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(ECON514)8dfab8 - EC51409Midterm2AK.pdf
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Mid-Term Exam # 2
Economics 514
Macroeconomic Analysis
Thursday, November 13th, 2009
1.
(25 points) Taxes and Unemployment



All workers in the economy are either employed or unemployed. In every period, 5% of employed workers lose their job, so the job separation rate is s = .04. In every period, all unemployed workers receive one job offer. That job offers them a wage per labor unit that ranges uniformly over the range 0 to 100. The cdf of a uniform distribution over this range is
.
Assume that the utility of a household is given by the function

(1.1)

If the household has a job, they must spend all of their time at work. Normalize total time to one, TIME = 1. If they dont have a job, lst = 1; if they do have a job, lst = 0, Lt = 1. If they do not have a job, they will be offered an unemployment benefit, b = 36.
a.
Calculate the reservation wage, the job finding rate and the steady state unemployment rate




The utility of an unemployed person is UU =
. The utility of an employed person is
where Ct = wtLt = wt . If the wage were wR = 64 then the household would have equal utitilty as unemployed or employed. Only 36% of the wage offers are above the reservation wage so f = .36. The unemployment rate is










.
b.
Suppose the household must pay a tax on any wage income equal they receive, so they will keep only a fraction of their pay (i.e. ). Calculate the reservation wage, the job finding rate and the steady state unemployment rate.






The utility of an unemployed person is UU =
. The utility of an employed person is
where Ct = wtLt = wt . If the wage were wR = 81 then the household would have equal utitilty as unemployed or employed. Only 19% of the wage offers are above the reservation wage so f = .19. The unemployment rate is



2.
(25 points) Interest Rates and The Student Household



Consider a household that lives for two periods, beginning period 0 with zero financial wealth. The household faces a real interest rate of 10%, (1+r = 1.10). The household maximizes a discounted utility function of
. The household earns Y0 from producing goods in period 0 and Y1 from producing goods in period 1. The first period, the household is a student and earns no income. In the second period, the household earns $242. The household will need to borrow some money in order to finance consumption today.
a.
Calculate the present value of lifetime income. Calculate period 0 consumption and savings under the permanent income hypothesis (i.e. ).




Present value of lifetime income is
. With Permanent Income hypothesis
C0 = C1. According to the budget constraint
. Savings is -


b.
Assume that the interest rate rises to 15% (but the discount factor stays constant,). Calculate the wealth effect. In other words, calculate how much the present value of lifetime income decreases? Draw a graph indicating how the budget c