Equivalence between tying and vertical integration with Pareto‐improving foreclosure

Yong Chao and Babu Nahata

Economic Inquiry, 2026, vol. 64, issue 3, 844-867

Abstract: This paper explores the relationships among tying, partial integration (PI), and full integration (FI) when an input monopolist can require downstream buyers to purchase a competitively supplied input from it (tying) or integrate forward in the downstream market. Both tying and integration foreclose the independent supply of the other input, yet we show that tying and PI are always equivalent in equilibrium, even under general production technologies—extending Blair and Kaserman, who focus on FI and linearly homogeneous production. In contrast, tying and FI are not always equivalent; we derive necessary and sufficient conditions for their equivalence and show that, when nonequivalent, tying can generate higher total welfare than FI. We also identify conditions under which either practice can be Pareto improving relative to the non‐tying/non‐integration benchmark. These findings contribute to the economic foundation for evaluating tying and integration in antitrust policy.

Date: 2026
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