Question

The market for wheat consists of 500 identical firms, each with the total and marginal cost functions shown:

TC = 90,000 + 0.00001Q2

MC = 0.00002Q,

where Q is measured in bushels per year. The market demand curve for wheat is Q = 90,000,000 - 20,000,000P, where Q is again measured in bushels and P is the price per bushel.

a. Determine the short-run equilibrium price and quantity of each firm.

b. Calculate the firm's short-run profit (loss) at that quantity.

c. Assume that the short-run profit or loss is representative of the current long-run prospects in this market. You may further assume that there are no barriers to entry or exit in the market. Describe the expected long-run response to the conditions described in part b. (The TC function for the firm may be regarded as an economic cost function that captures all implicit and explicit costs.)

Answer 1

The market for wheat consists of 500 identical firms, each with the total and marginal cost functions shown:

TC = 90,000 + 0.00001Q2

MC = 0.00002Q,

The market demand curve for wheat is Q = 90,000,000 - 20,000,000P.

Marginal cost function is the supply curve of firm.

P = 0.00002Q

Q = 50000P

For 500 firms, market supply is 500Q = Qs = 500*50000 = 25000000P.

a. Determine the short-run equilibrium price and quantity of each firm.

Market supply and demand is equated at

25,000,000P = 90,000,000 - 20,000,000P

45,000,000P = 90,000,000

P = $2

Q = 50,000,000 units.

For each firm, quantity is 50000*2 = 100,000 units.

b. Calculate the firm's short-run profit (loss) at that quantity.

Profit = TR – TC = (2*50,000,000) – (90,000 + 0.00001*(100,000^2)) = 99,810,000

c. Because there are profits, firms might enter the long run in order to get profits. This will reduce the price down to minimum of ATC. Quantity will increase as more and more firms will enter the market.