The representation problem and the efficiency of the price mechanism
In mathematical economics, it is standard to represent an allocation function in terms of net trades. This is done to avoid imposing superfluous demands upon any implementing mechanism. It is shown that even for simple trading economies, this goal cannot always be attained with net trades. A theory is developed, in terms of techniques from differential geometry, to determine the most efficient (with respect to the design of a mechanism) representation of the allocation, and to characterize the associated implementing mechanisms. This theory is applied to the standard model of the price mechanism to show that it is the most efficient Pareto seeking mechanism (in terms of the dimension of the message space) and to a simple model to demonstrate how the optimal representation of the allocation and the type of information change with the addition of an externality.
scientific article; zbMATH DE number 3939041