Subsidy policies and vertical integration in times of crisis: Can two virtues produce an evil?

Vertical integration in an environment without foreclosure, or more generally without any mechanisms that restrict competition among firms, and subsidization of firms' production are two separate mechanisms that raise consumer welfare, and both have been proposed as antidotes to certain aspects of the current economic crisis caused by COVID-19. In this paper we show that the interplay of the two can, surprisingly, be harmful for consumers. We consider a two-layer imperfectly competitive industry where each downstream firm purchases an input from its exclusive upstream supplier, in the presence of a welfare-maximizing government. We allow one (or more than one) of the downstream firms to integrate with its upstream counterpart and we identify two opposite resulting effects: on the one hand, integration alleviates the double marginalization problem and raises industry output and on the other, it alters the government's optimal subsidy policy in a way that reduces output. It turns out that the latter effect dominates the former and thus integration leads to lower market output and consumer surplus. This holds irrespective of the mode of downstream market competition (quantities or prices) or the nature of commodities (homogeneous or differentiated). It also holds when the fiscal policy of the government is subject to social costs. Our conclusions are in particular relevant to the current pandemic period which spurs heavy subsidization of firms and reformulation of firms' vertical relations.