Suppose a perfectly competitive industry whose demand and supply are characterized by the following demand and supply functions: Qd = 180 − 2P and Qs = 10P. Furthermore, assume that the total cost function for a representative firm in this industry is given by the following total cost function: T C(q) = 81 + q 2 .
(a) At the equilibrium, how many total units will be produced by this industry?
(b) How many units will the representative firm produce? Taking this quantity as the average per firm, how many firms will populate the industry?
(c) Given the profit-maximizing solution in part (b), in the short run is the representative firm earning a profit, incurring a loss, or breaking even? Given this profit situation, over the long run, what would you expect to happen in this industry?
(d) Suppose now that the industry supply curve shifts as a result of the change you predict in part (c), such that the new industry supply curve is: Q0 s = 8P Calculate the new market price (industry demand does not change), the average firm output, the number of firms in the industry, n (where n = Q/a ), and the profit outcome for the representative firm.
The entire market is capture by a single firm which can produce at a constant average and marginal cost of AC = MC = 10. The firm faces a market demand curve given by Q = 60 − P.
(a) Calculate the profit-maximizing price and quantity combination for the firm. What is the firm’s profit?
(b) Suppose that the market demand curve shifts outward and becomes steeper. Market demand is now described as Q = 45−0.5P.
(c) What is the firm’s profit-maximizing price and quantity combination now? What is the firm’s profit?
(d) Instead of the demand function assumed in part b, assume instead that the market demand shift outward and becomes flatter.