scholarly journals Solution of the system of nonlinear PDEs characterizing CES property under quasi-homogeneity conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Haila Alodan ◽  
Bang-Yen Chen ◽  
Sharief Deshmukh ◽  
Gabriel-Eduard Vîlcu
Keyword(s):  
Homogeneous Function ◽  
Nonlinear Partial Differential Equations ◽  
Production Functions ◽  
Nonlinear Pdes ◽  
Classification Result ◽  
Mathematical Economics ◽  
Constant Elasticity ◽  
Constant Elasticity Of Substitution ◽  
Homogeneity Condition ◽  
Production Models

AbstractThe constant elasticity of substitution (CES for short) is a basic property widely used in some areas of economics that involves a system of second-order nonlinear partial differential equations. One of the most remarkable results in mathematical economics states that under homogeneity condition i.e. the production function is a homogeneous function of a certain degree, there are no other production models with the CES property apart from the famous Cobb–Douglas and Arrow–Chenery–Minhas–Solow production functions. In this paper we generalize this classification result to a much wider framework of production functions under quasi-homogeneity conditions, showing in particular the existence of three new classes of production models with the CES property.

Using derived demand techniques to estimate Ontario roundwood demand

1983 ◽  
Vol 13 (6) ◽  
pp. 1174-1184 ◽  
Author(s):  
J. C. Nautiyal ◽  
B. K. Singh
Keyword(s):  
Paper Industry ◽  
Forest Products ◽  
Pulp And Paper Industry ◽  
The Other ◽  
Production Functions ◽  
Elasticity Of Substitution ◽  
Lumber Industry ◽  
Constant Elasticity ◽  
Constant Elasticity Of Substitution ◽  
Derived Demand

Derived demand for roundwood created by the three major forest-products industries in Ontario from 1952 to 1980 was estimated from the production functions of the industries. The Cobb–Douglas function represents the lumber and the veneer and plywood industries, and the constant elasticity of substitution (CES) function represents the pulp and paper industry. In all three industries, the derived demand for roundwood is price inelastic. A theorem that the sum of partial price elasticities of derived demand when output of the final product is held constant is equal to zero has been proved. Demand by the lumber industry showed regular fluctuations throughout the 29-year period of study, while that by the other two industries rose steadily except for a few slumps.

CONSTANT-ELASTICITY-OF-SUBSTITUTION PRODUCTION FUNCTION

2008 ◽  
Vol 12 (5) ◽  
pp. 694-701 ◽  
Author(s):  
Hideki Nakamura ◽  
Masakatsu Nakamura
Keyword(s):  
Production Function ◽  
Capital Accumulation ◽  
Specific Form ◽  
Production Functions ◽  
Elasticity Of Substitution ◽  
Intermediate Goods ◽  
Constant Elasticity ◽  
Constant Elasticity Of Substitution ◽  
Douglas Production Function

We consider endogenous changes of inputs from labor to capital in the production of intermediate goods, i.e., a form of mechanization. We derive complementary relationships between capital accumulation and mechanization by assuming a Cobb–Douglas production function for the production of final goods from intermediate goods. A constant-elasticity-of-substitution production function in which the elasticity of substitution exceeds unity can be endogenously derived as the envelope of Cobb–Douglas production functions when the efficiency of inputs is assumed in a specific form. The difficulty of mechanization represents the elasticity of substitution.

Public Input Provision, Tax Base Mobility, and External Ownership

2021 ◽  
Vol 49 (5) ◽  
pp. 754-776
Author(s):  
Mutsumi Matsumoto
Keyword(s):  
Public Policy ◽  
Production Functions ◽  
Elasticity Of Substitution ◽  
Tax Base ◽  
Constant Elasticity ◽  
Constant Elasticity Of Substitution ◽  
Public Input ◽  
Optimal Rule ◽  
Public Inputs ◽  
The Impact

This article investigates the distortionary impacts of tax base mobility and external ownership on public input provision. Regional governments compete for mobile tax bases (e.g., business capital). The impact of regional public policy partially accrues to non-residents because immobile factors (e.g., business land) are subject to external ownership. This article derives an optimal rule for regional public input provision that illustrates how these two distortionary impacts depend on the nature of production functions. The impact of external ownership is particularly complex. To explore this impact in detail, the case of production functions with constant elasticity of substitution is examined. Public inputs with different productivity impacts yield fairly different implications of external ownership for inefficient public input provision.

