Using License Fees to Make Positive Profit: Suppose you own one of many identical pharmaceudical companies producing a particular drug x.
A: Your production process has decreasing returns to scale but you incur an annually recurring fixed cost F for operating your business.
(a) Begin by illustrating your firm’s average long run cost curve and identify your output level assuming that the output price is such that you make zero long run profit.
(b) Next to your graph, illustrate the market demand and short run market supply curves that justify the zero-profit price as an equilibrium price.
(c) Next, suppose that the government introduces an annually recurring license fee G for any firm that produces this drug. Assume that your firm remains in the industry. What changes in your firm and in the market in both the short and long run as a result of the introduction of G and assuming that long run profits will again be zero in the new long run equilibrium?
(d) Now suppose that G is such that the number of firms required to sustain the zero-profit price in the new long run equilibrium is not an integer. In particular, suppose that we would re- quire 6.5 firms to sustain this price as an equilibrium in the market. Given that fractions of firms cannot exist, how many firms will actually exist in the long run?
(e) How does this affect the long run equilibrium price, the long run production level in your firm (assuming yours is one of the firms that remains in the market), and the long run profits for your firm?
(f) True or False: Sufficiently large fixed costs may in fact allow identical firms in a competitive industry to make positive long run profits.
(g) True or False: Sufficiently large license fees can cause a competitive industry to become more concentrated — where by “concentrated” we mean fewer firms competing for each customer.
B: Suppose that each firm in the industry uses the production function f (ℓ, k) = 10ℓ0.4k0.4 and each incurs a recurring annual fixed cost of $175,646.
(a) Determine how much each firm produces in the long run equilibrium if w = r = 20. (You can use the cost function derived for Cobb-Douglas technologies given in equation (13.45) in exercise 13.5 (and remember to add the fixed cost).)
(b) What price are consumers paying for the drugs produced in this industry?
(c) Suppose consumer demand is given by the aggregate demand function x(p) = 1, 000, 000 − 10, 000p. How many firms are in this industry?
(d) Suppose the government introduces a requirement that each company has to purchase an annual operating license costing $824,354. How do your answers to (a), (b) and (c) change in the short and long run?
(e) Are any of the firms that remain active in the industry better or worse off in the new long run equilibrium?
(f) Suppose instead that the government’s annual fee were set at $558,258. Calculate the price at which long run profits are equal to zero.
(g) How many firms would this imply will survive in the long run assuming fractions of firms can operate?
(h) Since fractions of firms cannot operate, how many firms will actually exist in the long run? Verify that this should imply an equilibrium price of approximately $48.2. (Use the supply function given for a Cobb-Douglas production process in equation (13.75) found in the footnote to exercise 13.7.)
(i) What does this imply for how much profit each of the remaining firms can actually make?