Measuring gains from trade and an application to fair allocation

In the classical model of exchange, gains from trade can be obtained if there exists a feasible allocation which each agent prefers to her endowment. There is no single accepted way of measuring these gains in terms of welfare, for interpersonal comparisons of welfare are needed. In this paper we propose a method of measuring gains from trade in terms of quantities of goods, avoiding welfare comparisons. The measure is given by the amount of resources that can be saved, relative to the aggregate endowment, while keeping each agent’s welfare unchanged. Then, based on Shapley’s algorithm, we propose a way of distributing gains from trade fairly among the agents. Since fair distribution of gains from trade can be inefficient, we show that a recursive procedure, which is fair at each step of the recursion, yields an efficient allocation.