. Suppose demand for a commodity is given by y = 100 p . There are only two possible factories that can produce this commodity, each with cost function: c_j = 50+ 2y_j , where j = 1, 2 denotes the factory. The total market output is the sum of the outputs from these two plants.

(a) Suppose the two firms form a cartel. Compute the profit maximizing total output, price, profits of the cartel in this situation

(b) Instead of a cartel, suppose the two plants are owned by Cournot duopolists. Find the CournotNash equilibrium output by each firm, the price, and the total profit.

(c) Instead of the Cournot assumption, suppose that firm 1 sets its output before firm 2 does. Firm 2 does observes the output choice of firm 1 before it makes its own output choice. Find the Stackelberg equilibrium output produced by each firm, the price, and total profit.