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Solutions: Section 1

The following payoff matrix represents the long-run payoffs for two duopolists faced with the option of buying or leasing buildings to use for production. Determine whether any dominant strategies exist and whether or not there is a Nash eąuilibrium.

Firm 1

Lease    Buy

Building    Building

Lease    FI =500    FI =750

Firm    F2 = 500    F2 = 400

2

Buy    FI = 300    FI = 600

F2 = 600    F2 = 200

The dominant strategy for firm 1 is to buy the building, sińce regardless of firm 2’s strategy, firm 1 is better off buying the building. Firm 2, on the other hand, is better off buying the building only if firm 1 leases; sińce firm 1 will not lease, firm 2 should lease. Nash equilibrium occurs when firm 1 buys and firm 2 leases, sińce this is the best strategy for each player given the strategy chosen by the other player.

Section 2: Discussion: What are the fundamental differences among the Cournot, Bertrand, and Stackelberg models of oligopoly?

The models differ in their assumptions about firm behaviour.

The Cournot model assumes that firms choose ąuantities simultaneously (taking as given the other firnfs ąuantity).

The Bertrand model assumes that firms choose prices simultaneously (taking as given the other firm’s price.)

The Stackelberg model assumes that one firm (the leader) chooses its ąuantity before the other firm (the follower) chooses its ąuantity, and that the leader takes into account how the follower will respond to the leader’s ąuantity decision.

Section 3: Applications

a) Pi=36-3Q = 36-3(Qi+Q2) = (36-3Q₂)-3Qi.

MR^ = (36 - 309) - 6Qi_ = MC = 18.

l’s reaction function: Qi = 3 - (1/2) Q2-