Showing papers in "Econometrica in 1967"

The Core of an N Person Game

Abstract: THE PROBLEMS of distribution in an economic system may be analysed either by means of the behavioral assumptions of a competitive model or by the more flexible techniques of n person game theory. In the competitive model, consumers are assumed to respond to a set of prices by maximizing utility subject to a budget constraint and producers by maximizing profit. Consistent production decisions and an allocation of commodities are obtained by the determination of a set of prices at which all markets are in equilibrium. The analysis of these problems by means of n person game theory requires us to specify the production and distribution activities that are available to an arbitrary coalition of economic agents. It is frequently sufficient to summarize the detailed strategic possibilities open to a coalition by the set of possible utility vectors that can be achieved by the coalition. For example, in a pure exchange economy each coalition will have associated with it the collection of all utility vectors that can be obtained by arbitrary redistributions of the resources of that coalition. The core of an n person game is a generalization of Edgeworth's contract curve. A vector of utility levels is suggested which is feasible for all of the players acting collectively, and an arbitrary coalition is examined to see whether it can provide higher utility levels for all of its members. If this is possible, the utility vector which was originally suggested is said to be blocked by the coalition. The core of the n person game consists of those utility vectors which are feasible for the entire group of players and which can be blocked by no coalition. As we have seen during the last several years, there is an intimate connection between these two methods of analysis. If the conventional assumptions of the competitive model are made, such as convexity of preferences and convexity and constant returns to scale for the production set, then there will be a price system at which all markets are in equilibrium and a resulting assignment of commodity bundles to consumers. The utility vector associated with this competitive equilibrium may be shown to be in the core. Even further, if the number of consumers tends

Objectives, Constraints, and Outcomes in Optimal Growth Models

Abstract: This paper surveys the results of mostly recent research on optimal aggregate economic growth models, and comments on the difficulties encountered and on desirable directions of further research.

A model of business firm growth

Abstract: A new method is proposed for deriving skew distributions of business finn sizes from the assumption of Gibrat's Law. The growth of the firm is decomposed into an industry-wide component and an individual component, the latter governed by a one-period Markov process. The model is fitted to data on the recent growth of large American firms. A NUMBER of stochastic models, embodying various forms of Gibrat's law of proportionate effect, have been shown to generate skew distribution functions resembling the actual size distributions of business firms. (See [2] and references cited there.) In a previous paper [1] we presented some results of the simultation of such a model permitting serial correlations over time in the size changes of individual firms. The aim of the present paper is to carry further the analysis of autocorrelated growth, by proposing an economically meaningful scheme for its analysis, and applying the scheme to some data on large American firms. In studying business firm growth, we often encounter cases where a firm suddenly acquires an impetus for growth. Perhaps by innovating in production or marketing processes, or perhaps as an effect of new management staffs or techniques, the firm grows much more rapidly than the other firms in the industry, as measured, say, by the ratio of the current firm size to its size in the previous time period. Thus, we may observe that, while most of the firms in the industry are growing at, say, 5% a year, some firms grow 10%. Furthermore, a firm that grew 10% last year is likely to grow more rapidly than average again this year as a result of the carry-over effects of an innovation that occurred in a previous year on operations in subsequent periods. This carry-over becomes more and more likely as we shorten the length of the time period we are considering from a year to a month, week, or day. Moreover, on the average, a firm which grew rapidly in one year subsequently retains a greater share of the industry assets (or market share if sales are used as a measure of firm size) from that time on than do firms that have enjoyed only the average industry growth. Therefore, not only the growth rate over and above the average growth rate, but also the period when the extra growth took place are important factors in the individual firm's growth relative to the industry growth. In this paper, we develop a model to represent such characteristics of firms' growth, so that the process may be analysed further. In the final section we estimate the key parameter of the model for the recent growth of large American business

Effective control through coherent decentralization with preemptive goals

Abstract: : This paper shows that control through decentralization can be affected in general if additional information in the form of preemptive goals is delegated to individual units as well as prices. It is shown that the procedure is a robust one and results in small errors in profit. The technique of preemptive goals providing further control advantages in an economy where structural change is taking place over time as reflected by changing technological coefficient matrices of individual units is indicated.

Control Systems with Jumps in the State Variables

Abstract: Pontryagin's Principle can be and has been used in inventory theory, production theory, capital theory and growth theory. The idea presented in this paper shows how the principle can be used also when a firm operates in a market economy or a country in a world market. The resulting jumps in the state variables-amount of capital, amount sold of a commodity, etc.-will disappear through a reinterpretation of the system. The idea is that time is one of the variables and the speed of time can be controlled. By stopping time and letting the other variables change, one can get jumps with respect to time.

Utility Maximization and the Demand for New Zealand Meats

Abstract: The pure theory of consumer demand is a thoroughly developed topic, more so than is its use in providing extra information to improve estimates of demand parameters. In this paper some aspects of the Slutsky-Hicks-Allen theory of demand are used in conjunction with multivariate statistical analysis to provide estimates of elasticities of domestic demand for several New Zealand meats. These estimates are more efficient, in a statistical sense, and considerably superior for prediction purposes than are corresponding results obtained by more standard methods. In addition, the utility maximization theory is tested to see if it is an hypothesis capable of explaining observed demand for the meats considered.

Preference Functions on Measure Spaces of Economic Agents

Abstract: Given a set of economic agents and a set of coalitions, a non-empty family of subsets of the first set closed under the formation of countable unions and complements, an allocation is a countably additive function from the set of coalitions to the closed positive orthant of the commodity space. To describe preferences in this context, one can either introduce a positive, finite real measure defined on the set of coalitions and specify, for each agent, a relation of preference or difference on the closed positive orthant of the commodity space, or specify, for each coalition, a relation of preference or indifference on the set of allocations. This article studies the extent to which these two approaches are equivalent.

A Continuous Leontief Production Model with Quadratic Objective Function

Abstract: This article is concerned with the theory of the "bottleneck" problem experienced by a developing economy, say that of an underdeveloped country which is trying to achieve specified production goals over a fixed time period, where there is competition for restricted resources and limited external aid, including for example competition between the needs for consumer goods and capital goods. The problem is viewed as a generalized type of nonlinear programming problem. Mathematically, a basic difficulty in such a model is of course its enormous size; and it is desirable to find methods of testing approximate solutions. One such test is provided by the duality theory of nonlinear programming, which is shown to apply to this situation, so that the problem can be regarded as either of two distinct problems, which are shown to have the same optimal solution. Economically, these two problems may be described in terms of determining the optimal procedure at any given time during the period in terms of what has already happened, or alternatively in terms of what is required to happen subsequent to that time. The two problems involve respectively maximization and minimization, so that, in particular, upper and lower bounds for the value of production can be calculated for any particular production plan.

Elimination of management bias from production functions fitted to cross-section data: a model and an application to African agriculture

Abstract: This paper presents a method for eliminating management bias from production functions fitted to cross-section data on multiproduct enterprises. The method is applied to a sample of peasant farms in Rhodesia. The estimates are used to calculate marginal productivities, to examine the efficiency of allocation in the sample, to assess the relative importance of factors in leading to increases in output, and to examine the characteristics of farms with a better than average performance.

Short-run adjustments of an individual bank

Abstract: Most dynamic theories of the monetary policy mechanism, and reserve position doctrine in particular, specify a homogeneous banking system response to monetary policy actions. This article argues that the micro models of bank behavior implicit in these monetary theories remain untested and perhaps misspecified. An experimental model of a single bank's weekly balance sheet adjustments is specified and estimated with the purpose of improving the micro foundations of the theory of monetary dynamics.