Knowledge that Transforms

[This paper is a study of econometric problems and methods involved in interpreting the variation between unemployed job seekers in the length of time they are out of work in the light of search theories. In particular we propose in equation (7.4) a parametric form for the duration of unemployment distribution which allows one to study the temporal variation in the chances of an unemployed man returning to work as well as to estimate a regression error variance. The study is illustrated by calculations using data from interviews with a sample of British unskilled workers.]

[An economy with production is considered where the labor time is the same for all working agents and for all types of labor. It is shown that a private goods equilibrium exists if the labor time is fixed. An equilibrium with public goods exists if the labor time is variable but the distribution of consumers over types of labor is given, where labor time appears as a public good. Optimality properties of solutions where the equilibrium conditions of both types of equilibrium are fulfilled simultaneously are analyzed.]

This paper provides a complete set of local duality results for a utility maximizing consumer (or single output cost minimizing firm). Given a continuous local expenditure function defined on a compact, convex set of positive prices we establish the existence of continuous local direct, indirect utility and distance functions. This procedure avoids troublesome continuity problems at the boundary of IR N. In addition it is shown that if two utility functions are second order approximations at some point, then their respective expenditure, distance, and indirect utility functions are also second-order approximations to each other at some point. This latter result provides additional impetus for using duality theory and substantial justification for the use of flexible functional forms which can provide second-order differential approximations to any twice continuously differentiable function at a point.

THE EXISTENCE of increasing returns to scale in production poses a number of difficult problems. In general equilibrium theory the problems are obvious. Standard results on the competitive equilibrium guarantee that when an equilibrium exists it is contained in the core of an economy. When the competitive equilibrium fails to exist, as is likely under increasing returns, the core may provide a useful equilibrium concept of its own. However, very little is known about the existence of a core except under conditions of constant returns to scale. One of the objectives of the present paper is to demonstrate the existence of the core in a general economy in which certain types of increasing returns are present. The second objective of this paper concerns partial equilibrium analysis. When it is asserted that a particular industry is an increasing returns industry it is not at all obvious what is being said, particularly when the industry produces more than one output. One aspect of increasing returns is the property of scale economies, which exist if by multiplying all inputs by a factor A > 1 it is possible to increase all outputs by at least a factor of A. A more primitive concept of increasing returns behavior is the concept of subadditivity of a cost function (or superadditivity of the production possibility set). Presumably the properties of subadditivity and economies of scale are both assumed of a given industry when it is said to have increasing returns. One particular problem involving increasing returns which has generated much recent research is the question of sustainability or supportability of natural monopoly.2 For this problem the existence of a core is of great interest, but at present, a set of necessary and sufficient conditions for a core to exist in a completely general model is not known. This paper is an attempt to advance the theory of natural monopoly, and of increasing returns industries in general, by considering a more general model of equilibrium than has previously been used. Thus, the paper is both a very general model of an essentially partial equilibrium problem and a rather specialized model of general economic equilibrium. In the next section, the basic model will be developed and its interpretation for both general and partial equilibrium will be discussed in greater detail.

[This paper considers a problem faced by players who are involved in a sequence of games: not necessarily the same games, not necessarily with the same opponents, and not necessarily under conditions of complete information. The players are assumed to act in response to stationary Markovian hypotheses which they form about the actions of their opponents. Conditions are explored which require that these hypotheses be correct on average and that the players actions be optimal in response to their hypotheses.]

[In large and complicated management systems, solutions with the same indices, but with different degrees of aggregation, are used and coordinated. For example, in hierarchical systems, those in higher management levels make decisions with more aggregated indices than those in lower management levels. Managers of an individual subsystem within a large and complicated system use detailed information about their own subsystem and aggregated information (in some degree or other) about other subsystems. The principal idea of the iterative aggregation method is to consecutively recompute the aggregated indices characterizing the activities of the whole system, followed by a recomputation of the detailed indices characterizing each of its subsystems. From a theoretical point of view these methods are generalizations of some classes of iterative and decomposition methods.]

BROWN AND CHANG [2] have sought the exact conditions of aggregation within and across sectors in a general equilibrium model of production. Complete intrasector aggregation of nonlabor inputs requires all gross rental rates to change in the same proportion, while complete intersector aggregation requires all prices of products and rental rates on capital aggregates to vary in the same proportion. Then, the full aggregation is to be established when all prices change in the same proportion, provided that all nonlabor inputs depreciate at the same rate [2, Theorems 1 and 8]. The necessary and sufficient condition for it is that labor's shares in total value of product are equal in equilibrium across sectors. This condition fails when nonlabor inputs depreciate at different rates because gross rental rates no longer change in the same proportion even if all prices change in the same proportion. Brown and Chang have derived a condition for the equiproportionate changes in gross rental rates [2, Theorem 8]. Though the condition allows intraand intersector aggregation of nonlabor inputs, it no longer permits intersector output aggregation because product prices do not vary at the same rate.