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. To model such
scenarios, we supplement the classical Fisher model of a market by introducing
{\em 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 {\em per unit} of j is p_j + \cij. This allows the same good
to be sold at different (effective) prices to different buyers.
We provide a combinatorial algorithm that computes ϵ-approximate
equilibrium prices and allocations in
O(ϵ1(n+logm)mnlog(B/ϵ)) operations -
where m is the number goods, n is the number of buyers and B is the sum
of the budgets of all the buyers