This paper illustrates the effect of market size on the decision of whether or not firms should vertically integrate or disintegrate. We use a model of two successive stages of production with Cournot competition in each stage. In this model, firms choose to specialize (either upstream or downstream) or to integrate the two stages, before making their production decisions. The decision of whether or not to integrate or specialize depends on the trade-off between "escaping from" the double marginalization problem or the gain from specializing in the production stage in which the firm is more efficient. We show (using simulations) that more firms choose to be vertically integrated as the valuation of the final product or the number of consumers increases, unless the number of firms increases proportionately.