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ECO 301 Problem Set 2
by email before the beginning of class
1. Assume that the labor force is 150 million people and there are 15 million
discouraged workers who do not have a job but are not looking for one either.
On average, it takes 2 months for an unemployed person to nd a job. A job
lasts for 30 months on average. Assume that the unemployment rate is 4 percent
at the beginning of April.
(a) How much will the unemployment rate be at the beginning of May?
(b) Assume that at the beginning of May, the 15 million discouraged workers start looking for a job. How much will the unemployment rate be at the
beginning of June?
(c) If we wait long enough, the unemployment rate will converge to some
value. Calculate this value.
2. An economy with 6,336 machines and 110 workers has a production
function Y = 3K L1 , where 0 < < 1 and CAPITAL INCOME is 1/3 of total income. (a) Find . (b) Assume that the government intervenes and sets a minimum real wage
of 8. Find the unemployment rate.
3. A closed economy has the following Cobb-Douglas production function:
3=4
F (K; L) = K 1=4 (EL) , where the notation is as in class. The depreciation
rate is 3% and the saving rate is 48%. The economy is in a steady state, where
investment I increases at a rate 3% and the real wage w increases at a rate 2%.
(a) Find the growth rates of the following variables:
(i) saving per worker, S=L
(ii) number of workers per machine, L=K
(iii) capital income per worker, rK=L
(iv) the di¤erence between labor income and consumption, wL
C
(b) If consumption C is 52 billion THIS year, nd the number of machines
K NEXT year.
(c) By how many percentage points should the government change the saving rate so that the economy may converge to the golden rule steady state
(use a + for an increase and a   for a decrease)? How would the current
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4. A closed economy has two factors of production: capital and labor. The
production function is known to exhibit constant returns to scale. The capital
stock is about 4 times one years real GDP. Approximately 8% of GDP is used
to replace depreciating capital. Labor income is 60% of real GDP. Real GDP
grows at an average rate of 3% per year. Assume the economy is in a steady
state.
(a) Calculate the marginal product of capital.
(b) Is the capital per e¤ective worker lower or larger than it would have been
in the golden rule steady state?
5. Consider a closed economy, where all prices are assumed xed in the short
run, and use graphical analysis (both IS-LM and AD-AS graphs) to illustrate
how the equilibrium output, price level, and interest rate would be a¤ected in
the short run and in the transition to the long run by:
(a) a substantial decrease in the usage of credit cards (absent any policy
response)
(i) What can the government do to stabilize the output?
(ii) Would the policy described in (a-i) stabilize the interest rate?
(b) a stock market crash (absent any policy response)
(i) What can the central bank do to stabilize the interest rate?
(ii) Compare the long-run price level in (b) with the one in (b-i). If
di¤erent, which one is bigger?
6. Consider a closed economy where the marginal propensity to consume
equals 0.6 and all prices are xed in the short run. Assume that government
spending G increases by \$6 billion and tax revenue increases by \$8 billion.
(a) Calculate the horizontal shift in the IS curve.
(b) Is the corresponding change in equilibrium income (in the short run)
greater, smaller, or equal (in absolute value).to the horizontal shift in the IS
curve? Explain.
(c) How would the price level evolve in the transition from the short run to
the long run (increase, decrease, or remain the same)?
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