1. Consider two firm which produce a homogeneous product with output levels y1 and y2,and thus an aggregate output of Y = y1 + y2. The market price associated with this output (the inverse demand function) is taken to be p(Y)= 100-0.5Y, Cost function of two firms is TC1=5y1, TC2= 0.5y2^2 (a) Find the reaction functions of two firms and plot the same graph the reaction functions of both firms. (b) Find the Cournot equilibrium output,price and profit of two firms. (c) Set up the maximization problem for firm 1 (firm 1 is a leader and firm 2 is a follower), derive the reaction function and solve for the optimal prices/output and equilibrium profits. (d) Assume the firm 1 is a follower and firm 2 is a leader, redo the problem (b). (e) Suppose the two firms are engaged in Betrand competition,solve for the equilibrium prices/output/profits of two firms. (f) Find the collusive equilibrium prices/output/profits of two firms. --

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