Question 1:  Dominant Firm

There is one dominant firm that has a low cost of producing telecommunication services, because it already has a large network. It’s total costs are 0.1qD(2)  where qD  is the firm’s output. A group of smaller firms supply telecommunication services that are identical to the dominant firm’s services. These small firms are perfectly competitive but have higher costs. Their total cost is 30qF  + 0.1qF(2), where qF  is the aggregate output of the fringe firms. The demand for telecommunication services is Q = 300 − 5p where p is the market price.

1. Find the residual demand faced by the dominant firm. Draw it on a diagram together with fringe supply and marginal cost for the dominant firm.

2. What is the dominant firm’s choice of qD ?

(Hint:  the dominant firm shares the market with the competitive fringe in equilibrium.)

3. What will be the equilibrium price, and supply by the competitive fringe?  Show these on your diagram.

Question 2:  Cournot model

Two firms engage in quantity (Cournot) competition. Demand is given by P(Q) = a − Q, where a is a constant. Firm i (i = 1, 2) faces the cost function Ci (qi ) = ci qi . That is, firm 1 has marginal cost c1  and firm 2 has marginal cost c2 . Let’s do some comparative statics.

1. What is the effect of an increase in market demand (higher a) on firm output, market output, and market price?

2. Suppose each firm has identical costs (c1  = c2  = c). What is the effect of an increase in the costs (higher c) for all firms on firm output, market output, and market price?