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Instruction: Answer all questions and provide full explanations. Imagine an economy that lasts only one period and consists of the representative...
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Question

This is a Macroeconomics question. Please answer it as precisely as possible.

Screen Shot 2020-07-08 at 11.17.55 AM.png

Screen Shot 2020-07-08 at 11.17.55 AM.png
Instruction: Answer all questions and provide full explanations. You may work in groups, but
please hand in individually. Imagine an economy that lasts only one period and consists of the representative consumer and the
representative firm. The consumer’s preference is given by U (C, I), where C is consumption and l is
leisure. The consumer is endowed with one unit of time, which can be allocated between work and
leisure. Also, the consumer owns K units of capital, which can be rented to the firm. Finally, the
consumer is the owner of the firm. The firm has a technology for producing consumption goods according to Y: 2F (K, N), where Yis
output, K is the capital input, N is the labor input, and z is a parameter representing total factor
productivity (TFP). There are no frictions. That is, all the markets are perfectly competitive. Denote real wages
by w, the rental price by 7‘. Also, suppose that U (C, l) and F(K , N ) satisfy all the assumptions
that we have learned in class. 1. The Consumer’s Problem a) Set up the consumer’s budget constraint.
b) Set up the consumer’s optimization problem. 0) Find the consumer’s first order conditions and interpret the results.
2. The Firm’s Problem a) Solve the firm’s profit maximization problem.
b) Find the firm’s profit and discuss. 3. A Competitive Equilibrium a) Define a competitive equilibrium b) Now, consider U(C,l) = 0:17,? +1! and F(K,N) = KaN1_“ where “y > 0 and a 6 (0,1). Find the closed form solutions for C, N, and w. c) Suppose an increase in 2. What would happen to aggregate consumption, 0, employment
N, and real wages 10? Provide your answer that involves business cycle facts covered in
class.

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