Business, competition and regulation

Suppose that a duopoly faces a market demand of Q =200 2?. The cost of production for each rm is given by C(q) = 409, where q represents the quantity of output for a rm. a) If the two rms operate according to a Cournot duopoly, what are the Nash-equilibrium quantities and prots of each rm? Explain how you derived your answer. (4 marks) b) Now, suppose that the two rms operated according to a Stackelberg duopoly, ie. one of the rms enter the industry rst (tie. the incumbent) and can produce its output level before its rival decides to enter. What is the prot-maximising output level for the incumbent rm and for its rival (1'. e. the entrant)? Explain how you derived you answer. Compare the prots and market price in this equilibrium to the situation in part (a) above. (4 marks) c) Now, suppose that the situation has changed, and the incumbent rm can commit to lowering its marginal cost to 30 by investing in a new technology that incurs a sunk cost of 500. Suppose, also, that the rival rm would incur a xed cost of 250 to enter (but its cost of production remain unchanged) so that its expected prot is reduced by 250. Using a game tree (or extensive form), analyse whether the incumbent rm will commit to the investment or not. (6 marks)