Market Equilibrium with Transaction Costs

Identical products being sold at different prices in different locations is a common phenomenon. Price differences might occur due to various reasons such as shipping costs, trade restrictions and price discrimination. This is modelled in traditional market models by adding a production that transfers the goods from one location to another. However, this approach is not always satisfactory since it would have the market determine the cost of production as well, as opposed to it being exogenously specified, and it would unnecessarily blow up the number of goods in the market, which affects the computational complexity of finding an equilibrium. We give a more direct way to model such scenarios by supplementing the classical Fisher model of a market by introducing transaction costs. For every buyer i and every good j, there is a transaction cost of cij ; if the price of good j is pj , then the cost to the buyer i per unit of j is pj + cij . This allows the same good to be sold at different (effective) prices to different buyers. We study questions regarding existence, uniqueness and computability of equilibrium in such a model. Our results can be summarized as such: The convex program of [Dev09] can be generalized to prove existence and uniqueness of equilibrium. We also provide a combinatorial algorithm that computes -approximate equilibrium prices and allocations in O ( 1 (n+ logm)mn log(B/ ) )