Our analysis incorporates transaction costs in economic analysis. Indeed, we consider the case where resources h ^e are used in the exchange process. They include transportation activities, information acquisition, etc. Transaction costs are given by the term in equation (5) or (7c). Since transaction costs are subtracted from aggregate net benefit in (5), they contribute to reducing the aggregate distributable surplus V( U) and to an inward shift in the Pareto utility frontier. Alternatively, reducing transaction costs (e.g., due to improvements in infrastructure and information technology) would improve efficiency, contributing to an increase in distributable surplus V( U) and an outward shift in the Pareto utility frontier. In general, lower transaction costs stimulate exchange, thus generating increased gains from trade. These gains can be measured by the associated increase in aggregate distributable surplus. This suggests that private management and/or public policy that reduce transaction costs can contribute to significant efficiency gains.

To obtain additional insights in the role of transaction costs, define the transaction cost function . Assume that the function C( , t ^e) is differentiable in t ^e. Then, consider the optimization in (7c) with respect to t _ijk( e _s) ? 0, the quantity of the k-th commodity exchanged between individuals i and j under state s. It implies the familiar Kuhn Tucker conditions:

(9a)

and

(9b)

In the context of a market equilibrium, equation (9a) implies that...