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In his paper “Does utility curvature matter for indeterminacy”, Kim (2005)
analyzed the relationship among the utility function form, curvature and indeterminacy,
concluding that the relationship between curvature and indeterminacy is not robust in neoclassical growth model and the indeterminacy may
disappear under the utility specification as in Greenwood et.al (1998). The
models he discussed are confined within one sector closed economy. Weder
(2001), Meng and Velasco (2004) extend the Benhabib and Farmer (1996) and
Benhabib and Nishimura (1998)’s closed economy two sector models into open
economy, showing that indeterminacy can occur under small external effects,
independently of the intertemporal elasticities in consumption. Meng and Velasco
(2003) went further, showing the independence between the elasticity of labor supply and indeterminacy in open economy. Under nonseparable utility
forms like in King, Plosser and Rebelo (1988, henceforth KPR) or Bennett-Farmer (2000) form, do we still have this property? In other words, is the
independence between curvature and indeterminacy in small open economy models robust to the specification of utility functions? In this note, I tackle
this issue under two different versions of nonseparable utility functions commonly
used in the literature. The answer is “yes” to KPR form but “no” to
Bennett-Farmer form. Endogenous time preference and consumable
nontradable goods are two elements to deliver this result.
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