Complementing Cournot’s analysis of complements: unidirectional complementarity and mergers

We study the price and welfare effects of a merger of firms producing unidirectional complements: a firm is producing a product (called an optional good) that is valuable only if it is consumed with the other product (called a base good) produced by another firm. Under the assumption that there are two types of consumers: (i) those who consume one unit of the base good only or nothing (having zero valuation of the optional good), and (ii) those who consume one unit of the composite good or nothing, we show that a merger of the two firms raises the price of the base good, resulting in lower consumer surplus for the former consumer group, if and only if the average willingness to pay in the latter consumer group is sufficiently low. This result is in sharp contrast to Cournot’s (Researches into the mathematical principles of the theory of wealth, <CitationRef CitationID="CR9">1838</CitationRef>) classical implication that a merger of firms producing strict complements makes all consumers strictly better off. Copyright Springer-Verlag Wien 2014