = 104.99
T = .25*(833.33)
T = 208.33
G = 100 + .16(208.33)
G = 133.33
Notice, adding the values for C + S + T, you get 833.33 (approximately
because of rounding errors). This is the value determined for Y in part C.
This is consistent with the identity from class, Y = C + S + (TTR).
e)
Is the government running a deficit or a surplus?
Are there capital inflows or
outflows?
The government is running a surplus.
TG = 75
There are capital outflows M – X = 50.
f)
In terms of variables, determine the GDP multiplier.
Hint: you should model the
equations as follows:
C = a + b(YT)
I = I
G = g + dT
X = X
M = M
T = tY
Y = [a + b(YT)] + I + [g + dT]
+ [XM]
Y = [a + b(YtY)] + I + [g + dtY] + X – M
Y = a + bY –btY + I + g + dtY + X – M
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 Spring '08
 Drozd
 Economics, Macroeconomics, Monetary Policy, Federal Reserve System, Fractionalreserve banking, reserve ratio

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