Nonlinear Multiplier-Accelerator Model with Investmetment and Consumption Delays

This paper shows how cyclic dynamics of national income and emerge in the multiplier-accelerator model with continuous time scale when delays in investment and consumption are presented. An S-shaped functional form of investment and linear consumption function are adopted to illustrate the phenomenon and to compute the stability-swithcing curves on whivch a stability gain or loss occurs. Assuming that the equilibrium national income is locally stable iif there are no delyas, it is demonstrated that one delay is harmless and with two delays, the system can produce limit cycles and the stability switch repeatedly occurs when one of the delays increased and the other is kept to be positive constant