Question 1: In Ghana, the capital share of GDP is about 40 percent, the average growth in output is about 2 percent per year, the depreciation rate is about 3 percent per year, and the capital–output ratio is about 1.5. Suppose that the production function is Cobb–Douglas and that Ghana has been in a steady state. a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state relationship, sy = (δ + n + g)k.] b. What is the marginal product of capital in the initial steady state? c. Suppose that public policy alters the saving rate so that the economy reaches the Golden Rule level of capital. What will the marginal product of capital be at the Golden Rule steady state? Compare the marginal product at the Golden Rule steady state to the marginal product in the initial steady state. Explain.
Question 1:
In Ghana, the capital share of
2 percent per year, the
is about 1.5. Suppose that the production function is Cobb–Douglas and that Ghana has been
in a steady state.
a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state
relationship, sy = (δ + n + g)k.]
b. What is the marginal product of capital in the initial steady state?
c. Suppose that public policy alters the saving rate so that the economy reaches the Golden
Rule level of capital. What will the marginal product of capital be at the Golden Rule steady
state? Compare the marginal product at the Golden Rule steady state to the marginal product
in the initial steady state. Explain.
d. What will the capital–output ratio be at the Golden Rule steady state? (Hint: For the Cobb–
Douglas production function, the capital–output ratio is related to the marginal product of
capital.)
e. What must the saving rate be to reach the Golden Rule steady state?
Question 2:
In the Keynesian cross model, assume that the consumption function is given by
C = 110 + 0.75(Y - T). Planned investment is 300; government purchases is 350. Assume a
balanced budget.
a. Graph planned expenditure as a function of income.
b. What is the equilibrium level of income?
c. If government purchases increase to 400, what is the new equilibrium income? What is the
multiplier for government purchases?
d. What level of government purchases is needed to achieve an income of 2,200? (Taxes remain
unchanged.)
e. What level of taxes is needed to achieve an income of 2,200? (Government purchases remain
at 350.)
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Question 3:
Consider the economy of Ghana.
The consumption function is given by C = 400 + 0.8(Y - T).
The investment function is I = 600 - 70r.
Government purchases is 400. Assume a balanced budget.
The money demand function is (M/P)d = Y - 180r.
The money supply M is 3,000 and the price level P is 3.
a. Find the equilibrium interest rate r and the equilibrium level of income Y.
b. Suppose that government purchases are increased from 400 to 600. What are the new
equilibrium interest rate and level of income?
c. Suppose instead that the money supply is increased from 3,000 to 3,500. What are the new
equilibrium interest rate and level of income?
d. With the initial values for monetary and fiscal policy, suppose that the price level rises from
3 to 5. What are the new equilibrium interest rate and level of income?
Question 4
Suppose that output is produced according to the production function Y = Kα[(1 - u)L]1-α, where
K is capital, L is the labor force, and u is the natural rate of
rate is s, the labor force grows at rate n, and capital depreciates at rate d.
a. Express output per worker (y = Y/L) as a function of capital per worker (k = K/L) and the
natural rate of unemployment (u).
b. Write an equation that describes the steady state of this economy. Find the steady state capital
per worker and steady state output per worker.
c. Does this production function have constant returns to scale? Explain.
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Question 5
2. A small open economy is described by the following equations:
C = 60 +.75(Y - T)
I = 150 - 20r
NX = 150 – 50e
M/P = Y - 40r
G = 1500
M = 2000
P = 2
R* = 5
Assume a balanced budget.
a. Derive and graph the IS* and LM* curves.
b. Calculate the equilibrium exchange rate, level of income, and net exports.
c. Assume a floating exchange rate. Calculate what happens to the exchange rate, the level of
income, and net exports if the government increases its spending by 50. Use a graph to explain
what you find.
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