Necessity of the Transversality Condition for Stochastic Models with CRRA Utility
AbstractThis paper shows that the standard transversality condition (STVC) is necessary for optimality for stochastic models with constant-relative-risk-aversion (CRRA) utility under general conditions. We consider an infinite-horizon stochastic maximization problem that takes a general form of multi-sector growth model with a single consumption good and CRRA utility. We establish two results. The first result is that the STVC is necessary in the case of logarithmic utility. The second result is that the STVC is necessary in the case of non-logarithmic CRRA utility as long as lifetime utility is finite at the optimum. These results apply to various stochastic growth models, including real business cycle (RBC) models with endogenous labor supply. Our results make it clear that there is practically no issue about necessity of the STVC for stochastic models with CRRA utility.
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Bibliographic InfoPaper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number 137.
Length: 13 pages
Date of creation: May 2003
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Transversality condition; Stochastic optimization; Stochastic growth; CRRA; Real business cycle;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D90 - Microeconomics - - Intertemporal Choice and Growth - - - General
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
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