Hopf Bifurcation in an Augmented IS-LM Linear Business Cycle Model with Two Time Delays

Abstract

This paper deals with the amalgamated basic IS-LM business cycle model with Kaldor’s growth model to form an augmented model. Pertaining to substantial evidence, IS-LM model in paradigm with a specific economic extension (Kaldor-Kalecki Business cycle model in our case) provides an adept explanation of a developing but strong economy like that of our country. Occurring in the equation of capital accumulation, the two time delays are a result of the assumption in the investment function being both income and capital stock dependent in past period and maturity period. Investigating a model combined with capital accumulation is both interesting and important. From economist point of view, production without capital is impossible to even imagine. Moreover capital accumulation is impeccable to large-scale production, specialisation and creation of employment opportunities. In our model ‘I’ the investment function, ‘S’ the savings function and ‘L’ the demand for money are depending linearly on their arguments. We adhere to a linear model, contrary to the popular belief of non- linear models being the undisputed style for modern economics. The model is first shown to be mathematically and economically poised. The local stability of boundary and interior equilibrium points has been investigated. Three cases arise, pertaining to two time delays. System dynamics exhibits mutation under the influence of time delays and may clinch or discharge its local stability when subjected to the latter. Hopf bifurcation occurs when the delay parameter crosses a critical value.

Keywords

• business cycle model
• time delay
• capital accumulation
• is-lm model
• hopf bifurcation