Question

Consider a publicly available technology of producing a good that is characterized by the variable cost function VC(Q) = 1/2(Q^2) and fixed costs FC = 2 for a firm that operates the technology. In the short run, fixed costs are unavoidable. In the long run, fixed costs are avoidable and it is free for any firm outside of the market to enter, should it want to. In the short run, the set of firms in the market is fixed. The market demand curve is given by demand function, Q^D (P) = 40 − 20P

a) In short run market equilibrium, what is the equilibrium price and quantity? What is the profit level of each producer?

b) Suppose market demand increases to Q^D(P) = 120 − 20P . Determine the new short run competitive equilibrium (state the new equilibrium price, the aggregate quantity supplied and demanded, how much each producer is producing, and the profit level of each producer).

c) In the long run, there is free entry, and so the number of firms will adjust so that in the competitive equilibrium, firm profits are zero. Subject to the new demand function, what is the long run competitive equilibrium price level? How many firms are there in the market? How much is each firm producing?

d) In the long run equilibrium, calculate aggregate surplus. In addition calculate producer surplus and consumer surplus.

e) Suppose as social planners, we dictate that relative to the long run equilibrium, all firms must each produce one additional unit of the good, which is then consumed by the consumers. What happens to aggregate surplus?

Answer 1