Abstract
We derive the relationships between the net and gross elasticities of substitution and complementarity (i.e., the elasticities that refer either to the conditional or unconditional, direct or inverse demand system) in the general case of non-homothetic, variable-returns-to-scale technologies. We also show that the so-called Hicks Elasticity of Complementarity (Hicks, Oxford economic Papers 22, 289–296 (1970)) is dual to a full-fledged elasticity of gross input substitution that we call the Hotelling/Lau Elasticity of Substitution (Lau, Production Economics: A Dual Approach to Theory and Applications. Amsterdam: North-Holand (1978)). The former is, in fact, the proper elasticity of substitution in the case of the inverse, unconditional input demand. Our results should clarify some issues about the input substitutability classification.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. D. R. Allen J. R. Hicks (1934) ArticleTitle“A Reconsideration of the Theory of Value, Part II” Economica 1 196–219
R. W. Anderson (1980) ArticleTitle“Some Theory of Inverse Demand for Applied Demand Analysis” European Economic Review 14 281–290
A. P. Barten L. J. Bettendorf (1989) ArticleTitle“Price Formation of Fish: An Application of an Inverse Demand System” European Economic Review 33 1509–1525 Occurrence Handle10.1016/0014-2921(89)90075-5
P. Bertoletti (2001) ArticleTitle“The Allen/Uzawa Elasticity of Substitution as a Measure of Gross Input Substitutability” Rivista italiana degli economisti 6 87–94
C. Blackorby R. R. Russell (1981) ArticleTitle“The Morishima Elasticity of Substitution; Symmetry, Constancy, Separability, and Its Relationship to the Hicks and Allen Elasticities” Review of Economic Studies 48 147–58
C. Blackorby R.R. Russell (1989) ArticleTitle“Will the Real Elasticity of Substitution Please Stand Up? (A comparison of the Allen/Uzawa and Morishima Elasticities)” American Economic Review 79 882–888
G. R. Chambers (1988) Applied Production Analysis Cambridge University Press Cambridge (UK)
R. Cornes (1992) Duality and Modern Economics Cambridge University Press Cambridge (UK)
A. Deaton (1979) ArticleTitle“The Distance Function in Consumer Behavior with Applications to Index Numbers and Optimal Taxation” Review of Economic Studies 46 391–405
J.S. Eales (1994) ArticleTitle“The Inverse Lewbel Demand System” American Journal of Agricultural and Resource Economics 19 173–182
J. S. Eales L. Unnevehr (1994) ArticleTitle“The Inverse almost Ideal Demand System” European Economic Review 38 101–115 Occurrence Handle10.1016/0014-2921(94)90008-6
R. Färe (1975) ArticleTitle“A Note on Ray-Homogeneous and Ray-Homothetic Production Functions” Swedish Journal of Economics 77 366–372
G. Hanoch (1975) ArticleTitle“The Elasticity of Scale and the Shape of Average Costs” American Economic Review 65 492–497
J. R. Hicks (1956) A Revision of Demand Theory Oxford University Press Oxford
J. R. Hicks (1970) ArticleTitle“Elasticities of Substitution Again: Substitutes and Complements” Oxford Economic Papers 22 289–296
M.T. Holt (2002) ArticleTitle“Inverse Demand Systems and Choice of Functional Forms” European Economic Review 46 117–142 Occurrence Handle10.1016/S0014-2921(00)00088-X
H. Y. Kim (1997) ArticleTitle“Functional Separability and Elasticities of Complementarity” American Journal of Agricultural Economics 79 1177–1181
H. Y. Kim (2000) ArticleTitle“The Antonelli Versus Hicks Elasticity of Complementarity and Inverse Input Demand Systems” Australian Economic Papers 39 245–261 Occurrence Handle10.1111/1467-8454.00089
U. Kohli (1985) ArticleTitle“Inverse Demand and Anti-Giffen Goods” European Economic Review 27 397–404
L. J. Lau (1978) Applications of Profit Functions M. Fuss D. McFadden (Eds) Production Economics: A Dual Approach to Theory and Applications NumberInSeriesVol. 1. North-Holland Amsterdam 133–216
A. Mas-Colell M.D. Whinston J.R. Green (1995) MiCRoeconomic Theory Oxford University Press Oxford
H. Park W. N. Thurman (1999) ArticleTitle“On Interpreting Inverse Demand System: A Primal Comparison of Scale Flexibilities and Income Elasticities” American Journal of Agricultural Economics 81 950–958
R. Sato T. Koizumi (1973) ArticleTitle“On the Elasticities of Substitution and Complementarity” Oxford Economic Papers 25 44–56
L. S. Seidman (1989) ArticleTitle“Complements and Substitutes: The Importance of Minding p’s and q’s” Southern Economic Journal 56 183–190
M. Syrquin G. Hollender (1982) ArticleTitle“Elasticities of Substitution and Complementarity: The General Case” Oxford Economic Papers 34 291–299
A. Takayama (1985) Mathematical Economics Cambridge University Press Cambridge (UK)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bertoletti, P. Elasticities of Substitution and Complementarity: A Synthesis. J Prod Anal 24, 183–196 (2005). https://doi.org/10.1007/s11123-005-4703-3
Issue Date:
DOI: https://doi.org/10.1007/s11123-005-4703-3