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Equilibrium in a Continuous-Time Overlapping Generations Model

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Title: Equilibrium in a Continuous-Time Overlapping Generations Model
Author(s): Heikkuri, Vesa-Matti
Contributor: University of Helsinki, Faculty of Science
Degree program: Master 's Programme in Mathematics and Statistics
Specialisation: Mathematics and applied mathematics
Language: English
Acceptance year: 2022
This thesis studies equilibrium in a continuous-time overlapping generations (OLG) model. OLG models are used in economics to study the effect of demographics and life-cycle behavior on macroeconomic variables such as the interest rate and aggregate investment. These models are typically set in discrete time but continuous-time versions have also received attention recently for their desirable properties. Competitive equilibrium in a continuous-time OLG model can be represented as a solution to an integral equation. This equation is linear in the special case of logarithmic utility function. This thesis provides the necessary and sufficient conditions under which the linear equation is a convolution type integral equation and derives a distributional solution using Fourier transform. We also show that the operator norm of the integral operator is not generally less than one. Hence, the equation cannot be solved using Neumann series. However, in a special case the distributional solution is characterized by a geometric series on the Fourier side when the operator norm is equal to one.
Keyword(s): Economic theory integral equation convolution equation

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