EXISTENCE AND UNIQUENESS OF STEADY-STATE EQUILIBRIUM IN A GENERALIZED OVERLAPPING GENERATIONS MODEL

2011 ◽  
Vol 16 (S3) ◽  
pp. 299-311 ◽  
Author(s):  
Jinlu Li ◽  
Shuanglin Lin
Keyword(s):  
Steady State ◽  
Existence And Uniqueness ◽  
Overlapping Generations ◽  
Optimization Problem ◽  
Utility Functions ◽  
Overlapping Generations Model ◽  
State Equilibrium ◽  
Derivatives Of ◽  
Uniqueness Of Equilibrium ◽  
Diamond Type

Galor and Ryder [Journal of Economic Theory 49 (1989), 360–375] establish conditions for the existence of equilibrium in a Diamond-type overlapping-generations (OLG) model. Although theoretically appealing, these conditions are implicit and not convenient to apply. This paper provides explicit and easily applied conditions for the existence and uniqueness of steady-state equilibrium, with which one only needs to check the first derivatives of the production and utility functions and their interactions, with no need to solve the optimization problem. Our theorems on the existence and uniqueness of steady-state equilibrium can be applied to a larger class of OLG models that do not require second-order differentiability of the production and utility functions. We present examples to show how to check the existence and uniqueness of equilibrium.

scholarly journals The impact of green preferences on the relevance of history versus expectations

2019 ◽  
Vol 24 (6) ◽  
pp. 583-607
Author(s):  
Andreas Schaefer ◽  
Anna Stünzi
Keyword(s):  
Steady State ◽  
Overlapping Generations ◽  
Clean Energy ◽  
Environmental Policies ◽  
Stable Steady State ◽  
Overlapping Generations Model ◽  
Environmental Preferences ◽  
Energy Taxes ◽  
Energy Tax ◽  
The Impact

AbstractIn an overlapping generations model with multiple steady states, we analyse the impact of endogenous environmental policies on the relevance of history and expectations for the equilibrium selection. In a polluting regime, environmental preferences cause an increasing energy tax which raises the risk that the economy transitions to the inferior equilibrium under pessimistic expectations. However, higher environmental preferences imply an earlier switch to the clean energy regime. Then, the conflict between production and environmental preferences is resolved and the prospects of selecting the superior equilibrium improve, since positive expectations become more relevant. In an empirical analysis we find that people with environmental preferences tend to have more optimistic expectations about economic development. Using these findings to analyse the steady-state dynamics implies that agents with environmental preferences support higher energy taxes and switch to clean production more quickly. Due to their optimism, the likelihood of reaching the superior stable steady state increases.

scholarly journals AUTOMATION, STAGNATION, AND THE IMPLICATIONS OF A ROBOT TAX

2020 ◽  
pp. 1-32 ◽  
Author(s):  
Emanuel Gasteiger ◽  
Klaus Prettner
Keyword(s):  
Steady State ◽  
Economic Impact ◽  
Technological Progress ◽  
Overlapping Generations ◽  
Investment Decisions ◽  
Cautionary Tale ◽  
Overlapping Generations Model ◽  
Long Run ◽  
Per Capita ◽  
Capita Output

We assess the long-run growth effects of automation in the overlapping generations framework. Although automation implies constant returns to capital and, thus, an AK production side of the economy, positive long-run growth does not emerge. The reason is that automation suppresses wage income, which is the only source of investment in the overlapping generations model. Our result stands in sharp contrast to the representative agent setting with automation, where sustained long-run growth is possible even without technological progress. Our analysis therefore provides a cautionary tale that the underlying modeling structure of saving/investment decisions matters for the derived economic impact of automation. In addition, we show that a robot tax has the potential to raise per capita output and welfare at the steady state. However, it cannot induce a takeoff toward positive long-run growth.

scholarly journals CONSEQUENCES OF MODELING HABIT PERSISTENCE

2009 ◽  
Vol 13 (3) ◽  
pp. 349-365 ◽  
Author(s):  
Luca Bossi ◽  
Pere Gomis-Porqueras
Keyword(s):  
Steady State ◽  
Overlapping Generations ◽  
Overlapping Generations Model ◽  
Habit Persistence ◽  
Local Dynamics ◽  
Pure Exchange

In this paper, we study the stationary and non-stationary equilibria of a deterministic, pure exchange, two-period overlapping generations model with habit persistence. We show that preferences with multiplicative habits can lead to quite different equilibrium outcomes compared to subtractive ones. The two most commonly adopted habit specifications can differ in terms of homotheticity, gross substitutability, and uniqueness of equilibria. We illustrate these differences in terms of steady-state equilibria, as well as local dynamics.

A NOTE ON THE EXISTENCE AND UNIQUENESS OF STATIONARY MONETARY EQUILIBRIUM IN A STOCHASTIC OLG MODEL

2013 ◽  
Vol 19 (3) ◽  
pp. 701-707 ◽  
Author(s):  
Eisei Ohtaki
Keyword(s):  
Existence And Uniqueness ◽  
Overlapping Generations ◽  
Olg Model ◽  
Initial Endowment ◽  
Overlapping Generations Model ◽  
Constructive Proofs ◽  
Monetary Equilibrium

This paper directly shows the equivalence between the existence of stationary monetary equilibrium and the conditional Pareto suboptimality of the initial endowment in a stochastic overlapping generations model. Especially, it gives short and constructive proofs for existence and uniqueness.

scholarly journals CAN EDUCATION BE GOOD FOR BOTH GROWTH AND THE ENVIRONMENT?

2013 ◽  
Vol 17 (5) ◽  
pp. 1135-1157 ◽  
Author(s):  
Fabien Prieur ◽  
Thierry Bréchet
Keyword(s):  
Public Policy ◽  
Steady State ◽  
Overlapping Generations ◽  
Environmental Awareness ◽  
Sustainable Growth ◽  
Growth Path ◽  
Overlapping Generations Model ◽  
Balanced Growth ◽  
Knowledge Growth ◽  
Balanced Growth Path

We develop an overlapping-generations model of growth and the environment in relation to public policy on education. Beyond the traditional mechanisms through which knowledge, growth, and the environment interplay, we stress the role played by education in environmental awareness. Assuming first that environmental awareness is constant, we show the existence of a balanced-growth path (BGP) along which environmental quality increases continually. Then, if education enhances environmental awareness, the equilibrium properties are modified: the economy can reach a steady state or converge to an asymptotic BGP. Therefore, education does not necessarily promote sustained and sustainable growth.

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