On some geometric properties of the generalized CES production functions

Vîlcu, Alina Daniela; Vîlcu, Gabriel-Eduard

doi:10.1016/j.amc.2011.05.061

Cited by 33 publications

(29 citation statements)

References 5 publications

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“…Theorem 3.3 is the Galilean version of the Theorem 3.2 of [34]. Also statement (A) of Theorem 3.3 is a special case of Theorem A of [14].…”

Section: 2mentioning

confidence: 99%

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Galilean geometry of corresponding surfaces to production models in economics

Aydın¹,

Sepet²

2015

Kragujevac J Math

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“…Theorem 3.3 is the Galilean version of the Theorem 3.2 of [34]. Also statement (A) of Theorem 3.3 is a special case of Theorem A of [14].…”

Section: 2mentioning

confidence: 99%

“…The author proved that the generalized CD production function has constant return to scale if and only if the corresponding hypersurface is developable. The author joint with A. D. Vilcu [34] generalized this result to the case of the generalized CES production function.…”

Section: Introductionmentioning

confidence: 99%

Galilean geometry of corresponding surfaces to production models in economics

Aydın¹,

Sepet²

2015

Kragujevac J Math

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“…If it is homogeneous of degree 1, it exhibits constant return to scale [5]. Many important properties of homogeneous production functions in economics were interpreted in terms of the geometry of their graphs by [5,9,10,18,19].…”

Section: Production Models In Economicsmentioning

confidence: 99%

Hessian determinants of composite functions with applications for production functions in economics

Aydın¹,

Ergüt²

2014

Kragujevac J Math

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“…Chen, A. D. Vîlcu and G. E. Vîlcu using production hypersurfaces [4,5,6,17,18]. Several applications of these geometric results to generalized CobbDouglas' and ACMS production functions can be found in these papers.…”

mentioning

confidence: 99%

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

Chen

2012

Tamkang J. Math.

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Abstract. 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 macroeconomics; 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 [12] 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 [12] that his proof does not work for production functions of n-inputs with n > 2.In this paper we settle this classification problem completely by classifying all h-homogeneous production functions which satisfy the CES property. More precisely, we prove that, for arbitrary number of inputs, the only twice differentiable h-homogeneous production functions satisfying the CES property are the generalized Cobb-Douglas production functions and the generalized ACMS production functions. IntroductionIn microeconomics and macroeconomics, a production function is a positive nonconstant function that specifies the output of a firm, an industry, or an entire economy for all combinations of inputs. 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. By assuming that the maximum output technologically possible from a given set of inputs is achieved, economists using a production function in analysis are abstracting from the engineering and managerial problems inherently associated with a particular production process.Let R denote the set of real numbers. Let us put R + = {r ∈ R : r > 0} and R n + = {(x 1 , . . . , x n ) ∈ R n : x 1 , . . . , x n > 0}.2010 Mathematics Subject Classification. Primary 90A11; Secondary 91B64.

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On some geometric properties of the generalized CES production functions

Cited by 33 publications

References 5 publications

Galilean geometry of corresponding surfaces to production models in economics

Galilean geometry of corresponding surfaces to production models in economics

Hessian determinants of composite functions with applications for production functions in economics

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

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