Q3. Consider the closed-economy one-period (CEOP) macroeconomic model we learned in class. In this model, the representative household chooses consumption C and leisure l that maximizes the utility (given by the function) U(C, l), subject to its budget constraint C = w(h l) + T, where w is the real wage, 2 is the firm's profit, and T is the lump-sum tax. Remember that the household also faces time constraint h = l + Ns , where h is the total time available to the household and Ns is the household's labor supply. The representative firm uses production function Y = zF(K, Nd ) to optimally choose labor demand Nd that will maximize its profit (). The government has to satisfy its budget constraint G = T. At the competitive equilibrium, quantity demanded must equal quantity supplied in labor markets such that Ns = Nd and the output market such that Y = C + G.

1. Using the information given, derive the production possibilities frontier (PPF) as we did in class. Start with the firm's production function. Then use some of the equilibrium conditions provided above derive the PPF that expresses consumption C as a function of leisure.

2. Now draw the above PPF in a graph in the space below. Then, show competitive equilibrium by drawing household's indifference curve in the same diagram. Also draw the consumer's budget constraint correctly. You must label all the axes, points, and curves correctly .

3. Define the competitive equilibrium as you learned in the class. What are the exogenous variables, which are the endogenous ones?

4. Show the point where we have competitive equilibrium. Explain your intuition on why we have MRTl,c = MPN = MRSl,c = w at competitive equilibrium.

5. Is the competitive equilibrium Pareto Optimum? Why?