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Econ 100B Fall Quarter 2008 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 Yd
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 / (1-0.6) ] 5600
Y = $14,000
Thus the equilibrium real GDP is $11000. (b) Solve for equilibrium disposable income, Yd We get the disposable income by subtracting taxes (net of transfers) from the equilibrium real
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. As shown in the above question the multiplier is [1 / (1-0.6)] 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 (G-T)? Thus we have government increasing by $100 billion and tax revenue increasing by $83.5 billion.
This implies that the government deficit (G-T) will increase by $16.5 billion.
3. An algebraic version of the simple model of the economy is: C = c0 + c1 Yd
Yd = Y – T
Ī (a) Solve for the algebraic expression for equilibrium GDP as in class or the text. Replacing 3.1, 3.2 and 3.3 in 3.4, we get Solving this (3.1)
(3.4) (b) Solve for an expression for the change in equilibrium GDP for an increase in government expenditures
equal to G when taxes are held constant. Δ The general expression for a change in government expenditure, investment and taxes can be
written as Given that there is a change in government expenditure only, the above equation reduces to 4. Problem 8, Chapter 3 of Blanchard, p. 61
a. We know that:
C= c0 + c1YD (1)
YD = Y – T (2)
I = b0 + b1Y (3)
We also assume exogenous constant government expenditures G.
We also know that
Y = C + I + G (4)
Plugging in (1-3) into (4) we obtain,
Y = c0 + c1YD + b0 + b1Y + G =>
Y = c0 + c1(Y - T) + b0 + b1Y + G =>
Y = c0 + c1Y - c1T + b0 + b1Y + G =>
Y - c1Y - b1Y = c0 - c1T + b0 + G =>
Y (1- c1- b1) = c0 - c1T + b0 + G =>
Y = [1/(1- c1- b1)] (c0 - c1T + b0 + G) =>
Y = 1/(1- (c1+ b1)) (c0 - c1T + b0 + G)
b. The expression 1/(1- (c1+ b1)) is the multiplier for our exercise.
The relation between investment and output affects the value of the multiplier through the
coefficient b1. b1 is positive implying that an increase in output increases investment. Higher
investment in turn leads to even higher output through the multiplier which is positive and greater than 1.The higher is b1, the higher is the value of the multiplier. The multiplier [1/(1- (c1+
b1))] is positive and greater than one as long as (c1+ b1) is less than one. This implies that the
denominator is less than one and hence the whole fraction i.e. the multiplier, is greater than one.
c. We observe that b0 affects investment positively. An increase in b0 will increase investment
and will increase equilibrium output by more than the increase in investment through the
multiplier which is greater than one.
Investment will increase by more than b0 because investment is also affected by the factor b1Y
and we just said that income will increase because of the increase in b0. Therefore investment
will increase for two reasons. First, because of the increase in b0 and then, because of the
increase in income that the increase in b0 caused.
We know that:
Y = C + I + G =>
I = Y – C – G =>
I = (Y – C - T) + (T– G) =>
I = Sp + Sg => (Investment is equal to private savings plus government savings)
I = Sn
Therefore Investment is equal to national savings. Since investment went up, savings also have
to go up. 5. Problem 4, Chapter 4 of Blanchard, p. 83. (a) For interest rate of 5%
M D = $Y *L(i)
M D = $100 *L(i)
MS = M D
$20 = $100 *(0.25 –i)
$20 = $25 – 100 * i
100 * i= 5
i = 0.05 = 5 %
M S = [Y * (0.25 –i)]
M S = [Y * 0.25 – Y * i)]
M S = (Y * 0.25) - (Y * i)
M S = (Y * 0.25) - (Y * i) since Y is remained constant,
M S = - (Y * i)
M S = - ($100* 0.1) Δ Δ Δ Δ Δ Δ Y=0 Δ Δ Δ Δ Δ Δ Δ Δ M S = - $ 10
M S = $ 10 FED should set the money supply to $10 .
Δ 6. Problem 5, Chapter 4, p. 83.
(a) The demand for bond is An increase in interest rate of 10% would result in an increase in demand for bonds of $6,000.
(b) An increase in wealth does not affect money demand (which depends on income).
Increase in wealth increases bond demand.
(c) Increase in income increases money demand, but decreases demand for bonds.
(d) When people earn more income, their wealth does not change right away. Therefore, they
increase their demand for money and decrease their demand for bonds ...
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- Spring '07