Spatial Competition with Production Before Sales

Abstract

Firms typically invest in productive capacity before output is earmarked to particular markets. This paper studies the sequential decision choice of production and allocation to spatially separated markets. The resulting equilibrium will generally differ from equilibrium with simultaneous choice. Whether total output is higher or lower in the sequential model depends on an allocation-shifting effect: firms wish to rearrange their rivals’ allocations out of the most profitable market (desire-to-shift effect), and changes in capacity are a strategic device enabling them to do this (ability-to-shift effect). If firms have both the desire and the ability, there will be allocation shifting. We examine allocation shifting for a duopoly serving two spatially separated markets. Numerical simulations for a cross-hauling model show that the allocation-shifting effect can be substantial. We also consider a case with firms at either end of a linear segment over which markets are evenly distributed. It is shown that the direction of allocation shifting depends on the convexity or concavity of demand: for linear demand the two-stage equilibrium is identical to that of the simultaneous game.