The sources of sharing externalities: Specialization vs Competition

In this paper, we undertake an in-depth inquiry into the nature of sharing externalities, and study how they affect the market outcome. We show that the key thing for understanding sharing externalities is the interplay between two forces: the specialization/complexity effect, on the one hand, and the competition effect, on the other hand. How the interaction between these two forces generates endogenous increasing returns to scale is definitely understudied in the literature because of the widely used assumption that technology in the final sector displays constant elasticity of substitution (CES) across the employed intermediates. Under CES technologies, the equilibrium markup, which may serve as a reverse measure of the toughness of competition, remains unaffected by entry, as well as by market-size shocks. As a consequence, the competition effect is washed out. The aim of our article is to fix this drawback. In order to achieve our purpose, we develop an extension of the Ethier's (1982) model to the case of a non-specified constant-returns-to-scale (CRS) technology in the final-good sector. The main result of our approach is a lucid decomposition of external increasing returns to scale into two components: (i) a competition effect, which stems from the market interactions between producers of intermediate inputs, and (ii) a specialization/complexity effect. Through this decomposition, we show that the gains from specialization are, in general, not the only factor of external increasing returns to scale. Competition in the intermediate sector also plays a fundamental role. In the CES case (which dominates in the literature), external increasing returns to scale are fully driven by the gains from specialization. At the other extreme is the translog technology, where the external increasing returns to scale are induced solely by the competition effect. In between these two limit-situations, we find that both effects (specialization/complexity and competition) do matter in shaping market outcomes. The other findings of the paper are as follows. First, we obtain a full characterization of the impact of horizontal innovation on prices, markups, and wages. Our model allows us to make a distinction between price-decreasing/increasing and markup-decreasing/increasing competition, and provides necessary and sufficient conditions for each type of competition to occur. Second, we also discriminate between wage-increasing and wage-decreasing competition, which suggests a microeconomic foundation for flexible functional forms of the relationship between. In addition, we find that the competition effect may either reinforce or weaken the impact of the specialization effect on aggregate output.