Aggregtae Production Functions. (30 points) 1 Consider an economy with Nt firms, each of whom produces output by hiring kit units of capital, with firm i producing y =Ak it it units of output. Assume that capital is the only factor of production, and let the rental rate of capital be Rt. As usual, normalize the price of output to 1. (a) Find the profit maximizing choice of capital for firm i. That is, find an expression for kit as a function of , A and the rental rate of capital. (b) There are Kt units of capital available in total, so the equilibrium rental rate of capital satisfies the capital-market clearing condition