scholarly journals Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Serena Brianzoni ◽  
Cristiana Mammana ◽  
Elisabetta Michetti
Keyword(s):  
Production Function ◽  
Growth Model ◽  
Discrete Time ◽  
Production Functions ◽  
Elasticity Of Substitution ◽  
Global Dynamics ◽  
Production Factors ◽  
Local And Global Dynamics ◽  
Complex Features

We study the dynamics shown by the discrete time neoclassical one-sector growth model with differential savings while assuming a nonconcave production function. We prove that complex features exhibited are related both to the structure of the coexixting attractors and to their basins. We also show that complexity emerges if the elasticity of substitution between production factors is low enough and shareholders save more than workers, confirming the results obtained while considering concave production functions.

Produkční funkce jako nástroj zobrazení ekonomické reality

2021 ◽  
Author(s):  
Jiří Mihola
Keyword(s):  
Production Function ◽  
Inflection Point ◽  
Production Functions ◽  
Limited Resources ◽  
Factor Productivity ◽  
Aggregate Production ◽  
China And India ◽  
Production Factors ◽  
Aggregate Production Function ◽  
The Relationship

The monograph develops the theory of production functions and their systematic typology. It looks at the relationship between inputs and outputs as a universal relationship that is used not only in economics but also in other disciplines. In addition to the static production function, special attention is paid to the dynamization of individual quantities and the issue of expressing the effect of changes in these quantities on the change in production. It is explained why in the aggregate production function expressed through aggregate factor input and aggregate factor productivity it is necessary to use a multiplicative relationship, why the multiplicative link is also suitable in terms of total input factor and why the share of weights in labor and capital should be the same. The use of the production function is demonstrated on the development of the economies of the USA, China and India and on the ten largest economies of the world in terms of absolute GDP, on cryptocurrencies and on the so-called farming role.In addition to a comprehensive overview of production functions, the monograph also enriches new ideas that arose during long-term computational and analytical activities of economic and business. Particularly innovative is the generalization of the production function to any system with variable inputs and outputs. The production function can thus be recognized in many identities. The original intention of the research was to examine the intensity of economic development, but it turned out that it is closely related to production functions. The impetus for this research comes from Prof. Ing. František Brabec, DrSc. a genius mathematician, designer, economist and manager, former general director of Škoda in Pilsen and later rector of ČVÚT.The presented typology of production functions is not limited to one area of economics, but goes beyond it. The monograph respects the definition of the static production function as the maximum amount of production that can be produced with a given number of production factors. On this function, which can be effectively displayed using polynomial functions of different orders,significant points can be systematically defined, ie the inflection point, the point of maximum efficiency, the point of maximum profit and the point of maximum production. The purpose is to optimize the number of inserted production factors. The text is preferred the point with the greatest effectiveness. If this quantity does not correspond, for example, to demand, it is possible to choose another technology, which will be reflected in a shift in the static production function. At the same time, the important points of these functions describe the trajectory, which has the nature of a dynamic production function. For a dynamic production function, the crucial question is how the change in individual factors contributes to the overall change in output. If the production function is expressed through inputs and their efficiency, dynamic parameters of extensibility and intensity can be defined, which exactly express the effect of changes in inputs and the effect of changes in efficiency on changes in outputs for all possible situations. Special attention is paid to the aggregate production function. It explains why it should be expressed as the product of the aggregate input factor (TIF) and aggregate factor productivity (TFP), or why the term TIF should be expressed as a weighted product of labor and capital, in which the value of labor and capital weights could be and identical. The monograph here surpasses the traditional additive view of the multi-factor production function by proposing a multiplicative link, which also allows the derivation of growth accounting, but with a new interpretation of weights and (1-), which do not need to be calculated for each subject and each year.The time production function is used to forecast the GDP development of the US, China and India economies until 2030 and 2050, respectively. It is also predicted an increase in the absolute GDP of Indonesia, a stable position of Russia and the loss of the elite position of Japan and Germany.The monograph also deals with the hitherto unresolved question of whether, even in economics, it is also necessary in certain circumstances to take into account a phenomenon called quantization in physics. It turns out that quantization is a common thing in economics, which is documented on specific forms of production functions that respect quantization in economics.The monograph also deals with the relationship between the efficiency of an individual given the use of a certain point on a specific static production function and common efficiency, ie all actors together. These examples assume limited resources. The sum of the outputs of all actors depends on how the actors share these limited resources. It can be expected that there will be at least one method of distribution that will bring the highest sum of outputs (products, crops) of all actors. This result, however, also depends on the shape of the production functions. This is investigated using EDM, i.e.elementary distribution models. EDM for polynomial production functions of the 2nd to 5th order are not yet published in summary. Of the new findings, they are the most interesting. When using two polynomial production functions, the EDM boundary becomes linear if the inflection point is used for both production functions. If we are above the inflection point, the EDM is properly concave. It turned out that the "bending" of the production function in the region of the inflection point can be modeled using a quantity of the order of the respective polynomial. The higher the order of the polynomial, the higher the deflection can be achieved. This proved to be a very important finding in modeling specific production functions. This effect cannot be achieved by combining other parameters.

