Consider a competitive industry in which each firm has the same production technology given by the production function q = K1/3L2/3, where K and L are two inputs and q is the amount of output. The unit price of K is $0.50 and the unit price of L is $1. Firms have no fixed costs. Suppose there are exactly 100 firms in the industry; they can leave if they are unprofitable; but no one else can enter even in the long run. (a) The firm’s production function exhibits increasing, decreasing, or constant returns to scale? (So, the following questions are concerned about market behavior associated with production functions of this type of returns to scale.) (b) If demand for the output is given by D(p) = 400 − 100p, what is the long-run equilibrium? Describe the long-run equilibrium by giving: the equilibrium price, quantity, number of firms, output per firm, amount of factors used by each firm, profit per firm. (c) Demand shifts to D(p) = 750 − 150p. What is the new short-run equilibrium where the firms can vary their usage of L but not their usage of K? Describe the short-run equilibrium by giving: the equilibrium price, quantity, number of firms, output per firm, amount of factors used by each firm, profit per firm.