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Optimal savings and the value of population
Kenneth J Arrow1, Alain Bensoussan, Qi Feng
1Department of Economics, Stanford University, Stanford, CA 94305, USA. arrow@stanford.edu
Summary
This study models economic growth with changing population dynamics, analyzing optimal paths and convergence to equilibrium using a two-dimensional phase diagram. Findings characterize approaches to classical curves and long-run equilibrium.
Area of Science:
- Economics
- Mathematical Economics
- Economic Growth Theory
Background:
- Economic growth models often simplify population dynamics.
- Understanding population's role in economic growth is crucial for long-term stability.
- Total utilitarianism provides a framework for evaluating societal welfare.
Purpose of the Study:
- To develop an economic growth model incorporating complex, exogenous population changes.
- To analyze optimal economic paths under varying population growth scenarios.
- To depict and characterize the convergence to equilibrium using phase diagrams.
Main Methods:
- Developed a two-state variable model (capital and population).
- Utilized population as a surrogate for time to create a phase diagram.
- Analyzed transient curves and their convergence to classical curves and equilibrium.
Main Results:
- Depicted optimal economic growth paths on a two-dimensional phase diagram.
- Identified distinct behaviors at critical population levels (exponential growth or saturation).
- Characterized the convergence of the transient curve to equilibrium under different population dynamics.
Conclusions:
- The model successfully integrates exogenous population dynamics into economic growth analysis.
- Phase diagrams are effective tools for visualizing economic dynamics with population changes.
- The study provides insights into economic stability under varying population scenarios.
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