The Lagrange multiplier is not the shadow value of the limiting resource in the presence of strategically interacting agents

In the case of a single net-benefit maximizing agent facing a resource constraint, the economic interpretation of the Lagrange multiplier is that of the shadow value of the constraining resource. The formal justification for this economic interpretation is by way of the classical envelope theorem. Once an environment of strategically interacting agents is contemplated, however, the Lagrange multiplier no longer represents the shadow value of the resource to an agent. A concise proof of this claim and a revised economic interpretation of the Lagrange multiplier are given in this note.

Optimal Control of Locusts in Subsistence Farming Areas

Locust swarms hit subsistence-staple-crop-growing households at random and are not privately controllable. An aerial-spraying optimal control model that supports the said households’ liveli-hood at least expected cost is therefore developed. The qualitative properties of the model are analysed under economically plausible but mild assumptions. The steady state comparative stat-ics reveal that the locust swarm size and the probability of a household’s crop being destroyed by a swarm decrease with the number of households, yield per household, and the staple crop’s replacement price, and increase with the marginal cost of spraying and the planner’s discount rate. A local comparative dynamics analysis is also conducted, as it provides the necessary eco-nomic intuition behind other ostensibly anomalous steady state comparative statics results.Optimal control, local stability, steady state comparative statics, local comparative dynamics

A Nonlinear Generalized Additive Error Model of Production and Cost

In 1944, Marschak and Andrews published a seminal paper on how to obtain consistent estimates of a production technology. The original formulation of the econometric model regarded the joint estimation of the production function together with the first-order necessary conditions for profit-maximizing behavior. In the seventies, with the advent of econometric duality, the preference seemed to have shifted to a dual approach. Recently, however, Mundlak resurrected the primal-versus-dual debate with a provocative paper titled “Production Function Estimation: Reviving the Primal.” In that paper, the author asserts that the dual estimator, unlike the primal approach, is not efficient because it fails to utilize all the available information. In this paper we demonstrate that efficient estimates of the production technology can be obtained only by jointly estimating all the relevant primal and dual relations. Thus, the primal approach of Mundlak and the dual approach of McElroy become nested special cases of the general specification. In the process of putting to rest the primal-versus-dual debate, we solve also the nonlinear errors-in-variables problem when all the variables are measured with error.Primal, Dual, Cobb-Douglas, Nonlinear errors-in-variables, Productivity Analysis, Research Methods/ Statistical Methods, D0, C3,

A Dual Approach to Estimation With Constant Prices

In a recent paper, Mundlak assumes that the price-taking, risk-neutral and profit-maximizing entrepreneur makes his decisions on the basis of a planning model that maximizes expected profit using expected prices. In the same paper, the author asserts that when there is no sample price variation across competitive firms, it is impossible to estimate the supply and factor demand functions from cross-section data using a dual approach. In a famous paper, titled “To Dual or not to Dual,” Pope asserted a similar opinion. This paper shows that, using Mundlak’s assumption about planning decisions based upon expected profit, it is possible to use a dual estimator to estimate supply and factor demand functions. This objective is achieved by using Mundlak’s assumption about the individuality of the firm’s expectation process. A two-phase procedure is suggested to obtain consistent estimates of the expected quantities and prices which are then used, in phase II, in a nonlinear seemingly unrelated equations problem to obtain efficient estimates of the technological parameters.Constant prices, Dual approach, Cobb-Douglas, Nonlinear errors-in-variables, Demand and Price Analysis, Research Methods/ Statistical Methods, D0, C3,

SENSITIVITY OF THE GME ESTIMATES TO SUPPORT BOUNDS

The claim has been made that the Generalized Maximum Entropy (GME) estimator of Golan, Judge and Miller is not sensitive to variations in the support bounds of either the parameters or the error terms. In this paper, we scrutinized this claim by means of Monte Carlo experiments and found that the parameter estimates are impacted in a substantial way by these changes. We also analyzed the famous data sample on the US manufacturing industry used by Cobb and Douglas in 1934 and found that the GME estimator is very sensitive to changes in support bounds. We conclude with a general result by Caputo and Paris according to which any support bound variation produces unexpected responses in the parameter estimates.Research Methods/ Statistical Methods,

