Problem 31 The sandbox industry is perfectly competitive and is composed of firms with the long-run cost function C(y) = 100 + 100y + 4y where the 100 represents a mandatory accreditation fee established by the sand- box sellers association. The demand for sandboxes is given by D(p) = 1280-2p 3 (b) (c) (d) Suppose that there are 80 firms in the industry. Derive the short-run supply curve. Find the equilibrium price and quantity (market and firm) of output. What will be the long-run number of firms (assume the cost function is the same in the long run). What will be the price and quantity in the market? Suppose the number of firms in the market is restricted to 40 through a licensing system. Only firms with the license will be allowed to operate. What will be the equilibrium price and quantity in the market? If licenses can be sold on an open market, what will be the price of a license? Do firms make a profit? Briefly explain.