The representation problem and the efficiency of the price mechanism

It is shown in this paper that the way in which an allocation is represented (net trades, final allocation, etc.) can affect the design of any realizing mechanism or incentive compatible system. The reason is that a poor choice of representation may be imposing superfluous conditions and demands upon the realizing mechanism. So, in this paper a technique is developed to (1) find the optimal representation of an allocation, and (2) to characterize the associated, realizing mechanisms. Although this approach is designed to be applied to any smooth economic model, it is illustrated and motivated here by applying it to the price mechanism. More specifically, there are assertions in the literature by Mount and Reiter and by Hurwicz that the price mechanism is informationally efficient over the class of Pareto seeking mechanisms. These proofs are incomplete because they consider only one choice of representation for the Pareto allocations. We use this technique to (a) reassert the dimensional efficiency of the price mechanism, (b) compare mechanisms for spaces of economics with and without externalities, (c) characterize for the space of quadratic functions the other dimensionally efficient allocation concepts, and (d) characterize those two agent economics where the price mechanism is dimensionally efficient.