Related Experiment Video
Updated: Mar 23, 2026
20:36
Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
9.3K
Expectation formation in an overlapping generation model with production.
Fausto Cavalli1, Ahmad Naimzada1
1Department of Economics, Management and Statistics, University of Milano-Bicocca, U6 Building, Piazza dell'Ateneo Nuovo 1, 20126 Milano, Italy.
Chaos (Woodbury, N.Y.)
|April 3, 2016
Summary
This study examines economic dynamics in an overlapping generations model, comparing perfect, myopic, and adaptive expectations. Adaptive expectations can lead to complex dynamics and multistability, unlike myopic expectations.
Area of Science:
- Economics
- Mathematical Economics
Background:
- Overlapping generations models are crucial for understanding macroeconomic dynamics.
- Expectations formation significantly impacts economic stability and outcomes.
Purpose of the Study:
- To analyze the dynamic properties of an overlapping generations model with capital accumulation.
- To compare the effects of perfect foresight, myopic foresight, and adaptive expectations on model dynamics.
- To investigate the conditions leading to complex dynamics and multistability under adaptive expectations.
Main Methods:
- Analytical investigation of model stability under different expectation mechanisms.
- Detailed analysis of adaptive expectations, including local and global stability.
- Numerical simulations to explore complex dynamics and multistability.
Main Results:
- The steady state is invariant across all expectation mechanisms.
- Global stability is proven for perfect foresight.
- Adaptive and myopic expectations can generate periodic and chaotic dynamics when agents allocate significant time to labor in their second period.
- Multistability, characterized by the coexistence of a stable steady state and chaotic attractors, emerges under adaptive expectations, but not under myopic expectations.
Conclusions:
- Reduced rationality, particularly adaptive expectations, can introduce significant complexity and multistability into economic models.
- The findings highlight the importance of considering sophisticated expectation formation for understanding economic fluctuations.
- Agents may benefit from learning by observing forecasting errors to improve their predictions.
Related Concept Videos
00:57Population Growth
29.4K
Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.
29.4K
01:25Modeling with Differential Equations
162
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
162
01:26Exponential Equations for Modeling Growth
417
Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
417
00:51Energy Budgets
11.1K
Organisms must balance energy intake with the energy required for growth, maintenance and reproduction. These trade-offs result in a variety of survivorship and reproductive strategies, including semelparity and iteroparity. Semelparous species, like annual plants, have only one reproductive episode in their lifetimes and consequently have short lifespans. Iteroparous species, by contrast, have many reproductive events during their lifetimes but have relatively few offspring. These two...
11.1K
01:13Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model
389
Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
389
01:27Growth Models with Integration: Problem Solving
85
In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
85