Question

The market for wheat consists of 100 identical farms, each with the total and marginal cost functions shown:
TC = 1,500 + 0.1q2 , MC = 0.2q,
The corresponding supply function for a firm is, qs=5P

where qs is measured in bushels per year for a firm. The market demand curve for wheat is QD = 24,000 – 100P, where Q is measured in bushels and P is the price

per bushel.

a. Determine the short-run equilibrium price and quantity that would exist in the market.
b. Calculate the profit maximizing quantity for the individual farm. Calculate the farm'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

(a)

The corresponding supply function of a firm is as follows -

q_s = 5P

There are 100 identical farms.

So,

Market supply function -

Q = 5P * 100 = 500P

Market demand function -

Q = 24,000 - 100P

Equilibrium exists when market demand equals market supply,

24,000 - 100P = 500P

600P = 24,000

P = 40

Q = 24,000 - 100P = 24,000 - (100*40) = 24,000 - 4,000 = 20,000

So,

The short-run market equilibrium price is $40 per bushel.

The short-run market equilibrium quantity is 20,000 bushels.

(b)

This market is perfectly competitive market.

In a perfectly competitive market, a firm maximizes profit when it produce that level of output corresponding to which price equals marginal cost.

Equating price and marginal cost to ascertain profit-maximizing output,

P = MC

40 = 0.2q

q = 40/0.2 = 200

The profit-maximizing quantity for individual farm is 200 bushels.

Calculate the short-run profit -

Short-run profit = Total revenue - Total cost = (P * q) - (1,500 + 0.1q²) = (40*200) - (1,500 + 0.1(200)²) = $2,500

The farm's short-run profit at that quantity is $2,500.

(c)

An individual farm is earning economic profit in the short-run. This existence of economic profitin the short-run will attract new farms to enter into the market for wheat.

This will lead to increase in supply and will also lead to decrease in market price in long-run.