Long Form Answers: 70 pts (3 pts for correctly identifying pages on turn in) 1. Labor Demand Derivation and Labor Market Equilibrium - Consumption Tax (20 pts) Suppose we have the household model from question (1) in problem set 2. If you did it correctly recall that the labor supply curve was given by the following function: NG = ((1%))1/5 Where T was the sales or consumption tax rate. Suppose the economy is operated by a single firm who purchases labor from the household at the given wage rate for each unit of labor hired. They have the following production function Y, = AF(K,, N,) = A KEN? (a) (3 pts) Write out the firm's maximization problem. What is the firm trying to maximize and what does it get to choose in the short run? (b) (4 pts) Solve for the firm's labor demand function. () (5 pts) Given your labor demand you found in part (b) and the labor supply function given to you, what is the equilibrium wage rate and quantity of labor demanded as functions of TFP (A), the tax rate (T) and the capital stock (K)? (d) (4 pts) Suppose the tax rate increases, show graphically how this impacts the labor market. What happens to the equilibrium wage and the equilibrium quantity of labor? (e) (4 pts) If the amount of capital stock in the economy doubles (holding all other factors constant) by what factor does the equilibrium wage in the market change