PS01-S11

# PS01-S11 - University of Minnesota Macroeconomic Policy...

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University of Minnesota Macroeconomic Policy 4731H, Spring 2010 Problem Set # 1 Instructor: Justin Barnette Due date: 2 / 8 / 2011 Question 1 (50 points) Consider an economy with a representative household and a representa- tive firm. The representative household maximizes X t =0 β t " c 1 - σ t 1 - σ - l 1+ φ t 1 + φ # σ, φ 0 subject to the budget constraint t c t + x t + q t b t +1 = w t l t + r t k t + b t and the capital law of motion t k t +1 = (1 - δ ) k t + x t where c t is time t consumption, l t is time t labor, x t is time t investment, k t +1 is time t + 1 capital, b t +1 is bond holdings at t + 1 and ( q t , w t , r t ) are the price of bonds, wage and rental rate of capital at time t . The representative firm maximizes in any t y t - w t l t - r t k t subject to the constant returns to scale (CRS) technology y t = Ak α t l 1 - α t where y t is the level of output. (a) (15 points) From the consumer’s problem, find: i ) consumption-labor decision, ii ) Euler equation, iii ) Non- arbitrage condition. 1

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University of Minnesota Macroeconomic Policy 4731H, Spring 2010 (b) (5 points) From the firm’s problem, obtain expressions for w t and r t .
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