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Optimal growth and impatience: A phase diagram analysis
Author(s) -
Chang FwuRanq
Publication year - 2009
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.1742-7363.2009.00107.x
Subject(s) - saddle point , bounded function , economics , mathematics , time preference , stability (learning theory) , function (biology) , phase diagram , constant (computer programming) , mathematical economics , derivative (finance) , regular polygon , growth rate , phase (matter) , mathematical analysis , computer science , physics , microeconomics , geometry , biology , quantum mechanics , machine learning , evolutionary biology , financial economics , programming language
When the time preference exhibits decreasing marginal impatience, the rate at which the discount function decreases plays a central role in the stability analysis. This paper shows that if the discount function is strictly decreasing, strictly convex and has a uniform bound on its first derivative, then the continuous‐time, one‐sector optimal growth problem has a unique steady state that exhibits the saddle‐point property. Moreover, the phase diagram analysis is geometrically similar to the case of a constant discount rate. The proposed bounded slope assumption is inspired by and in direct contrast with Magill and Nishimura's “division of countries” example.