scholarly journals MONETARY POLICY, FACTOR SUBSTITUTION, AND CONVERGENCE

2016 ◽  
Vol 22 (1) ◽  
pp. 63-76
Author(s):  
Rainer Klump ◽  
Anne Jurkat
Keyword(s):  
Monetary Policy ◽  
Steady State ◽  
Production Functions ◽  
Elasticity Of Substitution ◽  
Model Parameters ◽  
Speed Of Convergence ◽  
Constant Elasticity ◽  
Constant Elasticity Of Substitution ◽  
Factor Substitution ◽  
The Impact

In this paper, we examine the influence of monetary policy on the speed of convergence in a standard monetary growth model à la Sidrauski allowing for differences in the elasticity of substitution between factors of production. The respective changes in the rate of convergence and its sensitivities to the central model parameters are derived both analytically and numerically. By normalizing the constant elasticity of substitution (CES) production functions both outside the steady state and within the steady state, it is possible to distinguish between an efficiency and a distribution effect of a change in the elasticity of substitution. We show that monetary policy is the more effective, the lower is the elasticity of substitution, and that the impact of monetary policy on the speed of convergence is mainly channeled via the efficiency effect.

Inverse problems in analysis of input-output model in the class of CES functions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander A. Shananin ◽  
Anastasiya V. Rassokha
Keyword(s):  
Linear Models ◽  
Nonlinear Models ◽  
Production Functions ◽  
Elasticity Of Substitution ◽  
Input Output ◽  
Constant Elasticity ◽  
Constant Elasticity Of Substitution ◽  
Production Factors ◽  
Economic Statistics ◽  
The Cost

Abstract The article proposes a modification of the approach to the analysis of inter-industry balance. Instead of linear models of inter-industry balance, based on the hypothesis of W. Leontief about the constancy of the cost standards of production factors, the article studies nonlinear models. For the case of production functions with constant elasticity of substitution (CES) an algorithm for solving the inverse problem is proposed, which allows to identify the model of nonlinear inter-industry balance based on the data of the symmetric input-output table. Based on the Young transform and Fennel duality, with the help of this model, we develop a technology for analyzing inter-industry relationships. The technology has been tested on the data of economic statistics of Russia.

scholarly journals On Quasi-Homogeneous Production Functions

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 976 ◽  
Author(s):  
Alina-Daniela Vîlcu ◽  
Gabriel-Eduard Vîlcu
Keyword(s):  
Production Function ◽  
Production Functions ◽  
Marginal Rate ◽  
Constant Elasticity ◽  
Marginal Rate Of Substitution ◽  
Production Models ◽  
Homogeneous Production ◽  
Rate Of Substitution ◽  
Homogeneous Production Function

In this paper, we investigate the class of quasi-homogeneous production models, obtaining the classification of such models with constant elasticity with respect to an input as well as with respect to all inputs. Moreover, we prove that a quasi-homogeneous production function f satisfies the proportional marginal rate of substitution property if and only f reduces to some symmetric production functions.

scholarly journals Sectoral Technology and Structural Transformation

2015 ◽  
Vol 7 (4) ◽  
pp. 104-133 ◽  
Author(s):  
Berthold Herrendorf ◽  
Christopher Herrington ◽  
Ákos Valentinyi
Keyword(s):  
Structural Transformation ◽  
Technical Progress ◽  
Second Order ◽  
Production Functions ◽  
Elasticity Of Substitution ◽  
Constant Elasticity ◽  
Constant Elasticity Of Substitution ◽  
Production Factors

We assess how the properties of technology affect structural transformation, i.e., the reallocation of production factors across the broad sectors of agriculture, manufacturing, and services. To this end, we estimate sectoral constant elasticity of substitution (CES) and Cobb-Douglas production functions on postwar US data. We find that differences in technical progress across the three sectors are the dominant force behind structural transformation whereas other differences across sectoral technology are of second-order importance. Our findings imply that Cobb-Douglas sectoral production functions that differ only in technical progress capture the main technological forces behind the postwar US structural transformation. (JEL E16, E25, O33, O47)

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