Two Mathematical Models of Inequality in Economics

Open Access
Author:
Battaglia, Emily Louise
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Christopher H Griffin, Thesis Supervisor
  • Victoria V Sadovskaya, Honors Advisor
Keywords:
  • Income Inequality
  • Solow Model
  • Agent-based Model
Abstract:
The issues surrounding income inequality are a topic that has garnered a lot of attention in recent years. Since the mid-1980s, the United States has become the most unequal of the advanced industrial countries, with income inequality growing at a pace that has not been seen since the Great Depression. With increasing income inequality, the potential benefits and harms become more widely debated. Robert Reich, former United States Secretary of Labor under President Bill Clinton, argues that income inequality impedes the buying power of the middle class while simultaneously allowing the upper class to store more of its wealth, rather than spend it. This thesis studies Reich's claim that income inequality is a fundamental detriment to growth. Income inequality is primarily studied in this thesis through two different lenses: a macro Solow model and a micro agent-based model. Once the theoretical foundation of each model is formulated, the models are used to run simulations to qualitatively examine income inequality. Our results from the Solow model show that in the presence of income inequality, the per capita capital of the wealthiest continues to rise, while the per capita capital of the middle class remains stagnant and the per capita capital of the lower class decreases. The agent-based model shows that the savings of the poor and middle classes are stagnant with inequality, while the savings of the rich continues to rise.