CLASSIFICATION OF HOMOTHETIC FUNCTIONS WITH CONSTANT ELASTICITY OF SUBSTITUTION AND ITS GEOMETRIC APPLICATIONS

Bang-yen Chen

Research Article

CLASSIFICATION OF HOMOTHETIC FUNCTIONS WITH CONSTANT ELASTICITY OF SUBSTITUTION AND ITS GEOMETRIC APPLICATIONS

Year 2012, Volume: 5 Issue: 2, 67 - 78, 30.10.2012

Bang-yen Chen

Abstract

Keywords

Homothetic production function, constant elasticity of substitution, generalized Cobb-Douglas production function, generalized ACMS production function, Gauss- Kronecker curvature

References

[1] R. G. Allen and J. R. Hicks, A reconsideration of the theory of value, Pt. II, Economica 1 (1934), 196–219.
[2] K. J. Arrow, H. B. Chenery, B. S. Minhas and R. M. Solow, Capital-labor substitution and economic efficiency, Rev. Econom. Stat. 43 (1961), 225–250.
[3] B.-Y. Chen, Pseudo-Riemannian geometry, δ-invariants and applications, World Scientific, Hackensack, New Jersey, 2011.
[4] B.-Y. Chen, On some geometric properties of h-homogeneous production function in micro- economics, Kragujevac J. Math. 35 (2011), 343–357.
[5] B.-Y. Chen, On some geometric properties of quasi-sum production models, J. Math. Anal. Appl. 392 (2012), 192–199.
[6] B.-Y. Chen, Classification of h-homogeneous production functions with constant elasticity of substitution, Tamkang J. Math. 43 (2012), 321–328.
[7] P. H. Douglas, The Cobb-Douglas production function once again: Its history, its testing, and some new empirical values, J. Polit. Econom. 84 (1976), 903–916.
[8] J. Filipe and G. Adams, The estimation of the Cobb-Douglas function, Eastern Econom. J. 31 (2005), 427–445.
[9] G. Hanoch, CRESH production functions, Econometrica 39 (1971), 695–712.
[10] C. W. Cobb and P. H. Douglas, A theory of production, Amer. Econom. Rev. 18 (1928), 139–165.
[11] J. R. Hicks, Theory of Wages, London, Macmillan, 1932.
[12] L. Losonczi, Production functions having the CES property, Acta Math. Acad. Paedagog. Nyhzi. (N.S.) 26 (2010), 113–125.
[13] D. McFadden, Constant elasticity of substitution production functions, The Review of Eco- nomic Studies 30 (1963), 73–83.
[14] R. C. Reilly, On the Hessian of a function and the curvature of its graph, Michigan Math. J. 20 (1973), 373–383.
[15] A. D. Vˆılcu and G. E. Vˆılcu, On some geometric properties of the generalized CES production functions, Appl. Math. Comput. 218 (2011), 124–129,
[16] G. E. Vˆılcu, A geometric perspective on the generalized Cobb-Douglas production functions, Appl. Math. Lett. 24 (2011), 777–783.

