Being an Econ Major Ain't What It Used to Be

It was once thought that the collegiate major in economics provided a fortress in which students who wanted a practical degree without facing tough mathematics could take shelter.



However, as exemplified by four new Maple applications created by Dr. Sanjay Paul of St. Norbert College, this fortress is falling to the cannon of modern economic theory.

Collegiate economics and finance curricula are fast becoming as quantitative as engineering. This is higher education's response to the demand from the financial industry for tools to understand the forces that determine seemingly random phenomena, such as stock prices, consumer demand, and interest rates. By "tools", one may read "mathematical models". A classic success story of a mathematical model of economics working its way into daily practice is the Black-Scholes model for pricing European options, which has also been implemented as a Maple application by David Pintur.

Perhaps contrary to the stereotype of the lazy undergrad, this trend is also in response to student demand. (It is a day to celebrate, indeed, when students cry out to learn more mathematics!) Students see huge career opportunities (i.e., salaries) for themselves in the financial institutions. In the absence of this opportunity, those students might have gone into engineering or science instead, taking their precious math skills with them.

One of Dr. Paul's applications explores the Solow Model of Economic Growth, which predicts a country's production in terms of the level of technology, capital stock, and labour. Using Maple's differential equation solver, this application derives the Solow model's prediction that per-capita economic growth tends to slow down over time. Here are some excerpts from the application (downloadable in complete form at www.maplesoft.com/apps/ categories/econ_fin_eng/economics/html/acecocon.htm).

According to the Solow model, the per-capita production function in terms of the capital-labour ratio (k) and technology level (A) is given by

> y:=A*k^(1/4):

The differential equation governing the change in the capital-labour ratio (after some parameter substitutions) is

> eq:=diff(k(t),t) - (s*A)*k(t)^(1/4) + (n+delta)*k(t)=0;



Using the dsolve command for solving differential equations, obtain the time path of capital-labour ratio.

> soln:= dsolve({eq,ini},{k(t)},
type=numeric):

> odeplot(soln, [t,k(t)], 0..200,
axes=BOXED, title=`Growth of k`);



Thus, the Solow model predicts a slow down in economic growth over time.