MARKET POWER IN TRANSPORTATION Spatial Equilibrium and Welfare under Bertrand Competition

We develop spatial competition a la Bertrand for barge shipping along a waterway. Equilibrium prices are derived for two variations. For each case, we …rst give the perfectly competitive benchmark (when all modes are priced at marginal cost) before introducing market power on the modes. The paper emphasizes strategic rivalry (and market power) in two dimensions, and, for tractability, we consider each in isolation from the other. This gives rise to two variants of the base model. First, we analyze oligopolistic rivalry between barge operators and rail operators. The analysis indicates various ine¢ ciencies stemming from market power. In particular, the advantage that each transport mode has over some shippers gives it market power and so prices are not driven to marginal cost. More subtly, transporters’ equilibrium prices will tend to be overprice cost advantages (i.e., price di¤erences will be too small in equilibrium). In the second variant, we address rivalry among barge operators shipping from neighboring river terminals. Here, basic shipping costs increase with distance from the …nal market in a natural fashion in this setting. The model introduces demand elasticity in a novel fashion into a standard spatial approach by treating as …xed the shipping costs at the extremes of the market (this corresponds to shippers trucking directly to the market if they are close enough to the …nal market, and shipping to an alternative …nal market if they are far enough away). We thus derive the equilibrium for a “chain-linked”market system to show that operators with cost advantages parlay these into market size advantages. Welfare implications from transportation improvements are drawn. We break down the surplus changes accruing to di¤erent parties in order to indicate gainers, losers, and overall bene…ts. keywords: Market power, shipping price competition, spatial equilibrium, transportation networks We would like to thank the Navigation Economic Technologies (NETS) program for support. yDepartment of Economics, University of Virginia. zDepartment of Economics, University of Oregon, and Institute for Water Resources.