Three essays in mathematical economics
Abstract
Essay I formulates and analyzes a two-sector economic growth model. People can invest in capital or schooling and enjoy localized learning-by-doing effects. Necessary and sufficient conditions for optimality are given. Both the steady state and the path to it are unique. The influence of various factors, like depreciation, adjustment costs and population growth, on both the steady state and the speed of convergence is investigated. The system is locally and, under a certain condition, globally asymptotically stable. A comparison with the one-sector growth model is made. Essay II gives a non-technical literature review on allocation mechanisms. Special attention is given to incentive compatibility and informational efficiency. This serves as background material to essay III. In essay III a certain reallocation process is proposed. People are not omniscient and are risk averse in a certain sense. Some conditions for the process to be well-defined and have favourable outcomes are discussed. We introduce a "natural" measure of risk aversion in this situation and compare it to the one known from the literature, namely Arrow-Pratt risk aversion. A necessary and sufficient condition for a change in the Arrow-Pratt measure to coincide with a change in our measure is derived. By lying more people can gain up to a certain point. Some experimental data are discussed. It is suggested that more freedom leads to more reallocations and to lower scores; furthermore, that women are more risk averse than men and have higher scores. Finally, it is claimed that people are dishonest and leave room for deterioration.
Degree
Ph.D.
Advisors
Moore, Purdue University.
Subject Area
Economic theory
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