Natural monopoly and differential pricing

Under uniform pricing a monopolist cannot make a positive profit in equilibrium. I analyze how differential pricing can be exploited by a natural monopolist to deter entry when entry is costless. In a two-stage game with price competition before quantity competition I show that the incumbent firm can deter entry and make a positive profit in equilibrium. The incumbent sets two different prices, the low price to deter entry and the high price to generate profit. Entry is not possible because of scale effects. If dumping is allowed for all firms no positive profits are realizable, but welfare is reduced. I show that for some parameter values the incumbent is forced to engage in a stunt (i.e., set a negative low price) to keep entrants out.