Consider an economy with NV; firms, each of whom produces output by hiring k;; units of capital, with firm producing yie = Ak units of output. Assume that capital is the only factor of production, and let the rental rate of capital be R;. As usual, normalize the price of output to 1. (a) (b) (c) (d) () Find the profit maximizing choice of capital for firm 7. That is, find an expression for kj; as a function of a, A and the rental rate of capital. There are K; units of capital available in total, so the equilibrium rental rate of capital satisfies the capital-market clearing condition N K; = Z kit i=1 Find the equilibrium rental rate R; as a function of K;, N; and the parameters o and A. Using the expression for R; derived above, express the profit- maximizing choice of capital k;; as a function of K; and N;. Using the expression for k;; above, derive an aggregate production function Y; = F(Ky; Ny) that relates total output N Yi = Z Yit i=1 to the number of firms N, the total capital stock N, and the other parameters o and A. Determine whether the production function is increasing or decreasing in N;. Please provide economic intuition for your findings