Derivation of the Hicks Elasticity of Substitution from the Input Distance Function

Stern, David I. (2008): Derivation of the Hicks Elasticity of Substitution from the Input Distance Function.

Abstract

The Hicks or direct elasticity of substitution is traditionally derived from the production function. This paper exploits duality theory to present a more general derivation from the input distance function, which is exactly dual to the Shadow Elasticity of Substitution. The new elasticity is more general than the traditional one as it can handle situations of technical inefficiency, nonseparability between inputs and outputs, and multiple outputs, but is equal to the traditional elasticity under the classical conditions. The new derivation is related to the Morishima and Antonelli Elasticities of Complementarity in the same way that the Shadow Elasticity of Substitution is related to the Morishima and Allen-Uzawa Elasticities of Substitution. Furthermore, distance (technical efficiency) is not constant for the Morishima and Antonelli Elasticities of Complementarity

• Item Type: MPRA Paper
• Language: English
• Keywords: Microeconomics; production; substitution
• Subjects: D - Microeconomics > D2 - Production and Organizations > D21 - Firm Behavior: Theory; B - History of Economic Thought, Methodology, and Heterodox Approaches > B2 - History of Economic Thought since 1925 > B21 - Microeconomics; D - Microeconomics > D2 - Production and Organizations > D24 - Production ; Cost ; Capital ; Capital, Total Factor, and Multifactor Productivity ; Capacity

References

Allen, R. G. D., 1934, A comparison between different definitions of complementary and competitive goods, Econometrica 2, 168-175.

Allen, R. G. D., 1938, Mathematical Analysis for Economists. (Macmillan, London).

Berndt, E. R. and D. O. Wood, 1975, Technology, prices and the derived demand for energy, Review of Economics and Statistics 57, 259-268.

Blackorby, C. and R. R. Russell, 1975, The Partial lasticity of Substitution, Discussion Paper 75-1, Economics, University of California, San Diego.

Blackorby, C. and R. R. Russell, 1981, The Morishima elasticity of substitution: symmetry, constancy, separability, and relationship to the Hicks and Allen elasticities, Review of Economic Studies 43, 147-158.

Blackorby, C. and R. R. Russell, 1989, Will the real elasticity of substitution please stand up?, (A comparison of the Allen/Uzawa and Morishima elasticities). American Economic Review 79, 882-888.

Färe R. and D. Primont, 1995, Multi-Output Production and Duality: Theory and Applications. (Kluwer, Boston).

Hicks, J. R., 1932, Theory of Wages. (Macmillan, London).

Hicks, J. R. and R. G. D. Allen, 1934a, A reconsideration of the theory of value, part I, Economica 1, 52-76.

Hicks, J. R. and R. G. D. Allen 1934b, A reconsideration of the theory of value, part II, Economica 1, 196-219.

Kim, H. Y., 1992, The translog production function and variable returns to scale, Review of Economics and Statistics 74, 546-552.

Kim, H. Y., 2000, The Antonelli versus Hicks elasticity of complementary and inverse input demand systems, Australian Economic Papers 39, 245-261.

Lerner, A. P., 1933, Notes on the elasticity of substitution: II the diagrammatical representation, Review of Economic Studies 1, 68-70.

Lim, H. and C. R. Shumway, 1997, Technical change and model specification: U.S. agricultural production, American Journal of Agricultural Economics 79, 543-554.

McFadden, D., 1963, Constant elasticity of substitution production functions, Review of Economic Studies 31, 73-83.

Morishima, M., 1967, A few suggestions on the theory of elasticity (in Japanese), Keizai Hyoron (Economic Review) 16, 144-150.

Mundlak, Y., 1968, Elasticities of substitution and the theory of derived demand, Review of Economic Studies 35, 225-236.

Pigou, A. C., 1934, The elasticity of substitution, Economic Journal 44, 232-241. Robinson, J. V., 1933, The Economics of Imperfect Competition. (Macmillan, London).

Uzawa, H., 1962, Production functions with constant elasticities of substitution, Review of Economic Studies 30, 291-299.