E322 INTERMEDIATE MACROECONOMIC THEORY: ASSIGNMENT #3 Due Date: Sep 18, before c

Question

E322 INTERMEDIATE MACROECONOMIC THEORY: ASSIGNMENT #3 Due Date: Sep 18, before class 1. Closed-Economy One-Period Macroeconomic Model of Anarchy Suppose there is a country with no government, so T G 0. The utility of the representative consumer who wants to maximize it is UC,1) = InC+!nt as usual. Note that the represen- tative consumer is the only consumption(C) demander of total production because there is no government spending(G 0). The consumer provides labor Ns up to h hours to the represen- tative firm and receives hourly wage w and dividend from it. She enjoys leisure for the rest of the time h_Ns. The representative firm maximizes the profit by producing consumption products Y and sell it to the consumer and paying w for each labor it hired. The production technology of the firm is characterized as Y -zk" N where z is the total factor productivity, k is the given capital, Nd is the labor demand by firm and a is the share of capital of production ad 1-a (a) Write down the consumer's utility maximization problem and derive the optimality con- dition for the solution[Hint: Substitute the budget constraint to the objective function Then you can get the single optimality condition for one of the endogenous variables (b) Write down the firm's profit maximization problem and derive the optimality condition for the solution Hint: Substitute the technology constraint to the objective function. Then you can get the single optimality condition for one of the endogenous variables]. (c) The answer you get from (a) and (b) each represent the labor supply and demand func- tions. Find the equilibrium labor quantity N*-N°-Nd and the equilibrium wage u,- using your answer (a) and (b)[Hint: Use the budget constraint to substitute it with C (d) Write down the social planner's problem with the objective of maximizing consumer's utility subject to the two market- clearing conditions. (e) Derive the optimality condition of the social planner's problem by substituting the con- straints into the objective function (f) Does the First Welfare Theorem hold for this model economy? Justify your answer with the results you got from (a) to (e)

Explanation / Answer

supply and demand is an economic model of price determination in a market. It postulates that, holding all else equal, in a competitive market, the unit price for a particular good, or other traded item such as labor or liquid financial assets, will vary until it settles at a point where the quantity demanded (at the current price) will equal the quantity supplied (at the current price), resulting in an economic equilibrium for price and quantity transacted.

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