Imperfect Substitutes for Perfect Complements: Solving the Anticommons Problem

Abstract:     
An integrated monopoly, where all complements forming a composite good are offered by a single firm, is typically welfare superior to a complementary monopoly. This is the tragedy of the anticommons. We consider the possibility of competition in the market for each complement. We present a model with two perfect complements and introduce n imperfect substitutes for one and then for both complements. We prove that, when one complementary good is still produced by a monopolist, competition in the other sector may be preferred if and only if the substitutes of the complementary good differ in their quality, so that as their number increases, average quality and/or quality variance increases. Then, favoring competition in some sectors, leaving monopolies in others may be detrimental for consumers and producers alike when competition does not generate an adequate level of product differentiation. Results change when competition is introduced in each sector. In this case, if goods are close substitutes, we find that competition may be welfare superior for a sufficiently high number of competing firms in each sector, even with no quality differentiation.

Number of Pages in PDF File: 28

Keywords: Price Competition, Anticommons, Complements and Substitutes, Welfare Effects, Product Differentiation

JEL Classification: D43, K21, L13, L41

working papers series