The industry demand function for a particular good is D(p) = 24 - p, where p is the price of the good (in £/unit) and D(p) is the industry-wide quantity demanded. Suppose that there are n identical firms in this perfectly competitive industry, each with cost function C(q) = 9 + q^2 , where q(p) is each firm's output and S(p) = nq(p) is the industry-wide quantity supplied.
(a) Determine the average cost, average variable cost, average fixed cost, and marginal cost of each firm.
(b) Find each firm's supply function, the industry supply function, and the equilibrium price and quantity in this industry.
(c) What is the profit earned by each firm? In the long run, how many firms will be in this industry? Explain your answer in terms of a typical firm's profit.
(d) Calculate the consumer surplus, producer surplus, and total surplus when the profit per firm is constrained to be zero.
(e) Now assume that the government restricts the number of firms in the industry to one (therefore the industry is no longer a perfectly competitive one). Determine the new equilibrium price and quantity in this industry as well as the p.