Consider there are three potential firms in a market j = {1,2,3}. All with the same cost function c(q) = cx q where c is a positive cost parameter. The aggregate inverse demand function in this market is D(Q)= 100-Q, where Q=q₁ +92 +93. Assuming firm 1 is the only one allowed to participate in this market (92 93 = 0). Answer the following. 1. Write the problem of the monopolist choosing a uniform linear price. What is the optimal price offered by the monopolist. Draw a picture identifying demand, marginal income, marginal cost and the optimal price and quantity traded. Assume the firm is owned by the government and by law has to set a price that maximizes total welfare. 2. Write the problem of finding the price that maximizes welfare. What is the welfare maximizing price? How does it compare to the monopolist price? Draw again the graph in (1) and add the welfare maximizing price and quantity. 3. Estimate the deadweight loss of having a monopolist firm (with respect to a welfare maximizing sce- nario) ¹. Assume firm 2 is going to be allowed to participate in this market. Firm 1 and 2 are going to compete in quantities. 4. If firm 1 chooses first the quantity and then (observing what firm 1 choose) firm 2 decides its quantity. What would be the equilibrium quantities sold by each firm and the equilibrium price? (Stackelberg scenario). 5. What will be the the equilibrium prices and quantities if both firms choose their quantities at the same time (Cournot scenario). 6. Draw a graph with demand, marginal cost, and the quantities and prices in (1), (2) and in the Stackelber and Cournot scenarios. Estimate the deadweight loss of this two duopoly market structures². Assume firm 3 is also going to be allowed to participate in this market (oligopoly). 7. What will be the equilibrium price and and quantities if all firms choose quantities at the same time? 8. How does total welfare compare in the monopolist, duopoly and oligopoly scenarios? 9. Intuitively, what would happen as there are more firms in this market? 10. How many firms are needed such that firms choosing quantities simultaneously achieve the maximum total welfare? Assume now that firms compete choosing prices (Bertrand). 11. What would be the equilibrium price and quantity with two firms? 12. Is maximum total welfare achieved with two firms? If not with how many? 13. Compare and comment on your results in (10) and (12).
