We consider two firms, F1 and F2, operating on a market with inverse demand function P(Q) = 6 - Q where Q is the total quantity. Both firms produce at the same constant marginal cost c = 2. Firm F1 sets its production level first, committing not to revise it after F2 decides its own quantity. a) Compute the quantity produced by each firm, the total quantity and the market price. b) Compute the total surplus, defined as the profits plus the consumer surplus. c) If, instead of playing sequentially, F1 and F2 played simultaneously, a la Cournot, what would be the Nash equilibrium of the Cournot game? d) Assuming that F1 can commit not to play as a leader, and, instead, can commit to play simul- taneously, what is the minimum amount of money F2 would have to pay F1 to enter such an agreement? Would F2 actually make such proposal? e) Should a central planner maximizing total surplus (defined as the sum of profits and consumer surplus) forbid such agreement