1. Let demand for car batteries be such that Q = 10 2P. Assume constant marginal costs of 1. Compute the equilibrium price, quantity, consumer surplus, producer surplus for

(a) A perfectly competitive firm

(b) A monopoly

(c) Two firms engaged in Cournot Competition.

(d) Assume one of the two firms has a marginal cost of 2 but the other is as before. What is the oligopoly outcome in this case? [Hint you can't use the trick we used in class to get the second equation necessary to form your system of equations, so you have to consider both firms maximization problem.]

2. Assume an industry with a cost function of c(y) = 40+2y and a demand of 100y. Assume there is an entrant and an incumbent. Assume that the incumbent announces their price before the incumbent decides to enter the industry. What is the highest price (lowest quantity) that the incumbent can offer which keep the entrant outside the market? Show that is profitable for the incumbent to make that offer. Finally assume that if the incumbent is forbidden to make an announcement, there will be entry and both firms will adopt average cost pricing. Does it maximize total surplus to ban price announcements?