Knowledge that Transforms

This paper first takes a rather pessimistic look at what has been accomplished in recent years in understanding the price mechanism. It then takes up two points in some detail. First, it is shown that stationary expectations do not ensure the convergence of all equilibrium paths on to a steady state in a neoclassical model with heterogeneous capital goods (an appendix works an example). Secondly, a tatonnement process is outlined and discussed for an economy with constant returns to scale. I AM CONCERNED on this occasion with the performance of the invisible in a number of abstract economies which have been discussed in recent years. My findings are rather pessimistic in the sense that I see no support for the view that any of the traditional methods of response of various agents to changes in their economic environment makes the hand perform as it is often taken to perform. One cannot exclude the possibility that the world behaves a good deal better than the models-but it is the models that lead people to view the economic system as they do. It certainly is hard to find a justification for the great preoccupation of both research and teaching with equilibrium economics unless one is also prepared to believe in, at least, a Marshallian tendency to equilibrium. Of course one of the reasons why so much of our effort is devoted to the study of equilibria is that they are singularly well suited to study. We all know the endless variety of adjustment models, not uncongenial to commonsense, one is capable of constrUcting. No unifying principle, such as maximization, seems available; no elegant separation theorems reduce the mass of ugly differential or difference equations to the splendid order of a chapter in Debreu. To discuss and analyze how the economy works it may be necessary to go and look. The achievements of economic theory in the last two decades are both impressive and in many ways beautiful. But it cannot be denied that there is something scandalous in the spectacle of so many people refining the analyses of economic states which they give no reason to suppose will ever, or have ever, come about. It probably is also dangerous. Equilibrium economics, because of its well known welfare economics implication, is easily convertible into an apologia for existing

[Production correspondences are defined and their properties explored. Properties of the distance function of a production structure are studied and are related to properties of the correspondence. Homotheticity is generalized to allow discontinuities in returns to scale and to take cognizance of several outputs. The factorization of the distance function into the product of two functions, one depending only on output and the other only on input, is demonstrated. The cost function is then shown to give rise to a production structure. A Shephard-type duality theorem is proven which implies, among other things, that the cost function and the distance function are dually related; that is, given one, a minimization proglem yields the other. The duality theorem is then used to deduce necessary and sufficient conditions, in terms of the cost function, for a production correspondence to be homothetic. A few simple applications of the duality theorem are given which relate properties of the cost function to geometric properties of the correspondence.]

[The relationship between efficiency and competitiveness of production programs is explored in a general disaggregated model.]

[Hitherto, studies of the impact of government taxation and expenditure on the distribution of national income or product among income classes have used arbitrary rules of thumb for the distribution of the benefits from pure public goods or bads. This article demonstrates the logically correct method for distribution of these public good benefits. Application of this method requires information on consumer preferences for public goods; since this information is unavailable, we illustrate the application of the method to the 1961 United States income distribution by showing how various distributions would result from various consumer preference structures.]

Abstract : Sufficient conditions are given for the existence of continuous numerical representations (utilities) for partially ordered topological spaces. (Author)