Question

The total and marginal cost functions for a typical sub-bituminous coal producer are: T C = 75, 000 + 0.1Q 2 MC = 0.2Q where Q is measured in railroad cars per year. The industry consists of 55 identical producers. The market demand curve is: QD = 140, 000 − 425P where P is the price per carload. The market can be regarded as competitive. (a) Calculate the short run equilibrium price and quantity in the market. Calculate the quantity that each firm would produce. (b) Calculate producer surplus, consumer surplus, and total surplus at the equilibrium values. Calculate each firm’s profit (or loss). (c) Suppose that the sub-bituminous coal industry is a constant cost industry. What long-run price do you expect to observe? If demand is stable in the long run, what quantity of coal do you expect will be sold? How many coal producers do you expect int he long run?

Answer 1

(a) The individual supply would be where MC is equal to the price P, ie or or . As there are 55 identical producers, the market supply would hence be or .

The equilibrium price and quantity would be where the quantity demanded is equal to the quantity supplied, ie or or or dollars. The equilibrium quantity would be units.

As the firms are identical, each of the 55 firms would produce the same, which would be 55000/55 or 1000 units.

(b) The graph is as below.

The CS would be as or or or dollars. The PS would be as or or or dollars. The total surplus would be the sum of PS and CS, which would be as or dollars.

Each firm's profit would be as or or or dollars.