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These are real resource costs incurred only for the fulfillment of sequential budget constraints and technically unnecessary to implement the allocation. These costs, and any reallocation of consumption plans undertaken to avoid them, represent an efficiency loss. Introduction of fiat m o n e y assumed to be transaction costless- results in an allocation that is closer to Pareto efficient. Households may transfer purchasing power over time by accumulating and depleting their money balances and by the use of money futures contracts (loans).

A rule that actually makes full use of (C) would require traders to make trades based on the excess demands of other traders with whom they may have no remaining opportunity to trade in the balance of the round. Two weaker concepts of full execution are useful. In particular, we wish to consider a trading process that requires more than one round of meetings between pairs of traders to arrange for contracting and payment of obligations. Another approaches full execution as a limit after a multiplicity of repeated trading opportunities.

The correspondences "y~(p) are again homogeneous to degree zero in p(t). Let S ' denote t the unit simplex of dimensionality (n + 1)(K - t + 1). Let S~ denote the unit simplex of dimensionality n + 1 with the restriction that p ( T ) ~ S~ implies poK(K) = a, where 0 < ~ < 1. Define P~ = {(p(1), p ( 2 ) , . . , p(K)) I p(t) ~ S', p(K) E SK} . By the same reasoning as before, yh0 is convex, compact and upper semicontinuous. Use of P~ as the price space amounts to assuming that the terminal price of money is exogenously set at a > 0.