1. Consider the static general equilibrium model as in class. with the following functional forms, household utility is given by: 11(c,l} = V'FV'I, Households own the capital in xed supply I? which they rent to rms, and the budget constraint is c: w{h l} + TR+ Tr. The rm production is: Yzzvy. There is no government. [a] {bl is] write down the household's problem of choosing oonsumption and leisure to maxi mize utility'. nd the optimality conditions. and derive the household's labor supply curve. {Consider the interior solution for simplicity] Suppose there would be an increase in the household's capital I? but all else was xed {i.e. this is not yet equilibrium. so suppose w and r are unchanged]. How would the household's labor supply change'.' Interpret your answer. write down the rm's prot maximization problem, nd the optimality conditions, and derive the labor demand curve. If there were an increase in productivity 3, how would the rm's labor demand change?I Now impose market clearing [in all relevant markets) and nd expressions for the equilibrium levels of K. N, c. Y. in. r. Suppose that there were an increase in capital supplied R. How would the equilib rium N, c. I". 1e. 1" change? Interpret your answer. Suppose that there were an increase in productivity 3. How would the equilibrium N, c, Y, in. 3' change'.' Interpret your