Nonlinear Production Function Research Articles

A capital investment model for elastic demand and non-linear production capacity

A methodology is developed that determines the most desirable capital investment under the conditions of an elastic demand that is time dependent and a non-linear production function. The methodology also identifies the optimum yearly production rates and unit selling prices. The methodology is implemented by a computer program.

Computation of equilibria for nonlinear economies: Two experimental models

This paper represents an extension of a computational algorithm originally proposed for “piecewise linear” economies-those in which all production and utility functions are restricted to the form of linear activity analysis. Here we extend this procedure to allow for the possibility of nonlinear production and utility functions. The piecewise linear algorithm remains our basic computational tool, and this permits us to take advantage of linear programming methods for large, sparse matrices. Joint production (e.g., a putty-clay description of capital services from durable goods) may be analyzed directly in this way. It will be shown that the nonlinearities may be confined to specific “subproblems,” and that these may then be employed to generate new activities for a central problem. This is a column-generating scheme, and monotonocity can be guaranteed. However, we cannot guarantee convergence to a competitive equilibrium fixed-point in all cases. To date, our computational experience has been encouraging. We shall report on numerical results for two applications: an energy resource exhaustion model for the United States and an intertemporal multisector model of Korean development.

An evaluation of marginal waters as a natural resource in Israel

The scarcity of water in Israel and its possible effect on the socioeconomic development of the country have evinced considerable interest in the utilization of marginal waters. A nonlinear mathematical model was formulated, whose dual solution has shown that urban waste water and brackish water have substantial values ranging up to 65% of the cost of imported freshwater. The nonlinear production function in the mathematical model permitted the detailed analysis of the impact of the economies of scale on the primal and dual solutions. The optimal allocation of water for the Central Negev in 1992 calls for 40% of the forecast total water demand to be supplied by 26 million m3 of treated urban waste water and brackish water.

Numerical Solution of Nonlinear Planning Models

The use of numerical techniques for solving dynamic nonlinear multisectoral models for development planning is analyzed. A four sector model with nonlinear welfare, production, and investment functions is developed and solved using conjugate gradient and neighboring extremal methods. The model draws on recent developments in nonlinear theoretical growth models and linear development planning models. Sensitivity tests on the turnpike properties of the model and on changes in the elasticity of substitution parameters in the production function are discussed. The numerical techniques used have their origins in control theory applications and exploit the dynamic structure of the planning model. THIS PAPER discusses the application of numerical methods to the solution of nonlinear planning models of a type that could be used in the formulation of development programs for less developed countries. The numerical methods were originally developed by control theorists and our chief interest has been in testing their capability to solve moderately sized economic problems. In general, we have been satisfied with the results of these tests, and wish to demonstrate the usefulness of the nonlinear specification with a realistically formulated four sector model. This model is based on ideas drawn from two recent lines of thought about economic growth over time. The first is that of neoclassical theoretical models designed to analyze the characteristics of an economy in asymptotic optimal growth, viz. Samuelson and Solow [24] and Koopmans [19]. The other line is that of finite horizon linear programming planning models, viz. Bruno [4], Eckaus and Parikh [10], and Chakravarty and Lefeber [7]. We have attempted to blend the nonlinear production and welfare functions of the neoclassical models with the disaggregation and emphasis on foreign trade of the linear programs. In future applications this combination should offer growth theorists the possibility of using greater disaggregation than their present closed-form solution methods permit and at the same time give economic planners the opportunity to specify their models with nonlinear functions in both the performance index and the constraints.2

An interregional multisectoral model of economic growth with nonlinear production functions

An interregional multisectoral model of economic growth with nonlinear production functions

WAGES, EMPLOYMENT AND GROWTH

SUMMARY The paper presents a multisectoral growth model which is readily computable with non-linear production functions and is descriptive of economic conditions prevailing in over-populated countries. The purpose is to show the optimal allocation of resources over time in a labor surplus economy if the dominant social consideration is to increase the rate of employment as fast as possible. Given an institutionally stipulated minimum wage rate and certain other assumptions, the path that maximizes the rate of economic growth also approximates the path that minimizes the time needed to attein full employment as long as the rate of increase of the capital stock exceeds the rate of growth of the potential labor force. A rigorous proof of the proposition is presented with the help of the calculus of variations and the numerically computable solution of the growth model is derived from the conditions underlying the optimum at any moment of time. The model is an analogue of competitive markets under appropriate demand conditions. In addition, since it is computable, the model can be used by economic planners in countries where large scale unemploffment or under-employ-ment exists.

MARCH. 1954. Production and Administration Cost in Relation to Size of Firm. S. MELMAN. An Analysis of the Results of a Visual Test of Textile Yarn. A. G. BAKER, K. W. HILLIER and R. H. WOODWARD. Who Gets the Medicinequest; P. G. GRAY and ANN CARTWRIGHT. Too Good to be True? A. STUART. Some Uses of the Nomogram in Statistics.

MARCH. 1954. Production and Administration Cost in Relation to Size of Firm. S. MELMAN. An Analysis of the Results of a Visual Test of Textile Yarn. A. G. BAKER, K. W. HILLIER and R. H. WOODWARD. Who Gets the Medicinequest; P. G. GRAY and ANN CARTWRIGHT. Too Good to be True? A. STUART. Some Uses of the Nomogram in Statistics.