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On optimal growth models when the discount factor is near 1 or equal to 1
Author(s) -
Le Van Cuong,
Morhaim Lisa
Publication year - 2006
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.1365-2966.2006.0024.x
Subject(s) - economics , differentiable function , discounting , bellman equation , function (biology) , value (mathematics) , stock (firearms) , econometrics , growth model , capital (architecture) , mathematical economics , mathematics , statistics , finance , mathematical analysis , mechanical engineering , history , archaeology , evolutionary biology , engineering , biology
The aim of this paper is to fill the gap between intertemporal growth models when the discount factor is close to one and when it equals one. We show that the value function and the policy function are continuous with respect both to the discount factor, β, and the initial stock of capital, x 0 . We prove that the optimal policy g β ( x 0 ) is differentiable and that Dg β ( x 0 ) is continuous with respect to (β, x 0 ) . As a by‐product, a global turnpike result is proved.