Suppose a duopoly (two firms) faces the market demand curve is P = 40 -0.5Q.

Also assume that total costs for firm i are given by c(qi) = 10qi.

(a) Find the Cournot model equilibrium price, output levels and profits for this market. (2)

(b) Find the Bertrand model equilibrium price, output levels and profits for this market. (2)

(c) What happens to your answers to parts 6a and 6b if firm 1 develops a new production technology with total costs given by c(qi) = 5qi.

Firm 2's total costs do not change. (2)

(d) Now suppose entry occurs and has a xed

cost of $50. What is the long-run equilibrium number of firms in the Cournot situation where all firms have a total cost given by

c(qi) = 10qi + 50 and marginal cost constant at $10 for a unit of output. (2)