Bifurcation Analysis of the Keynesian Cross Model: Abstract and Introduction
:::info
Xinyu Li, University of Washington.
:::
Table of Links
Abstract and Introduction
2. Method and 2.1. G is constant
2.2. Linear Relation between G and I
2.3. Nonlinear Quadratic Relation between G and I
3. Results
4. Conclusion and References
Abstract
This study rigorously investigates the Keynesian cross model of a national economy with a focus on the dynamic relationship between government spending and economic equilibrium. The model consists of two ordinary differential equations regarding the rate of change of national income and the rate of consumer spending. Three dynamic relationships between national income and government spending are studied. This study aims to classify the stabilities of equilibrium states for the economy by discussing different cases of government spending. Furthermore, the implication of government spending on the national economy is investigated based on phase portraits and bifurcation analysis of the dynamical system in each scenario
1. Introduction
The original Keynesian model was first proposed to explain the persistent unemployment after the Great depression [1]. Since then, it has evolved into many modified models such as the neoclassical Keynesian model [2], the post Keynesian model [3], and the IS-LM model [4]. This paper focuses on one modification of the original Keynesian model – the Keynesian cross model [5].
\
In this paper, a simple model of a national economy is studied based on the Keynesian cross model. The model in this paper aims to quantify the dynamic relationship between national income and consumer spending, with special attention to the impact of government spending on economic stabilization. This paper applies bifurcation analysis, a technique commonly used in dynamical systems in mathematics, to investigate the dynamics between national income and consumer spending. The rest of the paper is organized as follows: Section 2 describes the methodology, variables, and the mathematics model used in this study; Results of the economic equilibrium are discussed in Section 2. Finally, Section 4 concludes the paper.
\
:::info
This paper is available on arxiv under CC 4.0 license.
:::
\
Welcome to Billionaire Club Co LLC, your gateway to a brand-new social media experience! Sign up today and dive into over 10,000 fresh daily articles and videos curated just for your enjoyment. Enjoy the ad free experience, unlimited content interactions, and get that coveted blue check verification—all for just $1 a month!
Account Frozen
Your account is frozen. You can still view content but cannot interact with it.
Please go to your settings to update your account status.
Open Profile Settings