Analysis of Economic Models Through Calculus of Variations

• Main Author: Arora, Raman
• Format: Others
• Published: TopSCHOLAR® 2005
• Subjects: Economics; Mathematics
• Online Access: http://digitalcommons.wku.edu/theses/453; http://digitalcommons.wku.edu/cgi/viewcontent.cgi?article=1456&context=theses

This thesis is a combination of two science fields: Mathematics and Economics. Mathematics is often used to formulate a clear and concise solution to economic problems. In my observation calculus of variation has often been used in various macroeconomic problems. This mathematical method deals with maximizing or minimizing of various objective functions given a set of constraints. This topic brings out one of the best ways to show the relationship between mathematics and economics. My thesis consists of three parts: The first chapter contains a review of the calculus of variations. Basic definitions and important conditions have been stated. The aim of this chapter was to set the groundwork for understanding calculus of variations so that it can be used in solving various economics models. In the second chapter we study an economic model from which calculus of variations has been used to solve it. The macroeconomic model deals with optimizing the social welfare function. The entire working of the model has been discussed and documented in the thesis report. The third chapter deals with the analysis of the Lucas model which concentrated on how the accumulation of human capital impacts the growth rate of the economy. Lucas assumes that the growth rate of the human capital is linearly related to its level. If we abandon this assumption, will the optimal value of the time devoted to education in the steady state exist? If it exists, will it be same or different? So we introduced a new model in which the only modification we made to the Lucas model was in the equation that describes the process of human accumulation by introducing a nonlinear component. On investigation of this new model we have shown that it is possible that optimal behavior for an individual can be not to educate himself.