Comparing Monopoly and Duopoly on a Two-Sided Market without Product Differentiation

We propose both a monopoly and a duopoly model of a two-sided market. Both settings are fully comparable, as we impose a homogeneous good produced at zero costs without capacity constraints, as well as identical parameterization of market sizes. We determine the duopoly equilibrium and the monopoly optimum in terms of the parameters and obtain solutions with and without subsidization (prices below marginal cost) of one market side. We show that there exists a continuum of economically plausible parameter sets for which duopoly equilibrium prices exceed optimal monopoly prices and one with no observable price effect of competition, i.e. one where optimum and equilibrium prices become equal. Despite the fact that virtually everything except for the number of platform operators is identical in the latter situations, total demand on both market sides in the duopoly market exceeds total demand in the monopoly market. Furthermore, even though there is no observable price effect, there is still a competitive effect in so far that total profits in the duopoly equilibrium are strictly smaller than monopoly profits. The relationship of total welfare is ambiguous in subsidization cases, while it is strictly greater in duopoly, if no subsidization takes place. Our results sharply contradict economic intuition and common economic knowledge from one-sided markets.