In this paper we consider the specification and estimation of the Cobb-Douglas production function model.After reviewing the "traditional" specifying assumptions for the model which are based on deterministic profit maximization, we develop a model in which profits are stochastic and in which maximization of the mathematical expectation of profits is posited."Sampling theory" and Bayesian estimation techniques for this model are presented.1. INTRODUCTION IN THIS PAPER we take up the problem of specifying and estimating a model of a profit maximizing firm operating with a Cobb-Douglas production function.Our model differs from the traditional production model considered in the literature, in that we assume that: (a) the production process is neither instantaneous nor deterministic; and (b) entrepreneurs are aware of the stochastic nature of production in their profit maximizing endeavors.This fundamental conceptual difference in our approach leads us to a new model with properties different from that of the traditional model.2Also we develop both sampling theory and Bayesian estimation procedures for the new model.The order of presentation is as follows.In Section 2 we review the traditional model, and then go on in Section 3 to formulate the new model.In Section 4, sampling theory estimation procedures are developed for the new model.In contrast with the traditional model, it is found that classical least squares provides consistent estimators of the parameters of the Cobb-Douglas production function.With a normality assumption, these are also unbiased and maximum likelihood estimators.Finally, in Section 5, a Bayesian analysis of the new model is presented.2. REVIEW OF THE TRADITIONAL MODEL According to economic theory, output, inputs, and profit of a firm are determined by the production function, the definition of profit, and the conditions of profit maximization.If the production function is of the Cobb-Douglas type with two

J. H. Dreze, D. de la Vallee Poussin; A Tâtonnement Process for Public Goods12, The Review of Economic Studies, Volume 38, Issue 2, 1 April 1971, Pages 133

In many economic situations, individuals carry out activities as coalitions, and have personal preferences for belonging to specific groups (coalitions). These situations are studied in the framework of cooperative games with coalition structures, by defining for each player a utility function with two arguments, namely his consumption bundle and the coalition to which (s)he belongs. The optimality analysis brings out a surprising property of the games with coalitions, namely that transfers among coalitions may be necessary to attain Pareto optimality. Moreover, quite restrictive assumptions are needed to rule out this property. The analysis is concerned with the conditions under which no has incentives and opportunities to change Two concepts of individual stability of a coalition structure are introduced, and their existence properties are analyzed. 1.1 Summary IN MANY ECONOMIC SITUATIONS, individuals carry out activities as Thus, individuals organize themselves in firms for production purposes and in clubs for consumption purposes; or they rely upon local communities for the provision of public goods. In such situations, individuals typically have personal preferences for belonging to specific groups (coalitions). First, they are concerned with the size of the group and personalities of its members. Second, they are concerned with qualitative and quantitative characteristics of the group activities: Working conditions in the firms, facilities available at the clubs, local public goods. Cooperative games with coalition structures provide a natural framework for a formal analysis of these situations, when the individuals partition themselves into A general way of introducing explicitly personal preferences for membership in specific coalitions is to define for each player a utility function with two arguments, namely his consumption bundle and the coalition to which he belongs. It then seems natural to speak about games with hedonic coalitions. A model of an economy, or cooperative game, with coalitions is introduced in Section 1.2. The agents organize themselves in coalitions which form a partition (i.e., each agent belongs to one and only one coalition). Each coalition, endowed with a production set, produces public and private goods. Each agent consumes the public goods produced by the coalition to which he belongs, and private goods. His preferences are represented by a utility function which is strictly increasing in private goods and continuous in private as well as public goods, but which depends upon the coalition in an arbitrary way. Our initial interest was to study the of coalitions in this model. Section 3 is devoted to that topic. However, in the course of our study, we encountered an

The paper deals with a measure theoretic model of a pure exchange economy. There are two kinds of traders: big traders, represented by atoms of the measure space, and small traders, represented by the atomless part of the measure space. The restriction of an allocation to the atomless sector is called competitive if there exists a price vector such that the consumption of every small trader is a maximal element (in terms of his preference) in the budget set defined by that price vector and by his initial endowment. We consider the set of allocations that are not blocked by any atomless coalition, or by the complement of any atomless coalition, and call it the 6~T2-core. The main results of the paper consist in defining sufficient conditions under which allocations in the Y'-core have a competitive restriction to the atomless sector, and vice versa. The economic implications and significance of the results are briefly discussed.