Natural monopoly, entry, and sunk costs

In this paper we analyze the properties of leader-follower equilibria in natural monopoly markets with sunk costs. We show that, given a well-specified market game with a profit/payoff maximizing incumbent firm and profit/payoff maximizing potential entrants, the incumbent firm will always deter entry and earn a positive profit, regardless of whether the market game is modeled as a simultaneous move game or a sequential move game. We show that this result holds under the assumption that the technology is characterized by globally increasing returns to scale as well as the weaker assumption that the technology is characterized by a sub-additive cost function. Our results are consistent with the claim of the sustainability-contestability theory that sunk costs are a major obstacle to perfect contestability and furthermore with Schmalensee's observation that an "aggressive" incumbent firm may be able to compete for the entire market and still earn a substantial excess profit. Specifically, we show that in a well specified market game between an incumbent firm and one or more potential entrant(s), the existence of sunk costs will result in entry deterrence despite a positive price-cost margin for the incumbent in equilibrium. Our analysis does provide support - by developing a game theoretic framework and equilibrium analysis - for those who have argued that public policy should be directed toward the reduction of sunk costs if competition for the market is supposed to replace competition within the market. Our analysis also provides an explanation of what the equilibrium outcome may be if the market is a so-called unsustainable natural monopoly market.