The h-Homogeneous Production Function with Constant Elasticity of Substitution: A Note

Econometrica ◽  
1966 ◽  
Vol 34 (1) ◽  
pp. 225 ◽  
Author(s):  
Jacob Paroush
Keyword(s):  
Production Function ◽  
Elasticity Of Substitution ◽  
Constant Elasticity ◽  
Constant Elasticity Of Substitution ◽  
Homogeneous Production ◽  
Homogeneous Production Function

scholarly journals Classification of $h$-homogeneous production functions with constant elasticity of substitution

2012 ◽  
Vol 43 (2) ◽  
pp. 321-328 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Production Function ◽  
Production Functions ◽  
Elasticity Of Substitution ◽  
Aggregate Level ◽  
Firm Level ◽  
Constant Elasticity ◽  
Constant Elasticity Of Substitution ◽  
Homogeneous Production ◽  
Almost All

Almost all economic theories presuppose a production function, either on the firm level or the aggregate level. In this sense the production function is one of the key concepts of mainstream neoclassical theories. There is a very important class of production functions that are often analyzed in both microeconomics and macroeonomics; namely, $h$-homogeneous production functions. This class of production functions includes two important production functions; namely, the generalized Cobb-Douglas production functions and ACMS production functions. It was proved in 2010 by L. Losonczi \cite{L} that twice differentiable two-inputs $h$-homogeneous production functions with constant elasticity of substitution (CES) property are Cobb-Douglas' and ACMS production functions. Lozonczi also pointed out in \cite{L} that his proof does not work for production functions of $n$-inputs with $n>2$

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 Intermetropolitan Comparisons Of Production Function

2011 ◽  
Vol 3 (2) ◽  
pp. 112
Author(s):  
Martin Williams ◽  
Tuan Ton-That
Keyword(s):  
Production Function ◽  
Production Technology ◽  
Returns To Scale ◽  
Elasticity Of Substitution ◽  
Constant Elasticity ◽  
Constant Elasticity Of Substitution ◽  
Different Levels ◽  
Variable Returns To Scale ◽  
Inputs And Outputs

A nonhomogeneous production is used to study the features of the production technology across U.S. cities. We compute marginal productivities and scale elasticities for different levels of inputs and outputs. The form of the production function allows variable returns to scale. We can also test the Cobb-Douglas and constant elasticity of substitution forms within the nonhomogeneous specification. Conclusions are drawn concerning returns to scale across cities of different sizes.

scholarly journals AUTOMATION, PARTIAL AND FULL

2021 ◽  
pp. 1-25
Author(s):  
Jakub Growiec
Keyword(s):  
Theoretical Analysis ◽  
Production Function ◽  
Downward Trend ◽  
Elasticity Of Substitution ◽  
Constant Elasticity ◽  
Secular Stagnation ◽  
Complex Tasks ◽  
Constant Elasticity Of Substitution ◽  
Technological Unemployment ◽  
Full Automation

When some steps of a complex, multi-step task are automated, the demand for human work in the remaining complementary sub-tasks goes up. In contrast, when the task is fully automated, the demand for human work declines. Upon aggregation to the macroeconomic scale, partial automatability of complex tasks creates a bottleneck of development, where further growth is constrained by the scarcity of essential human work. This bottleneck is removed once the tasks become fully automatable. Theoretical analysis using a two-level nested constant elasticity of substitution production function specification demonstrates that the shift from partial to full automation generates a non-convexity: humans and machines switch from complementary to substitutable, and the share of output accruing to human workers switches from an upward to a downward trend. This process has implications for inequality, the risk of technological unemployment, and the likelihood of a secular stagnation.

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.

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