Q1 Two firms produce a homogeneous good. The market demand is given by Q(p) = 20 - p, and the cost function is TC(q) = q. (Same for both firms.) The two firms compete in the style of Cournot by simultaneously choosing their quantities. Show that the Cournot equilibrium quantities are q1 = 6.33 for Firm 1 and q2 = 6.33 for Firm 2, and the implied price is P = 7.33.

Q2 Two firms produce a homogeneous good. The market demand is given by Q(p) = 20 - p, and the cost function is TC(q) = q. (Same for both firms.) Suppose the two firms compete in the style of Bertrand by simultaneously choosing their prices. The prices must be whole numbers. Verify that there are two Nash equilibria: #1: Both firms choose P = 1; #2: Both firms choose P = 2.

Q3 Compare the Cournot equilibrium price of Q1 with the equilibrium price(s) of Q2. Comment.