Equilibrium vertical structure with a common supplier

We consider a vertically related market, in which each downstream firm produces a differentiated product by assembling a key input produced by a common supplier and another input produced by a dedicated upstream firm. On the one hand, vertical integration has the advantage of inducing the common supplier to set a lower input price, but the disadvantage of reducing downstream firms' competitiveness in the downstream market. On the other hand, vertical separation has the advantage of increasing downstream firms' competitiveness in the downstream market but the disadvantage of inducing the common supplier to set a higher input price. Contrary to results of previous studies, we find that the existence of a common supplier can lead to vertical integration under Cournot competition, which emerges as a unique equilibrium when a common supplier adopts input discrimination. Although vertical integration is better for the individual firms, it reduces the total welfare. Even when the common supplier uses uniform input pricing, vertical integration also emerges in equilibrium.