A Two-Sector Overlapping-Generations Model: A Global Characterization of the Dynamical System

Econometrica ◽  
1992 ◽  
Vol 60 (6) ◽  
pp. 1351 ◽  
Author(s):  
Oded Galor
Keyword(s):  
Dynamical System ◽  
Overlapping Generations ◽  
Overlapping Generations Model

scholarly journals Business Cycles in a Two-Sided Altruism Model

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2054
Author(s):  
Hiroshi Fujiu
Keyword(s):  
Dynamical System ◽  
Business Cycles ◽  
Business Cycle ◽  
Overlapping Generations ◽  
Overlapping Generations Model ◽  
Periodic Fluctuations

This study demonstrates that business cycles with complex periodic fluctuations may arise in an overlapping generations model with two-sided altruism. The structure of an equilibrium dynamical system strongly depends on the degree of altruism in the model. If either altruism of a generation to the parent or the child disappears, the study also demonstrates that complex periodic fluctuations never occur. In this sense, two-sided altruism is essential for a complex business cycle.

scholarly journals A CLOSED-FORM SOLUTION TO A MODEL OF TWO-SIDED, PARTIAL ALTRUISM

2012 ◽  
Vol 16 (2) ◽  
pp. 230-239
Author(s):  
Ana Fernandes
Keyword(s):  
Closed Form ◽  
Overlapping Generations ◽  
Closed Form Solution ◽  
Form Solution ◽  
Allocation Of Resources ◽  
Overlapping Generations Model ◽  
Parents And Children ◽  
Saving Rates ◽  
Markov Strategies

This paper presents a closed-form characterization of the allocation of resources in an overlapping generations model of two-sided, partial altruism. Three assumptions are made: (i) parents and children play Markov strategies, (ii) utility takes the CRRA form, and (iii) the income of children is stochastic but proportional to the saving of parents. In families where children are rich relative to their parents, saving rates—measured as a function of the family's total resources—are higher than when children are poor relative to their parents. Income redistribution from the old to the young, therefore, leads to an increase in aggregate saving.

Li-Yorke chaos in models with backward dynamics

2016 ◽  
Vol 20 (5) ◽  
Author(s):  
David R. Stockman
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Overlapping Generations ◽  
Sufficient Conditions ◽  
Economic Models ◽  
Limited Commitment ◽  
Inverse Limits ◽  
Overlapping Generations Model ◽  
Definition Of ◽  
Cash In Advance

AbstractSome economic models like the cash-in-advance model of money, the overlapping generations model and a model of credit with limited commitment may have the property that the dynamical system characterizing equilibria in the model are multi-valued going forward in time, but single-valued going backward in time. Such models or dynamical systems are said to have backward dynamics. In such instances, what does it mean for a dynamical system (set-valued) to be chaotic? Furthermore, under what conditions are such dynamical systems chaotic? In this paper, I provide a definition of chaos that is in the spirit of Li and Yorke for a dynamical system with backward dynamics. I utilize the theory of inverse limits to provide sufficient conditions for such a dynamical system to be Li-Yorke chaotic.

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