Suppose two firms both have a cost of production c(yi) = 30%, and the inverse demand function is given by p(y1 + y2) = 120 - y1 - y2 (a) First suppose Firm 1 gets to decide output y, first, and then firm 2 observes then and gets to decide output 32. What are the optimal choices of y1 and y2? (b) Now suppose the two firms choose their output at the same time. What y1 and y2 are optimal now? (c) Finally, suppose instead of competing over quantities, the two firms are competing over prices, as in Bertrand competition. They each simultaneously choose a price pā and p2 (respectively), and the market then demands y = 120 - p, where p is the lower of p1 and p2. They only purchase from the firm with the lowest price. If both firms charge the same price, half of output is sold from Firm 1 and half is sold from Firm 2. What price is chosen in equilibrium? What profits are made by each firm?
