Effects of Incorporating Double Time Delays in an Investment Savings-Liquidity Preference Money Supply (IS-LM) Model

Abstract

The Investment Savings-Liquidity preference Money supply (IS-LM) model is represented as a graph depicting the intersection of products and the money market. It elaborates how an equilibrium of money supply versus interest rates may keep the economy in control. In this paper, we combine the basic business cycle IS-LM model with Kaldor’s growth model in order to create an augmented model. The IS-LM model, when coupled with a certain economics expansion (in our instance, the Kaldor–Kalecki Business Cycle Model), provides a comprehensive description of a developing but robust economy. Right after the introduction of capital stock into the system, it cannot be employed and also, while making some investment choices, this requires some time in execution, which ultimately alters resources, i.e. capital. Thus, in the capital accumulation, we will be incorporating double time delays in Gross product and Capital Stock. These time delays represent the time periods during which investment decisions were made and executed and the time spent in order for the capital to be put to productive use. After formulating a mathematical model using delayed differential equations, dynamic functioning of the system around equilibrium point is examined where three instances appeared based on time delays. These cases are: when both delays are not in action, when only one delay is in action and when both delays are in action. It is shown that time delay affects the stability of the equilibrium point and, as the delay crosses a critical point, Hopf bifurcation exists. It is observed that by using Kaldor type investment function, the delay residing in capital stock only will destabilize in less time as compared to when both the delays are present in the system. The system is sensitive to certain parameters which is also analyzed in this work.