Transcript Advanced Macroeconomics

MACROECONOMICS I
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SEMINAR 2
PROBLEM 1
Consider a Cobb–Douglas production function with three inputs. K is capital
(number of machines), L is labor (number of workers), and H is human capital
(number of college degrees among the workers). The production function is:
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Y K L H
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A. Derive an expression for the marginal product of labor (MPL). How does an
increase in the amount of human capital affect the MPL?
B. Derive an expression for the marginal product of human capital (MPH). How
does an increase in the amount of human capital affect the MPH?
C. What is the income share paid to labor and human capital? In the national
income accounts of the economy, what share of total income would workers
appear to receive?
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D. An unskilled worker earns the MPL, whereas a skilled worker earns the MPL
plus the MPH. Using your answers to (A and (B, find the ratio of the skilled wage
to the unskilled wage. How does an increase in the amount of human capital
affect this ratio?
PROBLEM 2
The government raises taxes by $100 billion. If the marginal propensity to
consume is 0.6, what happens to the following? Do they rise or fall? By what
amounts?
A. Public saving
B. Private saving
C. National saving
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D. Investment
PROBLEM 3
Consider an economy described by the following equations:
Y  C  I G
Y  5000
G  1000
T  1000
C  250  0.75* Y  T 
I  1000  50* r
A. Compute private saving, public saving, and national saving
B. Find the equilibrium interest rate
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C. Now suppose that G rises to 1250. Compute private saving, public saving
and national saving. Find the new equilibrium interest rate.
PROBLEM 4
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Suppose that the government increases taxes and government purchases by
equal amounts. What happens to the interest rate and investment in response
to this balanced-budget change? Does your answer depend on the marginal
propensity to consume?
PROBLEM 5
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• Suppose an automobile manufacturer is choosing between two
production options. It can produce 100 cars with 200 workers
and 50 machines, or it can produce 166 cars with 300 workers
and 75 machines. Would you describe the manufacturer’s
production function as exhibiting decreasing, constant, or
increasing returns to scale?