Minimization of Economic Rent in Spatial Price Equilibrium1

About ten years ago Paul Samuelson2 demonstrated how one could cast the CournotEnke spatial price equilibrium model artificially into an interesting maximum problem. In this problem, the conditions for competitive equilibrium in spatially separated markets with constant unit transportation costs were deduced from the principle that such markets behaved as if they were maximizing what Samuelson called " net social pay-off." The concept of net social pay-off was not intended to have any economic meaning or significance and Samuelson was careful to " underline the completely artificial nature of [his] procedure.' '3 In connection with some experimental studies of competitive markets4 I have been led to an interesting rent minimization formulation of the competitive market for a single commodity, which would seem to be entirely natural. Indeed, I think most economists might agree that, in the interests of strict efficiency, competitive markets might be expected and even encouraged to minimize economic rent. The objective in this paper is to show that the rent minimization principle can be employed to deduce the conditions of spatial price equilibrium. Of particular interest is the result that the rent minimization problem is the dual of a maximization problem which differs only by a constant from Samuelson's problem.