Problem 1: For a one-period model, suppose that the representative consumer’s preferences over consumption and leisure are described by the following utility function U(C; l) = ln(Cl)

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Problem 1: For a one-period model, suppose that the representative consumer’s preferences
over consumption and leisure are described by the following utility function
U(C; l) = ln(Cl)
The total time endowment, h, is normalized to 1. The representative rm produces output,
Y , using the following production function
zF(K;N) = zK N1􀀀
The government’s public spending program expends, G, which is nanced by a balanced
budget lump-sum tax, T, on the consumer. The consumer owns all the equity in the rm and
receives dividends equal to .
1. State the representative consumer’s optimization problem and solve it.
2. State the representative rm’s optimization problem and solve it.
3. List all the endogenous and exogenous variables in this economy. Why are they labeled as
such?
4. De ne the competitive equilibrium of this economy.
5. Compute the competitive equilibrium. That is, determine consumption, employment, out-
put, leisure, real wage, and pro ts in a competitive equilibrium, and explain your solutions.
Notes: You must hand in a PDF or Microsoft Word version of your assignment in the drop.
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