Duopoly Dynamics with a Barrier to Entry
This paper considers the effects of raising the cost of entry for a potential competitor on infinite-horizon Markov-perfect duopoly dynamics with ongoing demand uncertainty. All entrants serving the model industry incur sunk costs, and exit avoids future fixed costs. We focus on the unique equilibrium with last-in first-out expectations: A firm never exits leaving behind an active younger rival. We prove that raising a second producer’s sunk entry cost in an industry that supports at most two firms reduces the probability of having a duopoly but increases the probability that some firm will serve the industry. Numerical experiments indicate that a barrier to entry’s quantitative relevance depends on demand shocks’ serial correlation. If they are not very persistent, the direct entry-deterring effect of a barrier to a second firm’s entry greatly reduces the average number of active firms. The indirect entry-encouraging effect does little to offset this. With highly persistent demand shocks, the direct effect is small and the barrier to entry has no substantial effect on the number of competitors. This confirms Carlton’s (2004) assertion that the effects of a barrier depend crucially on industry dynamics that two-stage “short run/long run” models capture poorly.