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Weak concavity properties of indirect utility functions in multisector optimal growth models
Author(s) -
Venditti Alain
Publication year - 2012
Publication title -
international journal of economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.351
H-Index - 11
eISSN - 1742-7363
pISSN - 1742-7355
DOI - 10.1111/j.1742-7363.2011.00171.x
Subject(s) - isoelastic utility , concave function , differentiable function , function (biology) , bounded function , curvature , economics , stability (learning theory) , growth model , mathematics , mathematical economics , expected utility hypothesis , computer science , mathematical analysis , regular polygon , geometry , evolutionary biology , machine learning , biology
Studies of optimal growth in a multisector framework are generally addressed in reduced‐form models. These are defined by an indirect utility function which summarizes the consumers’ preferences and the technologies. Weak concavity assumptions of the indirect utility function allow one to prove differentiability of optimal solutions and stability of the steady state. This paper shows that if the consumption good production function is concave‐, and the instantaneous utility function is concave‐, then the indirect utility function is weakly concave, and its curvature coefficients are bounded from above by a function of and .