2. (4 points) Consider the general equilibrium in a static (one-period) model. We will solve for it. Suppose that there is a fixed capital stock k=1 and the representative firm employs Cobb Douglas technology as follows: y=An where (0,1), and A is a productivity shock. Consumer preferences over consumption c and leisure ( 1 is the total hours in the day to divide between the two activities) given by: u(c,)=lnc+ 1 where >0. There are no taxes or spending, and the consumer's unearned income equals firm profits plus capital income rk. Households own the firms and take wages as given. (a) The frontier of the production possibility set gives the maximum amount of consumption for a given amount of leisure in the economy. Find an equation that describes it. (b) Derive the optimality conditions of the consumer (household) and the firm in this economy. (c) Impose the market clearing conditions 1 and solve for the equilibrium values of c,n,r,w as functions of the exogenous variables (A,K) and parameters (,). (d) Suppose that there is an increase in total factor productivity A. How do the equilibrium values in the previous part change? Interpret your answer. Use some grpahs to provide intuition. 2. (4 points) Consider the general equilibrium in a static (one-period) model. We will solve for it. Suppose that there is a fixed capital stock k=1 and the representative firm employs Cobb Douglas technology as follows: y=An where (0,1), and A is a productivity shock. Consumer preferences over consumption c and leisure ( 1 is the total hours in the day to divide between the two activities) given by: u(c,)=lnc+ 1 where >0. There are no taxes or spending, and the consumer's unearned income equals firm profits plus capital income rk. Households own the firms and take wages as given. (a) The frontier of the production possibility set gives the maximum amount of consumption for a given amount of leisure in the economy. Find an equation that describes it. (b) Derive the optimality conditions of the consumer (household) and the firm in this economy. (c) Impose the market clearing conditions 1 and solve for the equilibrium values of c,n,r,w as functions of the exogenous variables (A,K) and parameters (,). (d) Suppose that there is an increase in total factor productivity A. How do the equilibrium values in the previous part change? Interpret your answer. Use some grpahs to provide intuition