ABSTRACT
Prior to the publication of Sargent and Wallace (1973), monetary growth models with perfect foresight were plagued by a well-known instability problem. 1 The problem may be seen most clearly in the simplest case in which output and the real rate of interest are treated as exogenous and the money supply is held constant. In this case, under the assumption that movements in the price level are continuous, a model of price dynamics in which money market equilibrium depends negatively on inflationary expectations, and in which perfect foresight and continuous market clearing are assumed, gives rise to a unique steady state equilibrium which is globally unstable. The following log linear specification for the demand for real balances is used by Sargent and Wallace to illustrate the point: https://www.w3.org/1998/Math/MathML"> 1 n ( M P ) = α π , α < 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203805763/00e1d30c-706a-4d0b-9f85-a9a5ef1cb61e/content/eqn6_1a_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where M denotes the stock of money, P the price level, and π the expected rate of inflation. If it is assumed that the relation (6.1) holds continuously, and that expectations are characterized by perfect foresight, then (6.1) may be written as: https://www.w3.org/1998/Math/MathML"> p ˙ = ( 1 / α ) [ m − p ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203805763/00e1d30c-706a-4d0b-9f85-a9a5ef1cb61e/content/eqn6_1a_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where lower case letters denote logarithms. Since α is negative, this onedimensional linear differential equation implies global instability of its steady state: a slight perturbation away from equilibrium triggers a process of everaccelerating inflation or deflation, if it is assumed that the price level moves continuously in the face of shocks to the money supply. We have the paradoxical result that a sudden increase in the money supply sets off an ever-accelerating deflation. Likewise, a downward shift in the money supply leads to accelerating inflation.
