Structured Problem-Solving in Class

Microeconomics: Concepts and Results

"I use Mathematica often for everything from calculating economic examples to sophisticated statistical analysis. These exercises are both valuable in themselves and an attempt to introduce the students to this wonderful analytic tool."

Hal R. Varian
University of California, Berkeley

After reading various press accounts about Mathematica, Hal Varian got his first glimpse of it at a conference in 1990 where he was able to play with it out of "just idle curiosity." Impressed by its ease of use, he began to see how he might use it in his research and teaching in microeconomics. That was the beginning of what has developed into a long relationship with Mathematica and the Mathematica community.

Enriching Text with Technology

Now, Hal Varian is Dean of the School of Information Management and Systems and Professor of Economics and Business at the University of California at Berkeley. He is the author of Microeconomic Analysis, a major graduate textbook first published in 1978. On sabbatical after the third edition appeared in 1992, he began experimenting with Mathematica notebooks based on the book's chapters--"just to see what its capabilities were," he says. "Every time I saw something that looked amenable to Mathematica, I put it in." Pleased with the result, Varian introduced this courseware to his students as a tutorial or study tool, what he calls a "suggested ancillary." Subsequently he has edited two other books in this area, Economic and Financial Modeling with Mathematica and Computational Economics and Finance: Modeling and Analysis with Mathematica.

Tackling Every Angle

About 50 first-year graduate students per year enrolled in Varian's microeconomics course during the early 90s when he began using his Mathematica courseware in the department's computer lab. He covered many topics, including the following:

• Functional Forms
• Integrability Theory
• Game Theory
• Profit Maximization
• Econometrics and Statistics
• Oligopoly Games
• Cost, Minimization, and Supply and Demand
• Systems of Equations
• Utility Maximization
• Monopoly

The microeconomics courseware uses straight Mathematica, with no special functions or commands, and makes extensive use of graphics. Its notebooks are "tied into the textbook fairly tightly," Varian says. They are not intended to be stand-alone lessons. "We're trying to get people to look at problems mathematically, graphically, and analytically," he explains. "Several of the notebooks draw pictures of different functions and see what happens, by changing the parameters and so on. It's easy to do this with Mathematica." These notebooks help students visualize optimization problems, equilibrium conditions, and econometric analyses. One involving "integrability theory," for example, solves differential equations, while another determines the optimal play in economic games.

Each week, students attend three hours of classes plus a 90-minute meeting in which they solve problems and do exercises. Those who choose to use the ancillary Mathematica courseware proceed at their own pace without scheduled computer labs. Most have no previous experience using the program, which they learn through various Mathematica tutorials.

Although Varian's duties as dean now preclude his day-to-day involvement in teaching graduate microeconomics, he hopes that others will be able to pick up where he left off and further develop these materials.

Contact Information
Dr. Hal R. Varian
University of California, Berkeley
web: http://www.sims.berkeley.edu/~hal
Send email to Hal Varian