Take the following functions for a duopoly market for Firm X and Firm Y:

P = $1,300 -2Q

MR (Stackelberg) =$775-2Q_X

MR (Cournot) =$1,300-4Q_X-2Q_Y

Assuming constant marginal cost for both firms of $250 and that market output is represented by the output of Firm X and Firm Y.

a) Calculate the output-reaction curves for Firms X and Y if both firms act simultaneously (show all workings).

b) Calculate the profit maximising level of output for each firm and the equilibrium market quantity and price if both firms act simultaneously (show all workings).

c) Calculate the profit maximising level of output for Firm X assuming that it has first mover advantage in this market and correctly anticipates the output reaction curve of Firm Y (show all workings). (2 marks)

d) Based on Part c) calculate the profit maximising level of output for Firm Y (show all workings).