This paper provides a formal model to help understand and motivate the empirical "sticky" cost literature. The verbal arguments used to generate hypotheses in the sticky cost literature emphasize the costs of adding or removing capacity and are often concerned with how managers are likely to react to various scenarios involving more or less excess capacity. Likewise, the model in this paper focuses on the decision to expand or contract capacity, which is a constraint that either limits output or results in a discontinuous increase in marginal cost. Tests run on simulated data from this model are strikingly similar to the results of tests on real world data and suggest that the formal model captures important real world phenomenon.