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Optimal Control of Age-structured Populations in Economy, Demography, and the Environment
This book covers a wide range of topics within mathematical modelling and the optimization of economic, demographic, technological and environmental phenomena. Each chapter is written by experts in their field and represents new advances in modelling theory and practice. These essays are exemplary of the fruitful interaction between theory and practice when exploring global and local changes. The unifying theme of the book is the use of mathematical models and optimization methods to describe age-structured populations in economy, demography, technological change, and the environment. Emphasis is placed on deterministic dynamic models that take age or size structures, delay effects, and non-...
Competitive Growth in a Life-Cycle Model
The dynamic behavior of the capital growth rate is analyzed using an overlapping-generations model with continuous trading. Assuming a technology satisfying constant social returns to capital, the equilibrium growth rate is piecewise-defined by functional differential equations with both delayed and advanced terms. The main result concerns the existence of a solution expressed as a series of exponentials, which is shown to crucially depend on the initial wealth distribution among cohorts. Upon existence, the dynamics of the capital growth rate has a saddle-point trajectory that converges to a unique steady state. Along the transition path, the growth rate exhibits exponentially decreasing oscillations.
Continuous-Time Overlapping Generations Models
Age structured populations are studied in economics through overlapping generations models. These models allow for a realistic characterization of life-cycle behaviors and display intertemporal equilibrium that are not necessarily efficient. This article uses the latest developments in continuous time overlapping generations models to show the influence of the vintage structure of the population on the volatility of intertemporal prices. Permanent cycles can be found on the neighborhood of steady-states while the transitional dynamics are generically governed by short run fluctuations.
