Consider the following one-period model. Suppose that Cookie Monster's production flmction is given by Y = zx/K N d with z = 16 and K 2 %. Suppose also that 'w z I. (a) Write his prot maximization problem, [ind optimal labor demand N '1'\" and compute the maximized prot 71'. (b) Suppose that Cookie Monster's utility function is given by a(c, E) = c + LIVE + 2. Given w and 71' found in part (a), h = 16 and G = T I 2, write his utility maxi- mization problem and nd his optimal consumption bundle (3* and P. (c) Write the production possibility frontier as a function of I. (d) Would the labor market clear with the labor demand and supply found in parts (a) and (b)? Justify. If not, is w too high or too low? In which direction does the labor market push w? (e) Compute the equilibrium (Hint: You may start from labor market clearing condition then nd numerical values for m, N d, N '9, Y, :3, 7T, C)