DYNAMICS OF BUSINESS CYCLE MODELS WITH DELAYS IN INVESTMENT

Gaurav RAINA (University of Cambridge)

We analyse the stability properties of a class of business cycle models (in income and capital) which incorporate a constant gestation time period of investment. The time lag which represents the delay in the investment process gives rise to a coupled system of non-linear delayed-differential equations. We provide a unifying mathematical framework to identify and analyse the local stability conditions arising out of this class of dynamical systems. Previous models have emphasized the importance of the role played by the speed of reaction to the excess demand as a destabilizing factor. In a model with gestation time lags the duration of the time period also plays a very important role in maintaining stability: the dynamical system necessarily looses stability as the delay increases. Further, it is interesting to note that the lags can produce stable regimes which are unstable without delays. We also show that the system undergoes a Hopf bifurcation when local stability (in the presence of delays) is lost.