Spatial market equilibrium in the case of linear transportation costs

In this article, we study the spatial market equilibrium in the case of fixed demands and supply values, the requirement of equality in regard to overall supply and overall demand, and linear transportation costs. The problem is formulated as a nonlinear optimization program with dual variables reflecting supply and demand prices. It is shown that the unique equilibrium commodity assignment pattern is obtained explicitly via equilibrium prices. Moreover, it is proved that in order to obtain absolute values of equilibrium prices, it is necessary to establish a certain base market price. Therefore, once the base market price is given, then other prices are adjusted according to spatial market equilibrium.