scholarly journals Evaluation of the Imitation Potential of IT Companies Using the Cobb-Douglas Production Function

Vestnik NSUEM ◽  
2019 ◽  
pp. 130-142
Author(s):  
E. N. Akerman ◽  
A. A. Mikhalchuk ◽  
V. V. Spitsyn ◽  
N. O. Chistyakova
Keyword(s):  
Production Function ◽  
Cluster Model ◽  
Production Functions ◽  
Production Volume ◽  
High Quality ◽  
Production Factors ◽  
Factor Production ◽  
Fixed Assets ◽  
Main Factors ◽  
Douglas Production Function

The relevance of the study has been determined by the acceleration of innovation growth, which encourages companies to use imitation strategies in response to disruptive technological changes.The study used the Cobb-Douglas production function to evaluate the effectiveness of the used production factors of Russian IT companies. A high-quality 3-cluster model of IT companies was built, as well as highly significant two-factor production functions of Cobb-Douglas, which made it possible to identify the contribution of the main factors (wage and fixed assets) to the production volume (revenue) for each cluster.

Educational Production Functions

1978 ◽  
Vol 3 (3) ◽  
pp. 209-231 ◽  
Author(s):  
Solomon W. Polachek ◽  
Thomas J. Kniesner ◽  
Henrick J. Harwood
Keyword(s):  
Academic Achievement ◽  
Maximum Likelihood ◽  
Production Function ◽  
Production Functions ◽  
Elasticity Of Substitution ◽  
Likelihood Methods ◽  
Educational Backgrounds ◽  
Scholastic Performance ◽  
Maximum Likelihood Methods ◽  
Educational Production

This research examines scholastic performance within the context of an individual’s production function. A constant partial elasticity of substitution production function for academic achievement is presented and estimated with non linear maximum likelihood methods. We find that ability and time devoted to various aspects of the learning process are the most important determinants of students’ accomplishments. Our results underscore the potential for students to compensate for relatively “poor” educational backgrounds by spending more time on study and class attendance.

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.

scholarly journals A Generalized Constant Elasticity of Substitution Production Function Model and Its Application

2016 ◽  
Vol 4 (3) ◽  
pp. 269-279
Author(s):  
Maolin Cheng
Keyword(s):  
Economic Growth ◽  
Growth Factors ◽  
Production Function ◽  
High Speed ◽  
Elasticity Of Substitution ◽  
Function Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Substitution ◽  
Production Factors ◽  
Economic Growth Factors

AbstractThe constant elasticity of substitution production function describes the relationship between production results and production factors in the technological production process. The common production factors include capital and labor. In order to comprehensively reflect the input-output relationship, this paper generalizes the model and adds factors including energy, consumption, and import and export. With respect to estimating the parameters of the model, the paper proposes a high-precision and high-speed nonlinear regression method. The constant elasticity of substitution production function model is mainly used to calculate the contribution rates of economic growth factors, and this paper proposes a scientific and reliable calculating method. The final section of the paper proposes an empirical analysis of the contribution rates of Chinese economic growth factors.

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 The Two-level CES Production Function for the Manufacturing Sector of Pakistan

1989 ◽  
Vol 28 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Ashfaque H. Khan
Keyword(s):  
Production Function ◽  
Technical Progress ◽  
Manufacturing Sector ◽  
Relevant Literature ◽  
Returns To Scale ◽  
Appropriate Technology ◽  
Production Functions ◽  
Elasticity Of Substitution ◽  
Two Factors ◽  
Factors Of Production

Production functions have been widely studied in the relevant literature. In this paper, apart from labour and capital, we have used energy as a factor input and calculated the elasticity of substitution between these inputs, measured technical progress, and determined the returns to scale in the manufacturing sector of Pakistan. Since we have more than two factors of production, the standard Cobb· Douglas and CES production functions do not provide satisfactory results. Hence, two·level (nested) CES production function becomes the natural choice for the appropriate technology. Using this technology, we have found low elasticity of substitution between the three factors of production. Furthermore, the manufacturing sector is found to exhibit decreasing returns to scale, having experienced disembodied technical progress at the rate of 3.7 percent per annum.

scholarly journals Production Function and Robotization - How Can CES Technology Help?

2021 ◽  
Author(s):  
Françoise Larbre
Keyword(s):  
Production Function ◽  
Returns To Scale ◽  
Production Functions ◽  
Elasticity Of Substitution ◽  
Cost Functions ◽  
Helpful Tool ◽  
Joint Product ◽  
Short Run ◽  
The Cost

Depending on the workers qualification, the use of robots is perceived either as a helpful tool or as a competitor. We analyze the substitution of capital for labor, including the case where the product is entirely made by robots. We use CES production functions and their derived cost functions (the later being surprisingly missing in the literature). We focus on short-run and the case of an elasticity of substitution greater than 1. We highlight a level of product for which the cost is identical regardless of the factor used. As a joint product, we provide a foundation to cost functions exhibiting first increasing and then decreasing returns to scale (a so far missing justification to the usually assumed shape of cost functions).

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