CAUDEX OCTAVUS

Abstract

In 1952–1953 Martin Beckmann proposed one of the most ingenious models that ever appeared in economics; for interregional commodity trade and pricing. In his short first article the entire problem was set in form of two short partial differential equations. For comparison, Paul Samuelson the same year dealt with the same problem for a discrete set of locations, in a way which makes an extremely clumsy impression if one has ever seen Beckmann’s model (and understood it, which has been difficult for economists unfamiliar with differential operators other than derivatives). The main idea is that there are local excess supplies and demands that have to be levelled through trade in a 2D space region, and that there is a given transport cost field reflecting local transport facilities. The solution is that local price reflects local scarcity and that trade flows in the direction of the price gradient as reflecting maximum earnings from transportation. Moreover, competition among transporters puts a pressure on profit margins so that in the flow direction price differences exactly equal transportation cost. Later, in 1977 Beckmann proposed a dynamic version of the model, for temporal price change and reorientation of trade flow. This provides the basis for the proposed discretized model in this stub. We consider two alternatives, the full model, which has a number of snags, and a simpler model involving just interregional price formation which can be distilled and separated from the complete model.