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

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 &gt; 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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