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Existence, optimality and dynamics of equilibria with endogenous time preference

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  • Erol, Selman
  • Le Van, Cuong
  • Saglam, Cagri

Abstract

Abstract This paper studies the dynamic implications of the endogenous rate of time preference depending on the stock of capital, in a one-sector growth model. The planner's problem is presented and the optimal paths are characterized. We prove that there exists a critical value of initial stock, in the vicinity of which, small differences lead to permanent differences in the optimal path. Indeed, we show that a development trap can arise even under a strictly convex technology. In contrast with the early contributions that consider recursive preferences, the critical stock is not an unstable steady state so that if an economy starts at this stock, an indeterminacy will emerge. We also show that even under a convex-concave technology, the optimal path can exhibit global convergence to a unique stationary point. The multipliers system associated with an optimal path is proven to be the supporting price system of a competitive equilibrium under externality and detailed results concerning the properties of optimal (equilibrium) paths are provided. We show that the model exhibits globally monotone capital sequences yielding a richer set of potential dynamics than the classic model with exogenous discounting.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 47 (2011)
Issue (Month): 2 (March)
Pages: 170-179

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Handle: RePEc:eee:mateco:v:47:y:2011:i:2:p:170-179

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Endogenous time preference Optimal growth Competitive equilibrium Multiple steady-states;

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Citations

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Cited by:
  1. Taketo Kawagishi & Kazuo Mino, 2012. "Time Preference and Long-Run Growth: the Role of Patience Capital," Economics Bulletin, AccessEcon, vol. 32(4), pages 3243-3249.
  2. Kirill Borissov, 2013. "The existence of equilibrium paths in an AK-model with endogenous time preferences and borrowing constraints," EUSP Deparment of Economics Working Paper Series Ec-01/13, European University at St. Petersburg, Department of Economics.
  3. Borissov, Kirill, 2013. "Growth and distribution in a model with endogenous time preferences and borrowing constraints," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 117-128.
  4. Crettez, Bertrand & Morhaim, Lisa, 2012. "Existence of competitive equilibrium in a non-optimal one-sector economy without conditions on the distorted marginal product of capital," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 197-206.

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