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Volume 17,     Number 4,     Winter 2009

 

DEVELOPING UTILITY FUNCTIONS FOR
OPTIMAL CONSUMPTION IN MODELS WITH
HABIT FORMATION AND CATCHING UP
WITH THE JONESES
ROMAN NARYSHKIN AND MATT DAVISON

Abstract. This paper analyzes popular time-nonseparable utility functions that describe "habit formation" consumer preferences comparing current consumption with the time averaged past consumption of the same individual and "catching up with the Joneses" (CuJ) models comparing individual consumption with a cross-sectional average consumption level. Few of these models give reasonable optimum consumption time series. We introduce theoretically justified utility specifications leading to a plausible consumption behavior to show that habit formation preferences must be described by a power CRRA utility function different from the exponential CARA used for CuJ. We also introduce a continuous time formulation for the habit formation problem which yields a nonlinear ordinary differential equation (ODE). The numerical solutions of this ODE are presented and analyzed.

 

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