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

where Yt and Xt are subject to random errors of measurement ut and vt, respectively, with E(u) = E(vt) = 0, E(u2) = u, E(v2) = 2, E(utvt) = , and E(utu')E(vtsv) = 0 for t # t', is applied to a simple system of difference equations. The paper treats two such models, which differ in that one system is specified as deterministic except for measurement error, while the second model includes random in the equations as well. The investigation focuses on the possible consistency of least squares estimates of structural parameters in both cases. Mann and Wald [3] have demonstrated the consistency property of least squares estimates in stochastic difference equations which contain a shock term, and T. W. Anderson [1] has more recently shown such estimates to possess asymptotic normal distributions. One way argue, and perhaps quite legitimately, against the inclusion of measurement errors and shocks as separate entities in systems such as those under consideration. This separation, however, does provide a useful contrast with regard to the consistency property of LS estimates as compared to the case when only shocks (which subsume measurement error) are present in the specification of the system. When measurement errors are separated from shocks, LS yields consistent estimates for the explosive case of cobweb equilibrium and inconsistent estimates under convergence. The above phenomenon rests on the perhaps more interesting results for a recursive model where only measurement errors are present. This change in how the random terms enter the system, as contrasted to the Mann and Wald or Anderson formulations, causes zero correlation between observed variables and inconsistent LS estimates in the equations under convergence. Again, under explosion, LS provides consistent estimators of structural parameters.

A simplified model for interregional planning in agriculture appears to offer a method for solving linear programming problems of a given structure (each variable being represented in one constraint and in another constraint which includes all variables). This structure enables us to represent the model in a two dimensional space and to construct potentiality curves, which constitute a first selection of the variables. The resolution with the remaining variables is easy. Thus, even large programmes can be solved by graphical representations and hand computations. The method proposed is, in fact, an application of a well-known algorithm, the primal-dual method of Dantzig, Ford, and Fulkerson.

In recent years, a number of power spectra have been estimated from economic data and the majority have been found to be of a similar shape. A number of implications of this shape are discussed, particular attention being paid to the reality of business cycles, stability and control problems, and model building.

It is well known, and easy to establish, that there exist markets that do not have competitive equilibria, provided the traders do not have convex preferences--that is, that the set of commodity bundles preferred or indifferent to a given bundle is not always convex. It is proved, nevertheless, that in a market consisting of a continuum of traders, each one individually insignificant, there is always a competitive equilibrium, even when the preferences are not convex. (Author)