Inspecting the stability of non-linear IS-LM model with dual time delay

Abstract

Capital stock is a strong pillar in the macroeconomics paradigm and plays a significant role when dealing with macroeconomic problems. Also, implementation of the investment decisions and employment of capital into productive use are two ignored time delays in accumulation of capital. Hence, a mathematical model with dual time delays in capital accumulation is formulated in this work. Furthermore, by adhering to functions that do not follow regularity, i.e., considering non-linear functional forms will not only influence policy making but also broaden our viewpoint towards realistic scenarios. Therefore, non-linear functional forms for investment, liquidity preference and government expenditure are considered. First, the equilibrium point is established, which is unique in this case. For analysing stability around the equilibrium point, the work is divided into three delay-dependent cases. When the time delay reaches a critical value, the complex dynamics of the system, such as stability switches and Hopf bifurcation, are investigated. The system is sensitive to a few parameters, such as depreciation rate, propensity to invest in capital stock, and average tax rate. The behavioural change is observed by altering these parameters. This study establishes a time limit within which the available capital for production should be put to productive use, and investment decisions should be made, which will aid in effective policymaking.