1 A firm produces output y with a production function y = LK, where L is the amount of labor and K is the amount of capital input. The firm buys the inputs from the competitive markets in which the price of labor is w = 1 and the price of capital is r = 1. The firm sells its output at price p in a competitive market whose demand is given by p(Y) = 20-Y, where Y is the market quantity. A. What kind of technology does the firm have in terms of returns to scale? Why? Suppose that the capital input is fixed at K = 16. Derive the conditional factor demand for labor and the cost function. Does the firm have the economies of scale? Why or why not? Suppose that both inputs are variable. Derive the conditional factor demands for labor and capital, and the cost function. Does the firm have the economies of scale? Why or why not? B. Suppose that the capital input is fixed at K = 16. Derive the supply curve (inverse supply function) and explain why it has such a shape. Suppose that there are 100 firms (who have the same technology of y= LEK) in the market. What are the (short-run) equilibrium price and output each firm sells? How much profit (or loss) does each firm have? Explain your answers (about the short-run equilibrium) using graphs. What will happen in the market price in the long-run?