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(ECON514)EC51408Midterm02AK.pdf
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Midterm Exam
Economics 514
Macroeconomic Analysis
November 13, 2008

Each Question 14
Points Each.
1.
Permanent Income Hypothesis Two households born at time 0 lives through time T = . The household begins period zero with zero financial wealth Thus, the present value of lifetime consumption is equal to the present value of lifetime income.





the interest rate is 20% (i.e. r = .2). Each household has initial income Y0.and chooses consumption according to the permanent income hypothesis. In each case, we can write consumption as proportional to initial income C0 = mpcY0.
A.
The first household experiences continuously declining income in all future periods. The level of income in each period is a fraction of the last period. Yt = Yt-1. Solve for mpc when = .9










Please write your answers on this exam paper.

B.
The second household experiences constant growth in output through period N, when the household retires from work. Yt = (1+g)Yt-1 if tN At time N+1 and for all periods after, the household has zero income. Solve for mpc when N = 9 and g = .2.







C.
Explain in words why mpc is an increasing function of in part A. and an increasing function of N in part B




The household attempts to smooth consumption by consuming a weighted average of current and future income. A more permanent level of income indicated by a high is also consistent with a higher future income; A longer working life, consistent with a high N also indicates a higher average.
















2.
Implied Capital Rental Rate The inflation rate of output goods price is 6% (i.e. = .06). The nominal interest rate is 9% (i = .09). The relative price of investment goods to output goods is always Itp=.75 and the depreciation rate is 9%. Solve for capital productivity and the capital labor ratio when the marginal productivity of capital equals the capital rental rate and production is given by the Cobb-Douglass function.








Please write your answers on this exam paper.

3.
Precautionary Savings A household lives for two periods. The household begins with zero financial wealth and earns Y0 = 100. The household is perfectly patient with discount rate =1 and faces an interest rate (1+r) = 1. The household faces uncertainty about future income. The household maximizes expected utility []1()uCwhere the felicity function is u(C) = 1000 C C. C2 and marginal utility of consumption is U(C) = 1000 C C subject to the present value of consumption being equal to the present value of output.


A.
The household has a chance of receiving Y1 = 150 and a chance of receiving Y1 = 60. Calculate the expected value of Y1 and the saving in the first period.







The household maximizes



S = 5