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Using Mathematica Animations to Teach Undergraduate Economics

Craig Marcott
University of St. Thomas

This presentation will demonstrate several of the author's Mathematica notebooks and packages that feature animated diagrammatic economic models. The animations have been successful in engaging students who are naturally reluctant to confront difficult material. Active learning is encouraged by allowing students to change parameters, and simple VCR-like controls can be used to change animation direction and speed. The animations make fairly complicated ideas (e.g., the Slutsky equation, Jacob Viner's problem) visually apparent to quantitatively unsophisticated students. The long-term goal of the project is to provide animated versions of most of the diagrams included in introductory and intermediate microeconomics and macroeconomics courses. Over two hundred animations have already been written covering topics such as cost and production, consumer choice, circular flow, the Slutsky equation, labor economics, macroeconomics, expected utility, the competitive model, income inequality, and welfare economics. Approximately 60 animations can be viewed at http://milkweed.econ.stthomas.edu/~csmarcot/my.html. This web page also provides a link to download MathReader, a free program that can be used to view the notebooks and render the animations.

One example of an animation that has been used effectively in class is the standard competitive model showing the market and the unit-cost curves of a representative firm. This is augmented with two additional quadrants showing the budget-line indifference curve diagram and demand curve for a representative consumer. The animations show the short- and long-run effects of demand shifts and changes in production costs. A second example shows how the expected utility model relates to the standard indifference curve analysis (i.e., the Arrow-Debreu contingent claims approach to uncertainty).

By studying animations showing the expected utility diagram directly above the indifference curve diagram, the user can visualize how changes in the probability of ending up in the bad state of the world correspond to changes in the shape the indifference curves. Linking the von Neumann-Morgenstern utility and classical indifference curve approaches in this way makes it easier to understand how insurance demand is related to risk aversion. This construct is used to demonstrate Arrow's result that risk-averse individuals will always choose full insurance whenever the insurance contract is actuarially fair.

The animated graphics discussed in this paper show promise for improving introductory and intermediate undergraduate students' understanding of graphical economic models. Anecdotal evidence indicates that students enjoy using the animations both in class and in the laboratory. Currently, these tools are freely available to anyone with a computer and with internet access. Licensed Mathematica users can obtain the code from the author and use the notebooks and packages to generate animations for different sets of parameters.