Does Cost Uncertainty in the Bertrand Model Soften Competition?

The answer is no. Although naive intuition may suggest the opposite, uncertainty about costs in the homogeneous-good Bertrand model intensifies competition: it lowers price and raises total surplus (but also makes profits go up). For some economic environments, this is implied by Hansen’s (RAND, 1988) analysis of a procurement auction. However, several authors appear to have overlooked Hansen’s results. Moreover, his results are derived under two assumptions that, if relaxed, conceivably could reverse them. The contributions of the present paper are threefold. First, it clarifies the implications of Hansen’s results for the relationship between uncertainty and competition in the Bertrand model. Second, it shows that his results hold also if drastic innovations are possible. Finally, the paper assumes asymmetric cost distributions and shows, using numerical methods, that then uncertainty lowers price and raises total surplus even more than under symmetry. If the asymmetry is large enough, however, 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.