Nonexclusionary input prices under quantity competition: vertical integration, foreclosure and sabotage

Abstract

A vertically integrated provider is a monopoly supplier of an input essential for its rival to produce downstream output. Market exclusion in the form of inefficient foreclosure or sabotage can arise when input prices are, respectively, ‘too high’ or ‘too low’ relative to the downstream price. The range of nonexclusionary input prices within which neither form of market exclusion arises is determined by displacement ratios. The safe harbour range of downstream-to-upstream ‘price-cost’ margin ratios is decreasing in the degree of product homogeneity and approaches a single ratio in the limit as the products become perfectly homogeneous. The bounds of nonexclusionary input prices are markedly wider under Bertrand–Nash competition than they are under Stackelberg competition.

Keywords:

• Input prices
• vertical integration
• foreclosure
• sabotage

JEL Classification:

• L51
• L96

Notes

¹ Weisman (2002) and Hausman and Tardiff (1995).

² Mandy and Sappington (2007) and Sibley and Weisman (1998).

³ Weisman (2014) examines a similar problem in a price-competition framework in which the VIP is the leader and the rival is the follower.

⁴ Appealing to Lemmas 1 and 2, it is readily shown for this example that and In the limit, which implies and

⁵ Recall that is defined as the input price at which the VIP is indifferent between selling an additional unit of downstream output and selling an additional unit of the input to its rival.