Notes, Comments, and Letters to the Editor
Indeterminacy with Non-separable Utility

https://doi.org/10.1006/jeth.1999.2633Get rights and content

Abstract

J. Benhabib and R. E. A. Farmer (1994, J. Econ. Theory63, 19–41) showed that a single sector growth model in the presence of increasing returns-to-scale may display an indeterminate equilibrium if the demand and supply curves cross with the “wrong slopes.” We generalize their result to a model with preferences that are non-separable in consumption and leisure. We provide a simple analog of the Benhabib– Farmer condition that works in the non-separable case. Our condition is easy to check in practice and it allows for equilibria to be indeterminate, even when demand and supply curves have the standard slopes. We illustrate that equilibrium can be indeterminate when demand and supply curves have standard slopes and the degree of increasing returns-to-scale is well within recent estimates by S. Basu and J. Fernald (1997, J. Polit. Econ.105, 249–283) for U. S. manufacturing. Journal of Economic Literature Classification Numbers: E10, E32, D90.

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    In particular, multiplicative separable preferences, proposed by King et al. (1988) and known as KPR preferences (see e.g., Stockman and Tesar, 1995; Benigno and Thoenissen, 2008), imply the existence of non-trivial constraints on the preference parameters that are necessary to ensure positive non-increasing marginal utilities. The assumption of additive separable preferences between consumption and leisure also appears quite restrictive since it implies that the inter-temporal elasticity of substitution must equal one (see e.g., Bennet and Farmer, 2000; Domeij and Floden, 2006). Blundell and Walker (1982) tested the restrictions implied by the separability assumption, i.e. that all goods are normal and leisure is a substitute for all commodities, which is a rather unattractive assumption since some consumption activities may be complementary to leisure.

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We thank Michael Woodford, Jess Benhabib, Jang-Ting Guo, Sharon Harrison, Stephanie Schmidt-Grohé, Amartya Lahiri, Martin Uribe, Mark Weder, and two anonymous referees of this journal, all of whom have made valuable suggestions that have contributed to the final version of the paper. Any remaining errors are ours.

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The views expressed are those of the author and not necessarily those of the Federal Deposit Insurance Corporation.

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Farmer's research was supported by NSF Grant SBR 9515036 and by a grant from the Academic Senate of the University of California at Los Angeles.

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