Problem 6.2: An increase in capital. (20 points) Suppose that the production function is L L r; = {1th L? where Y; is output, K; is the stock of capital and L; is amount of labor rms hire. Assume that K: = 100, At = 2. (a) Firms in this economy maximize their prots, given by revenue net of labor costs: Y; ItVtLt. Derive the rm's labor demand curve. (1)) Workers in this economy maximize their utility, given by MC\" Ni) 2 log(Ct) Ni, where C; is consumption and Ni is the amount of labor workers supply. Their budget constraint is C; = W'tNt. Derive the workers1 labor supply curve. (c) Calculate the equilibrium wage rate and employment in this economy using the expressions for labor demand and supply you derived above. Also calculate the total amount of output the economy produces. (d) Suppose that capital doubles, to K: = 200. Calculate what happens to the wage rate, employment and output. Illustrate the effects of this increase in capital graphically, using a labor demand/ supply diagram