Question

Wheat is produced under perfectly competitive conditions. Individual wheat farmers have U-shaped long-run average cost curves that reach a minimum average cost of $4 per bushel when 2,000 bushels are produced. a) Suppose that the market demand curve for wheat is given by Q = 2,600,000 - 200,000P. In long-run equilibrium, what will be the equilibrium price, quantity, and number of wheat producers? b) Suppose market demand shifts outward to Q = 3,200,000 - 200,000P. If farmers cannot adjust their output in the short run, what will the market price be? What will the profits of the representative firm be? c) Given the new demand curve, find the new long-run equilibrium.

Answer 1

(a) In long run equilibrium, Price = Minimum average cost = $4

Market demand: Q = 2,600,000 - (200,000 x 4) = 2,600,000 - 800,000 = 1,800,000

Number of producers = Market quantity / Firm quantity = 1,800,000 / 2,000 = 900

(b) Since farmers cannot adjust output, Market output = 900 x 2,000 = 1,800,000.

Substituting in market demand function,

1,800,000 = 3,200,000 - 200,000P

200,000P = 1,400,000

P = $7

Profit = Farm output x (P - AC) = 2,000 x $(7 - 4) = 2,000 x $3 = $6,000

(c) In new long run equilibrium, P = minimum AC = $4

From new demand function,

Market demand = 3,200,000 - (200,000 x 4) = 3,200,000 - 800,000 = 2,400,000