Knowledge that Transforms

This article uses the concept of cone of interior displacements, which extends the notion of differentiability, to set up a characterization of Pareto optima in non-convex economies. A general theorem asserting that a Pareto optimum is a PA equilibrium is given and specifications are discussed. It is finally argued that the usual formulation of the doctrine of marginal cost pricingas a doctrine for achieving Pareto optimal states in a non-convex decentralized economy has unsatisfactory logical basis, and a way of defining a minimum degree of centralization inherent to non-convex economies is suggested. THE MAIN RESULTS of the economic theory of allocation of resources rest upon assumptions of convexity: convexity of production sets, and convexity of preferences. The relevance of these assumptions is often doubtful; even if in a many consumer economy the classical statements can be extended to the case of nonconvex preferences (this idea, pointed out first by Farrell [13] and Rothenberg [24], was developed in the general framework of economics with a continuum of agents as introduced by Aumann [4]; see W. Hildenbrand [18 and 19]), the indivisibilities arising in production are often large and create non-convexities that cannot be overlooked. Furthermore, non-convexities may arise with externalities (see Baumol [5], Kolm [20], and Starrett [25]), exchange of information (see Radner [23]), or stock markets (see Dreze [10]). Even if one must take the risk of producing less elegant results, a relevant economic theory cannot ignore non-convexities.

[Models of the behavior of populations of self-reproducible natural resources in an economic framework have rarely anticipated the consequences of different forms of production functions. This paper investigates sufficient conditions for extinction in a very general model as well as a model having a specific production function. In the second section additional considerations relating to extinction are deduced as well as the existence of a watershed level of population. These conclusions are exemplified using data from one particular population of red deer.]

[The model extlesstex-math extgreater$Y_\it\= extbackslashSigma _\k\( extbackslashbeta _\k\+ extbackslashdelta _\ik\+y_\tk\)x_\ikt\= extbackslashvarepsilon _\it\$ extless/tex-math extgreater with extlesstex-math extgreater$ extbackslashdelta _\ik\$ extless/tex-math extgreater and extlesstex-math extgreatery_\tk\ extless/tex-math extgreater random is considered as a means of pooling the time series of a cross-section sample. The model is placed in a mixed analysis of variance framework. Relationships between various estimation criteria are derived and their asymptotic properties compared. Some implementation problems are also discussed.]

In this paper we estimate the Hicksian equivalent variation of consumer's surplus for a sample of public housing tenants and examine the distribution of these surpluses by household characteristics. To do this we estimate the parameters of a generalized CES utility function (imposing second order constraints as needed) and of a Cobb-Douglas utility function. The Cobb-Douglas specification is rejected statistically and benefit estimates based on it follow a significantly different distributional pattern than those estimated with the generalized CES, although there is not much difference in average benefits.

[A model is developed to describe the allocation of laborers to tasks. The relation between the distributions of earnings and abilities is found to depend on the presence of comparative advantage. Various features of the distribution of earnings are explained in terms of the time taken by a given grade of labor to perform a task of a given difficulty.]