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. This paper is available on arxiv under CC 4.0 license. Xinyu Li, University of Washington. 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 and Introduction Abstract and Introduction 2. Method and 2.1. G is constant 2. Method and 2.1. G is constant 2.2. Linear Relation between G and I 2.2. Linear Relation between G and I 2.3. Nonlinear Quadratic Relation between G and I 2.3. Nonlinear Quadratic Relation between G and I 3. Results 3. Results 4. Conclusion and References 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. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Part of HackerNoon's growing list of open-source research papers, promoting free access to academic material.

Bifurcation Analysis of the Keynesian Cross Model: Results

Bifurcation Analysis of the Keynesian Cross Model: Method and G is constant

Keynesian.TECH

Too Long; Didn't Read

Boost your HackerNoon story @ $159.99! 🚀

Bifurcation Analysis of the Keynesian Cross Model: Abstract and Introduction

About Author

Comments

TOPICS

THIS ARTICLE WAS FEATURED IN

Related Stories

Untitled Story

A Beginner's Guide to Homology

Bifurcation Analysis of the Keynesian Cross Model: Conclusion and References

Bifurcation Analysis of the Keynesian Cross Model: Method and G is constant

Bifurcation Analysis of the Keynesian Cross Model: Results

Why New Keynesian Economics Needs a Stochastic Overhaul

A Beginner's Guide to Homology

Bifurcation Analysis of the Keynesian Cross Model: Conclusion and References

Bifurcation Analysis of the Keynesian Cross Model: Method and G is constant

Bifurcation Analysis of the Keynesian Cross Model: Results

Why New Keynesian Economics Needs a Stochastic Overhaul

Light-Mode

Classic

Newspaper

Dark-Mode

Neon Noir

Minty

HN StartUps