Year 2012, Volume: 5 Issue: 2, 67 - 78, 30.10.2012

Bang-yen Chen

Abstract

References

[1] R. G. Allen and J. R. Hicks, A reconsideration of the theory of value, Pt. II, Economica 1 (1934), 196–219.
[2] K. J. Arrow, H. B. Chenery, B. S. Minhas and R. M. Solow, Capital-labor substitution and economic efficiency, Rev. Econom. Stat. 43 (1961), 225–250.
[3] B.-Y. Chen, Pseudo-Riemannian geometry, δ-invariants and applications, World Scientific, Hackensack, New Jersey, 2011.
[4] B.-Y. Chen, On some geometric properties of h-homogeneous production function in micro- economics, Kragujevac J. Math. 35 (2011), 343–357.
[5] B.-Y. Chen, On some geometric properties of quasi-sum production models, J. Math. Anal. Appl. 392 (2012), 192–199.
[6] B.-Y. Chen, Classification of h-homogeneous production functions with constant elasticity of substitution, Tamkang J. Math. 43 (2012), 321–328.
[7] P. H. Douglas, The Cobb-Douglas production function once again: Its history, its testing, and some new empirical values, J. Polit. Econom. 84 (1976), 903–916.
[8] J. Filipe and G. Adams, The estimation of the Cobb-Douglas function, Eastern Econom. J. 31 (2005), 427–445.
[9] G. Hanoch, CRESH production functions, Econometrica 39 (1971), 695–712.
[10] C. W. Cobb and P. H. Douglas, A theory of production, Amer. Econom. Rev. 18 (1928), 139–165.
[11] J. R. Hicks, Theory of Wages, London, Macmillan, 1932.
[12] L. Losonczi, Production functions having the CES property, Acta Math. Acad. Paedagog. Nyhzi. (N.S.) 26 (2010), 113–125.
[13] D. McFadden, Constant elasticity of substitution production functions, The Review of Eco- nomic Studies 30 (1963), 73–83.
[14] R. C. Reilly, On the Hessian of a function and the curvature of its graph, Michigan Math. J. 20 (1973), 373–383.
[15] A. D. Vˆılcu and G. E. Vˆılcu, On some geometric properties of the generalized CES production functions, Appl. Math. Comput. 218 (2011), 124–129,
[16] G. E. Vˆılcu, A geometric perspective on the generalized Cobb-Douglas production functions, Appl. Math. Lett. 24 (2011), 777–783.

There are 16 citations in total.

Details

Primary Language	English
Journal Section	Research Article
Authors	Bang-yen Chen
Publication Date	October 30, 2012
Published in Issue	Year 2012 Volume: 5 Issue: 2

Cite

APA	Chen, B.-y. (2012). CLASSIFICATION OF HOMOTHETIC FUNCTIONS WITH CONSTANT ELASTICITY OF SUBSTITUTION AND ITS GEOMETRIC APPLICATIONS. International Electronic Journal of Geometry, 5(2), 67-78.
AMA	Chen By. CLASSIFICATION OF HOMOTHETIC FUNCTIONS WITH CONSTANT ELASTICITY OF SUBSTITUTION AND ITS GEOMETRIC APPLICATIONS. Int. Electron. J. Geom. October 2012;5(2):67-78.
Chicago	Chen, Bang-yen. “CLASSIFICATION OF HOMOTHETIC FUNCTIONS WITH CONSTANT ELASTICITY OF SUBSTITUTION AND ITS GEOMETRIC APPLICATIONS”. International Electronic Journal of Geometry 5, no. 2 (October 2012): 67-78.
EndNote	Chen B-y (October 1, 2012) CLASSIFICATION OF HOMOTHETIC FUNCTIONS WITH CONSTANT ELASTICITY OF SUBSTITUTION AND ITS GEOMETRIC APPLICATIONS. International Electronic Journal of Geometry 5 2 67–78.
IEEE	B.-y. Chen, “CLASSIFICATION OF HOMOTHETIC FUNCTIONS WITH CONSTANT ELASTICITY OF SUBSTITUTION AND ITS GEOMETRIC APPLICATIONS”, Int. Electron. J. Geom., vol. 5, no. 2, pp. 67–78, 2012.
ISNAD	Chen, Bang-yen. “CLASSIFICATION OF HOMOTHETIC FUNCTIONS WITH CONSTANT ELASTICITY OF SUBSTITUTION AND ITS GEOMETRIC APPLICATIONS”. International Electronic Journal of Geometry 5/2 (October 2012), 67-78.
JAMA	Chen B-y. CLASSIFICATION OF HOMOTHETIC FUNCTIONS WITH CONSTANT ELASTICITY OF SUBSTITUTION AND ITS GEOMETRIC APPLICATIONS. Int. Electron. J. Geom. 2012;5:67–78.
MLA	Chen, Bang-yen. “CLASSIFICATION OF HOMOTHETIC FUNCTIONS WITH CONSTANT ELASTICITY OF SUBSTITUTION AND ITS GEOMETRIC APPLICATIONS”. International Electronic Journal of Geometry, vol. 5, no. 2, 2012, pp. 67-78.
Vancouver	Chen B-y. CLASSIFICATION OF HOMOTHETIC FUNCTIONS WITH CONSTANT ELASTICITY OF SUBSTITUTION AND ITS GEOMETRIC APPLICATIONS. Int. Electron. J. Geom. 2012;5(2):67-78.