Abstract
In this paper, we study a class of business cycle models related to the relationship between the gross product and the capital stock. The model is extended by adding general terms of the investment and the saving functions. In addition, a time delay which is represented an expectation and time lag for investment is also added into the model. The aim for this work is to find the sufficient conditions in which the model's solution is periodic. We study the existence of unique positive equilibrium. Next, the linearization method is used to analyze local behavior of the model. In addition, by considering time delay as a bifurcation parameter, we investigate sufficient conditions for the existence of a Hopf bifurcation of the model. Our results are applied to represent conditions for an occurrence of business cycles, which can happen in many business situations. Finally, some numerical simulations are illustrated to support our theoretical results.
Highlights
Business cycle is an economic behavior which is fluctuations of macroeconomic variables caused by uncertainty of business systems
In this paper, we study a class of business cycle models related to the relationship between the gross product and the capital stock
This paper is focused on the usage of mathematical theorems and methods to study factors that cause the business cycle related to the relation between the gross product and the capital stock
Summary
Business cycle is an economic behavior which is fluctuations of macroeconomic variables caused by uncertainty of business systems. In 1940, Kaldor [2] presented mechanisms of cyclic fluctuations for a business cycle model with nonlinear investment and saving functions, which are important in economical analysis. Note that model (1) is usually called the Kaldor-Kalecki model to explain business cycle related to the gross products and the capital stocks. In 1994, the Kaldor-Kalecki model (1) was improved by Grasman and Wentzel [4] by adding a linear saving function on the change rate of the capital stock. We study a class of business cycle model, which called the Kaldor-Kalecki business cycle model with time delays and an impact of expected capital stock on the current investment decisions. We illustrate numerical simulations to support the analytical results
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