Tutorial 1

Exercise 1 Consider a perfectly competitive market. Market demand is Q =

860 10p. There are initially n = 20 identical …rms in the market, and each

…rm’ costs are C (q) = 200 + 2q + 0:5q 2 . s 1. Find the supply curve of an individual …rm and the aggregate supply curve of all …rms. Calculate the competitive equilibrium price. Determine the equilibrium output and pro…t of an individual …rm.

2. Derive expressions for the price elasticity of market demand, , the elasticity of residual demand facing one …rm, i , and the elasticity of supply of all but one …rm, i as functions of price. Evaluate these elasticities at the competitive equilibrium price and verify that the relationship

1) holds. i = n i (n

3. Suppose that additional identical …rms can enter the market. Find the long run equilibrium output of an individual …rm, the equilibrium price and the equilibrium number of …rms in the market.

Exercise 2 The government imposes a …xed fee per year on each (identical)

…rm that operates in a competitive market. What happens to total output, the optimal scale of a …rm, the number of …rms in the market, and price if there is free entry into the market?

How do your answers change if besides competitive (fringe) …rms, there is a dominant …rm present in the market. Also, how does the dominant …rm’ s share of the market change because of the fee?

Exercise 3 If the demand curve is Q = 200 p and the cost function of monopolist is C = 20Q + Q2 , how large is the deadweight loss from monopoly?

(Assume that the marginal cost curve of monopolist also represents the market supply function in the perfectly competitive market.) Verify that the relationship

1

p MC

=

p holds at the monopoly price and output.

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