Equilibria in overlapping generations models

Abstract

Bibliography: pages vi-viii.Interest rates are fundamental in the explanation of equilibrium prices over time, because they provide the link between the present and the future. Capturing this dynamic feature, the overlapping generations model is particularly suitable to address the interest rate problem, as has been shown by Paul Samuelson, David Gale and Costas Azariadis. This thesis reviews their contribution to the theory of interest: with his consumption-loan model, Samuelson sets the analytical framework for subsequent research. Furthermore, he demonstrates that the optimal interest rate is unstable, implying that a competitive economy may fail to approach the social optimum. The Samuelson and classical sets of assumptions are consolidated in the intertemporal exchange model of Gale. Its equilibrium nature, however, ignores the sequential adjustment of disequilibrium interest rates to their equilibrium values. Consequently it is difficult to comment on the direction of causality involved in the interest rate determination, unless a clearing house is introduced which simultaneously resolves the starting-up, continuity and causality problems. Departing from the full certainty scenario, Azariadis analyses the existence and likelihood of self-fulfilling prophecies. It is shown that the implications of the economy's assumed Markovian structure are twofold: while facilitating the parametric treatment of the transition probabilities, it negates the question concerning the likelihood of sunspot equilibria. Within the specified framework it is impossible to explain how the economy arrives at such equilibria; it is only possible to identify the conditions that maintain (once they exist) these self-fulfilling prophecies