Knowledge that Transforms

and to estimate their magnitude, by giving a rational basis to extrapolative expectations. Rationality implies the use of economic theory, considering the cost of information and computation. Extrapolative expectations are derived as the prediction of the equilibrium by the use of estimated excess demand functions, and it is shown that the coefficients of expectations thus derived are such that the system of multiple markets is stable when gross substitutability and tatonnement are also assumed. THE DYNAMIC stability of multiple markets was studied in [3] under the assumption of extrapolative expectations, with the result that stability depends, when gross substitutability and tatonnement are assumed, on the magnitude of the coefficients of expectations whose economic meaning is not necessarily clear. In this note, we shall give some rational basis to extrapolative expectations. The rational expectation hypothesis advanced by Muth [4] is that expectations are essentially the same as the predictions of the relevant economic theory; that the economy generally does not waste information; and that expectations depend specifically on the structure of the entire system. However, since there is cost of information and computation, expectations may also be called rational when they are formed as the prediction based on a simplified and approximated version of the economic theory, using only limited amounts of information on a part of the system. Extrapolative expectations will be derived below as the prediction of the equilibrium by the use of estimated excess demand functions, and it will be shown that the coefficients of expectations thus derived are such that the system of multiple markets is stable when gross substitutability and tatonnement are assumed.

Every now and then, one encounters an allocation problem in which the variable is a point in an infinite-dimensional space. In such problems, the existence of an optimal choice among all permissible choices is not always assured. The present discussion is devoted to an investigation of this issue for a specific (but fairly common) class of allocation problems. Conditions for the existence of an optimal choice are derived and discussed.