Self-generated fertility waves in a non-linear continuous overlapping generations model

Area of Science:

• Economics
• Mathematical Economics
• Economic Cycles

Background:

• The Easterlin theory, particularly Samuelson's simplified version, has been influential in understanding economic cycles.
• Previous models often utilized discrete-time approaches, limiting insights into cycle dynamics.

Purpose of the Study:

• To extend Samuelson's simplified Easterlin theory into a continuous-time framework.
• To analyze economic cycles within a model incorporating three distinct age groups.
• To determine the period length of these economic cycles.

Main Methods:

• Development of a continuous-time model based on Samuelson's Easterlin theory.
• Application of qualitative theory of nonlinear differential equations.
• Analysis of a three-age-group economic system.

Main Results:

• Demonstrated the existence of Easterlin-type cycles within the continuous-time model.
• Provided insights into the period length of economic cycles, a feature not readily available in discrete-time models.
• The continuous-time approach facilitates a more nuanced understanding of cycle dynamics.

Conclusions:

• The continuous-time extension of the Easterlin theory is a viable framework for studying economic cycles.
• This model offers a more detailed analysis of cycle characteristics, including their duration.
• The findings contribute to the theoretical understanding of macroeconomic fluctuations and age-group dynamics.