AN ATEMPORAL MICROECONOMIC THEORY AND AN EMPIRICAL TEST OF PRICE-INDUCED TECHNICAL PROGRESS

An exhaustive comparative statics analysis of a general price taking cost-minimizing model of the firm operating under the influence of price-induced technical progress is carried out from a dual vista. The resulting refutable implications are observable and thus amenable to empirical verification, and take on the form of a symmetric and negative semidefinite matrix. Using data from individual cotton gins in Californias San Joaquin Valley, we empirically test the complete set of implications of the price-induced technical progress theory using both classical and Bayesian statistical procedures. We find that the data are fully consistent with the atemporal, costminimizing, price-induced microeconomic theory of technical progress.Research and Development/Tech Change/Emerging Technologies,

EFFICIENT ESTIMATES OF A MODEL OF PRODUCTION AND COST

In 1944, Marschak and Andrews published a seminal paper on how to obtain consistent estimates of a production technology. The original formulation of the econometric model regarded the joint estimation of the production function together with the first-order necessary conditions for profit-maximizing behavior. In the seventies, with the advent of econometric duality, the preference seemed to have shifted to a dual approach. Recently, however, Mundlak resurrected the primal-versus-dual debate with a provocative paper titled "Production Function Estimation: Reviving the Primal." In that paper, the author asserts that the dual estimator, unlike the primal approach, is not efficient because it fails to utilize all the available information. In this paper we demonstrate that efficient estimates of the production technology can be obtained only by jointly estimating all the relevant primal and dual relations. Thus, the primal approach of Mundlak and the dual approach of McElroy become nested special cases of the general specification. In the process of putting to rest the primal-versus-dual debate, we solve also the nonlinear errors-in-variables problem when all the variables are measured with error.Research Methods/ Statistical Methods,

COMPARATIVE STATICS OF MONEY-GOODS SPECIFICATIONS OF THE UTILITY FUNCTION

The introduction of real-cash balances into the neoclassical model of the consumer wrecks havoc, in general, on the empirically observable refutable comparative statics properties of the model. We provide the most general solution of this problem to date by deriving a symmetric and negative semidefinite generalized Slutsky matrix that is empirically observable and which contains all other such comparative statics results as a special case. In addition, we clarify and correct two aspects of Samuelson and Satos (1984) treatment of this problem.Research Methods/ Statistical Methods,

Efficient Estimates of a Model of Production and Cost

In 1944, Marschak and Andrews published a seminal paper on how to obtain consistent estimates of a production technology. The original formulation of the econometric model regarded the joint estimation of the production function together with the first-order necessary conditions for profit-maximizing behavior. In the seventies, with the advent of duality theory, the preference seemed to have shifted to a dual approach. Recently, however, Mundlak resurrected the primal-versus-dual debate with a provocative paper titled “Production Function Estimation: Reviving the Primal.” In that paper, the author asserts that the dual estimator, unlike the primal approach, is not efficient because it fails to utilize all the available information. In this paper we argue that efficient estimates of the production technology can be obtained only by jointly estimating all the relevant primal and dual relations. Thus, the primal approach of Mundlak and the dual approach of McElroy become nested special cases of our general specification. The theory of the price-taking cost-minimizing, risk-neutral firm is based upon the expectation of prices and quantities as the relevant information used by the entrepreneur in making her decisions. The econometrician intervenes later on and collects information about those quantities and prices. In so doing, measurement errors creep into the econometric specification. A two-phase procedure is suggested to implement the primal-dual approach. A Monte Carlo analysis indicates that our primal-dual approach produces estimates that exhibit a smaller variance of the estimates than those obtained from either the traditional primal or the dual specification separately implemented. A bootstrapping approach is used to compute the standard errors of the model’s estimates.Primal, Dual, Cobb-Douglas, Nonlinear errors-in-variables, Productivity Analysis, Research Methods/ Statistical Methods, D0, C3,