Can someone show me how to get the answers on this. I am at a total loss.

1. A perfectly competitive industry has demand curve: P = 100 - .5Q, where Q is total output produced. All firms in the industry have identical technology and face the same cost curve: C(Q) = 500 + 10Q + 0.5Q2 . There are 10 firms in the industry.

a. Derive the supply curve for a typical firm in the industry.

b. Derive the industry supply curve.

c. Find the equilibrium price and quantity.

d. How much profit is the typical firm making?

e. Is this a short run or long run equilibrium? Explain in words and illustrate using graph(s).

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Sixta KovacekLv2

1 Jan 2019

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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?