Does Cost Uncertainty in the Bertrand Model Soften Competition?

Abstract

Although naive intuition may indicate the opposite, the existing literature suggests that uncertainty about costs in the homogeneous-good Bertrand model intensifies competition: it lowers price and raises total surplus (but also makes profits go up). Those results, however, are derived under two assumptions that, if relaxed, conceivably could reverse the results. The present paper first shows that the results hold also if drastic innovations are possible. Next, the paper assumes asymmetric cost distributions, a possibility that is empirically highly plausible but which has been neglected in the previous literature. Using numerical methods it is shown that, under this assumption, uncertainty lowers price and raises total surplus even more than with identical distributions. However, if the asymmetry is large enough, industry profits are lower under uncertainty; this is in contrast to the known results and reinforces the notion that uncertainty intensifies competition rather than softens it.

Keywords: asymmetric auctions, asymmetric firms, auctions with endogenous quantity, Bertrand competition, boundary value method, Hansen-Spulber model, information sharing, oligopoly, private information

JEL Classification: D43, D44, L13