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(a) Write down the profit maximization problem of retails firms and obtain demand for good j in terms of ε, pj , P, and y.
(b) What is the marginal cost of producing one unit of output? Using the demand function obtained in part (a), solve for the profit maximizing price of the wholesale firms in terms of ε, P, and w. Econ 237- Advanced Macro
(c) Consider a symmetric equilibrium where Pi = P for the rest of the question. What is the market clearing wage rate in terms of ε?
(d) Calculate total profits for retail firms in terms of ε, P and y.
(e) Calculate total profits for wholesale firms in terms of ε, P and y.
(f) Find the optimal level of consumption and leisure the representative individual chooses in the market equilibrium in terms of ε only.
(g) Calculate the utility level the representative consumer gets under market allocation in terms of ε only.
(h) Now suppose that there is a benevolent social planner who chooses labor allocation across the wholesale producers. What is resource constraint, i.e. production possibilities frontier, he faces?
(i) To maximize representative household’s utility, what level of consumption and leisure does he choose?
(j) Calculate the utility level the representative household gets under social planner’s allocation.
k) Compared to the market equilibrium you calculated in part f, is he any better off under social planner’s allocation? Explain your answer.
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