A Remark on the Structure of Exchange in Barter and Monetary Economies

In his recent paper entitled The Structure of Exchange in Barter and Monetary Economies,' R. M. Starr examined the structure of exchange in barter and monetary economies on the assumption of the classical dichotomy to demonstrate the superiority of the latter to the former in some appropriate sense. In particular, in Corollary 2 to Theorem 3 he proved that the class of all barter exchanges that are monotonically-excess-demand-diminishing, excess-demand-fulfilling, and price-consistent at prices p, is smaller, in set-theoretic sense, than the family of the real counterpart of a monetary exchange having those properties at PM. Though this is clearly the comparison of the structure of exchange at equilibrium prices, the greater flexibility of monetary trade is not confined to trade at equilibrium prices. That is, we can further prove that the class of all barter exchanges that are monotonically-excess-demand-diminishing and price-consistent at an arbitrary price system p is smaller, again in set-theoretic sense, than the family of the real counterpart of a monetary exchange having those two properties at an arbitrary pM; that is, the following: