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(ECON514)53c8de - EC51409PracticeMidterm01.pdf
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Mid-Term Exam # 1
Economics 514
Macroeconomic Analysis
Thursday, October 14th , 2008

Write your answers on this white exam paper. Do not write your answers on the blue book! Do not hand in your blue book!

1.
Substitution Effect and Capital


A.
Price taking firms produce goods with the production functiontYKL=, where Lt is labor and Kt is capital and sell their goods at price Pt, hire workers at wage Wt and capital at rental rate Rt.



i.
Write the first order conditions (FOCs) that determine the demand for capital and labor.



FOC: K




FOC: L






ii.
Assume that capital is always supplied elastically at the fixed relative rental price of capital . Calculate the profit maximizing capital labor ratio using the FOC for capital. Calculate the real wage rate at that capital labor ratio.






k _______________



w ________________





Please write your answers on this exam paper.


Please write your answers on this exam paper.


B.
The workers in the economy have a utility function of the form so that marginal utility of consumption is U... while marginal utiltity of leisure is U... where 1.<<. The workers have a limited amount of time T=Lt + lst budget constraint of (). Normalize the time to T = 1.






i.
Write the first order conditions that determine the supply of labor. Calculate the elasticity of substitution between consumption and leisure when and when . Combine the first order condition with the budget constraint and the time constraint and show that we can write the frication of time, T, spent on leisure can be written as a function of tw so that ()






FOC






Elasticity of Substitution




Fraction of time spent on leisure as a function of






ii.
Calculate the amount of labor that would be supplied at the wage rate that you solved for in 1.A.ii when and when . Calculate consumption at each level of .








L _____________

C ______________





L _____________

C ______________









C.
Now assume that the rental price of capital drops to. Would the equilibrium labor in the economy rise or fall when and when? Explain the intuition. (Note you do not need to solve for the new level unless you find it helpful in your explanation).






Please write your answers on this exam paper.

Please write your answers on this exam paper.


Please write your answers on this exam