The daily demand for travel at a small regional airport is initially QD = 1000 - p; where quantity is in passengers and price is in dollars per passenger. There are initially 10 price-taking firms serving this market and each of them has the production function: q = sqrt (lk) where q is in passengers, and labor and capital are in some appropriately specified units. The price of a unit of labor is w = 100 per day; the price of a unit of capital is v = 100 per day, and this industry has constant costs. Each firm initially has a capital stock of k0 = 80. day; and this industry has constant costs. Each firm initially has a capital stock of k0 = 80.
(a) Derive the short-run cost function, SC(q), for each firm in the market.
(b) Derive the short-run market supply function, QS.
(c) Find the short-run competitive equilibrium price, p*, and quantity, Q*. How much labor, L*, does the industry employ at the competitive equilibrium?
(d) Derive the long-run cost function, C(q), of each firm in the industry.
(e) Describe the long-run market supply curve. Does the short-run competitive equilibrium at (Q*; p*) also correspond to a long-run competitive equilibrium? Explain why or why not.
Now, imagine that a catastrophic event causes the daily demand for air travel in this market to fall unexpectedly to ~QD = 750 - p Continue to assume that each of the 10 firms has a capital of k0 = 80 in the short run.
(f) Find the new short-run competitive equilibrium price, p**, and quantity, Q**, in this market. How much labor, L**, does the industry employ in the new short-run competitive equilibrium?
(g) What is the new long-run competitive equilibrium price, p***, and quantity, Q***? Describe what must happen as the industry moves from the short-run competitive equilibrium at (Q**; p**) to the long-run competitive equilibrium at (Q***; p***). How much labor L*** does the industry employ at the new long-run equilibrium?
