Discrete Spatial Price Equilibrium

In this paper we consider how the flow of a single commodity is distributed between regional markets in a transportation network. We assume that there is an unlimited number of price-taking ’shippers’ who can enter the market and ship a single unit of commodity between some supply and demand points whenever there is a profit to be made. A common assumption made for this problem is that the shippers in the system behave rationally. In this case, a shipment of the commodity will usually take place only if the procurement costs at the supply market plus the transportation costs are less than, or equal, to the price obtained for the commodity at the demand market. If perfect competition prevails, no shipments will be made if procurement costs plus transportation costs are greater then the price obtained at the demand market. These are the equilibrium conditions defining a spatial price equilibrium model. The classical way to derive the conditions, according to Samuelson (1952) and Takayama and Judge (1971), is to formulate a mathematical program, and to obtain the equilibrium conditions as the optimal conditions of the mathematical program.