. Consider two firms, 1 and 2, each producing an identical good simultaneously. This good has market demand given by the inverse demand function = 10 2, where is price, and = 1 + 2 is market quantity. represents the amount produced by firm . Suppose production cost is zero for both firms. (30 points)

(1) Solve algebraically for these firms' reaction functions, expressing each firm's optimal output level given some level of its competitor's output.

(2) Graph these reaction functions and show the equilibrium point. Include iso-profit contours through the equilibrium point for both firms.

(3) Solve algebraically for the equilibrium: Determine the equilibrium market price, as well as each firm's equilibrium quantity and profit.

(4) Solve for the collusive outcome in which two firms split monopoly profits. Is the profit for each firm in the collusive outcome larger than in the non-collusive outcome? Do you think firms will choose the quantities in the collusive equilibrium? Why?