The value of switching costs

We study a dynamic model with an incumbent monopolist and entry in every subsequent period. We first show that if all consumers have the same switching cost, then the intertemporal profits of the incumbent are the same as if there was only one period. We then study the consequences of heterogeneity of switching costs. We prove that even low switching cost customers have value for the incumbent: when there are more of them its profits increase as their presence hinders entrants who find it more costly to attract high switching cost customers.