Indeterminacy with Non-separable Utility

Abstract

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 thè`w rong slopes.'' We generalize their result to a model with preferences that are nonseparable 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

Consumption taxation, social status and indeterminacy in models of endogenous growth with elastic labor supply

“…To put it differently, the elastic elasticity of substitution in consumption (i.e., σ < 1) is a necessary condition for indeterminacy, which is consistent with those models without status preferences such as those of Bennett and Farmer (2000), and Pelloni and Waldmann (2000). Moreover, by setting γ = 0 and θ = 1 in (18), respectively, we have: …”

“…12 As correctly pointed out by Hintermaier (2003), the 'wrong' slope of the Frisch labor supply curve is not consistent with the concavity of the nonseparable utility function posited by Bennett and Farmer (2000). In light of this fact, we can say that the presence of a household's status concern makes it possible for the Frisch labor supply curve to cross the labor demand curve with the 'wrong' slopes without violating the concavity of the utility function.…”

“…We use Romer's (1986) learning-by-doing, one-sector model of endogenous growth augmented with endogenous labor supply and with nonseparable preferences in consumption, social status and leisure. According to Bennett and Farmer (2000), the inclusion of endogenous labor supply in the nonseparable utility function makes indeterminacy of equilibria possible. Specifically, unlike Weder (2000) and Alonso-Carrera et al (2005), we assume the CRRA form for an instantaneous utility function to model such preferences, which enables us to study a wider class of status preferences models by varying only the parameter values that represent the strength of social status concern and/or the degree of externalities generated by others' wealth holdings or others' consumption.…”

“…11 According to Bennett and Farmer (2000), the Frisch labor supply curve is where labor supply is a function of the real wage holding the marginal utility of consumption (i.e., λ) constant.…”

Unemployment and Indeterminacy

“…2 Our analysis shows that indeterminacy is more likely to occur if there is more inequality in consumption between the employed and the unemployed. In our calibration exercise, indeterminacy occurs with constant returns technology if the consumption of the unemployed is less than 2 Our work is closely related to Bennett and Farmer (2000), who have emphasized the potential importance of a downward sloping Frisch labor supply curve to generate indeterminacy. As shown by Hintermaier (2003) and Nakajima (2001), however, as long as utility is concave between consumption and leisure, the Frisch labor supply curve cannot slope down.…”