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A NOTE ON THE CHARACTERIZATION OF THE NEOCLASSICAL PRODUCTION FUNCTION

Published online by Cambridge University Press:  09 August 2016

Andreas Irmen
Affiliation:
University of Luxembourg and CESifo, Munich
Alfred Maußner*
Affiliation:
University of Augsburg
*
Address correspondence to: Alfred Maußner, Chair of Empirical Macroeconomics, University of Augsburg, Universitätsstrasse 16, D-86316 Augsburg, Germany; e-mail: alfred.maussner@wiwi.uni-augsburg.de.

Abstract

We study production functions with capital and labor as arguments that exhibit positive, yet diminishing marginal products and constant returns to scale. We show that such functions satisfy the Inada conditions if (i) both inputs are essential and (ii) an unbounded quantity of either input leads to unbounded output. This allows for an alternative characterization of the neoclassical production function that altogether dispenses with the Inada conditions. Although this proposition generalizes to the case of n > 2 factors of production, its converse does not hold: 2n Inada conditions do not imply that each factor is essential.

Type
Notes
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

This paper is a revised version of our CESifo Discussion Paper “Essential Inputs and Unbounded Output: An Alternative Characterization of the Neoclassical Production Function.” We are grateful to the editor, two anonymous referees, Hendrik Hakenes, Amer Tabaković, and Gautam Tripathi for useful comments and suggestions. Andreas Irmen gratefully acknowledges financial support from the University of Luxembourg under the program “Agecon C—Population Aging: An Exploration of its Effect on Economic Performance and Culture.”

References

REFERENCES

Acemoglu, D. (2009) Introduction to Modern Economic Growth. Princeton, NJ: Princeton University Press.Google Scholar
Barro, R.J. and Sala-í-Martin, X. (2004) Economic Growth, 2nd ed. Cambridge, MA: MIT Press.Google Scholar
Burmeister, E. and Dobell, R.A. (1970) Mathematical Theories of Economic Growth. London: Collier-Macmillian.Google Scholar
de la Croix, D. and Michel, P. (2002) A Theory of Economic Growth–-Dynamics and Policy in Overlapping Generations. Cambridge, UK: Cambridge University Press.Google Scholar
Fáre, R. (1980) Laws of Diminishing Returns. Berlin: Springer.Google Scholar
Fáre, R. and Primont, D. (2002) Inada conditions and the law of diminishing returns. International Journal of Business Economics 1, 18.Google Scholar
Hakenes, H. and Irmen, A. (2008) Neoclassical growth and the “trivial” steady state. Journal of Macroeconomics 30 (3), 10971103.Google Scholar
Inada, K.-I. (1963) On two-sector models of economic growth: Comments and a generalization. Review of Economic Studies 30, 119127.Google Scholar
Irmen, A. and Maußner, A. (2014) Essential Inputs and Unbounded Output: an Alternative Characterization of the Neoclassical Production Function. CESifo working paper 5126, CESifo Group Munich.Google Scholar
Litina, A. and Palivos, T. (2008) Do Inada conditions imply that production function must be asymptotically Cobb–Douglas? A comment. Economics Letters 99, 498499.Google Scholar
Romer, D. (2012) Advanced Macroeconomics, 4th ed. New York: McGraw Hill.Google Scholar
Shephard, R.W. (1970) Proof of the law of diminishing returns. Zeitschrift für Nationalökonomie 30, 734.Google Scholar
Solow, R.M. (1956) A contribution to the theory of economic growth. Quarterly Journal of Economics 70 (1), 6594.CrossRefGoogle Scholar