Efficient Sequences of Non-Monetary Exchange

Abstract

Consider a pure exchange economy of m traders and n goods. Suppose that only certain groups of traders are allowed to meet, and suppose that the set of all m traders is not one of these groups. Suppose further that whenever one of these permitted groups of traders does meet an allocation ensues which makes no member of the group worse off than he was before this trade and which is Pareto efficient for that group, i.e. no member of the group can be made better off without making some member of the group worse off. For convenience we refer to allocations which satisfy both these criteria as groupwise Pareto efficient (GPE) allocations. We present here a number of theorems which show conditions under which sequences of such GPE allocations bring the economy (close) to overall Pareto efficiency, i.e. to an allocation which cannot be improved upon by any group of traders. We prove these theorems in three stages. (a) Section 4. Here we pose the question: If an allocation is GPE for the permitted trading groups is it overall Pareto efficient? Under general conditions, if the permitted trading groups include all groups with (n +1) members, then overall Pareto efficiency is ensured (Theorem 1). Under less general conditions, stronger theorems are proved