Dynamic models in disequilibrium theory

Abstract

The thesis offers various contributions to the formulation of dynamical disequilibrium models in economic theory. Until now static disequilibrium situations have usually been analyzed by assuming prices fixed so that equilibrium is obtained only by quantity adjustments. We consider in this work dynamical models, where the evolution of a rationed equilibrium economy through time is described by varations in both prices and quantities. Using Malinvaud's static macromodel as the starting point, we introduce in Chapter I a simple dynamization by requiring quantities to adjust infinitely fast to the equilibrium values. This implies that the evolution of the economy is determined by the evolution in prices. Explicit differential equations for the changes in prices are formulated, and a global stability theorem for the Walrasian (no rationing at all) equilibrium is obtained by assuming a specific behaviour on the boundary between the regions of Repressed inflation and Keynesian equilibrium. In Chapter II the model is changed by supposing quantities to adjust quickly, though not instantaneously, compared with prices. Assuming the differential equation describing the fast adjustment in quantities to depend smoothly on prices, we show that equilibria exhibit "exchange of stability" whenever the prices cross the boundary between two equilibrium regions in the parameter plane. Using methods from catastrophe theory a generic description of the long term evolution is obtained by introducing new "dual" equilibria in the quantity space and increasing the dimension of the parameter space by introducing parameters, which are usually "hidden" in the standard description. Chapter III is devoted to an extension of this result to a situation, where consumers may gain by saving money from one period to the next, a case excluded in Chapter II by an assumption on the consumer's money holdings being unchanged from period to period. The result is obtained by dividing the consumers into unemployed, spending the same fixed amount of unemployment benefit every period, and employed consumers, who are allowed to save. The results of changes in either the unemployment benefit or the government's demand are also considered. Finally Chapter IV is devoted to a specific analysis of the long term evolution in the neighbourhood of the Repressed inflation - Keynesian boundary. This analysis is necessary because of a discontinuity of the vector field describing the adjustments in prices on this boundary. Introducing timelags in agents' response to changes in prices we show how the discontinuous vector field gives rise to a smooth evolution around this boundary. Further, depending on the distribution of timelags, the economy exhibits either decreasing oscillations around the boundary eventually converging to zero, or (semi-)stable steady oscillations between the two regions. In this way the results contribute to a clarification of the claim that a basic feature of modem economies is the cycling motion between Repressed inflation and Keynesian equilibria