Drawing this argument in an informal way gives the below "best response functions P(P2) 0 Nash equilibrium (P1,P2)=(c,c The firms price at marginal cost the efficient outcome. It makes no difference how many firms are in the market. The basic idea is that the firms will continue to undercut one another until they reach marginal cost. They will go no lower as this would involve making a loss. This is very different to Cournot. However, the Cournot equilibrium can be recovered with capacity constraints. action- Oligopoly A Price Leadership Game Consider the following price leadership game- note the similarity with Stackelberg leadership. Note the difference between this and Varians rather odd game, where profits accrue to firm I during the game. Firm I chooses Pl Firm 2 chooses P2 Again, working from the back: Firm 2 will choose to undercut firm 1s initial price in order to gain the whole market Firm 1. unable to make positive profits, can choose any price above marginal cost. Either firm 2 will undercut and make positive profits or, if firm I chooses to price at marginal cost both firms make zero profit In particular (P1, P2)=(c e)is still an equilibrium- another difference between price and quantity competition. Again, it seems collusion could result in higher profits. But firms are unable to collude successfully. WhyProduction — Oligopoly 11 Reaction Curves and Nash Equilibrium • Drawing this argument in an informal way gives the below “best response functions”. ................................................................................................................................................................................................................................................................................ .......................................................................................... . . . . . . . . 0 p2 p1 c c p1(p2) p2(p1) • The only place where the two curves cross — the Nash equilibrium — is at (p1, p2) = (c, c). • The firms price at marginal cost — the efficient outcome. It makes no difference how many firms are in the market. • The basic idea is that the firms will continue to undercut one another until they reach marginal cost. They will go no lower as this would involve making a loss. • This is very different to Cournot. However, the Cournot equilibrium can be recovered with capacity constraints. Production — Oligopoly 12 A Price Leadership Game • Consider the following price leadership game — note the similarity with Stackelberg leadership. Note the difference between this and Varian’s rather odd game, where profits accrue to firm 1 during the game. ................................................................................................................................................................................................................................................................................................................ ................................................................................................................................................................................................................................................................................................................ ................................................................................................................................................................................................................................................................................................................ . ................................................................................................................................................................................................................................................................................................................ . . . . . . . . . . . . . . . . . . . . . • Firm 1 chooses p1 • Firm 2 chooses p2 =⇒ (π1, π2) • Again, working from the back: Firm 2 will choose to undercut firm 1’s initial price in order to gain the whole market. • Firm 1, unable to make positive profits, can choose any price above marginal cost. Either firm 2 will undercut and make positive profits or, if firm 1 chooses to price at marginal cost both firms make zero profit. • In particular (p1, p2) = (c, c) is still an equilibrium — another difference between price and quantity competition. • Again, it seems collusion could result in higher profits. But firms are unable to collude successfully. Why?