i. ('Bertrand Equilibrium'). Two firms i = 1,2 produce an identical product subject to marginal cost c < 1. Market demand is given by q = 1-p. The strategy of firm i is to set price p1 >= c. The payoff to firm1 is

=(p1 -c)(1-p1) if p1

=12(p1 -c)(1-p1) ifp1 =p2

= 0 if p1 > p2

and similarly for firm 2.

Prove that the unique Nash Equilibrium is p1= p2= c.

ii. Now consider the following 2-stage game. In stage 1, each firm decides to 'Enter' (in which case it pays a very small sunk cost> 0) or 'Don't Enter'. In stage 2, if one firm has entered he acts as a monopolist facing the market demand schedule p = 1 - q; if both firms enter they play the Bertrand game described in part (a). Describe the Subgame Perfect Nash Equilibrium outcome of this 2- stage game.

iii. What difference does it make in question (ii) if we assume that the 2 firms 'play Cournot' (i.e. we seek a Nash Equilibrium in quantities at the second stage).

iv. What conclusions can you draw as to the relationship between price competition and entry?