Existence, optimality and dynamics of equilibria with endogenous time preference
AbstractAbstract 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 InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 47 (2011)
Issue (Month): 2 (March)
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Web page: http://www.elsevier.com/locate/jmateco
Endogenous time preference Optimal growth Competitive equilibrium Multiple steady-states;
Other versions of this item:
- Cuong Le Van & Cagri Saglam & Selman Erol, 2011. "Existence, Optimality and Dynamics of Equilibria with Endogenous Time Preference," Working Papers 04, Development and Policies Research Center (DEPOCEN), Vietnam.
- Cuong Le Van & Cagri Saglam & Selman Erol, 2011. "Existence, Optimality and Dynamics of Equilibria with Endogenous Time Preference," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00639731, HAL.
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D90 - Microeconomics - - Intertemporal Choice - - - General
- O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
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