An Active-Learning Approach to Visualising Multivariate Functions using Balloons

This hands-on multi-class exercise helps students with limited mathematical training better visualise how economists represent three-dimensional surfaces in two dimensions as indifference curves, isoquants and isoprofit contours using a balloon. Many students study microeconomics with limited formal mathematical training in analysing multivariate functions. Despite this weakness, the marginal analysis that is at the core of microeconomic analysis requires that we teach students to think in terms of marginal tradeoffs and to understand how these tradeoffs must be balanced to achieve an optimal outcome. One could use this exercise in introductory level classes by simply ignoring the calculus footnotes. The exercise protocol provides detailed instructions in PowerPoint slides for building the balloon as well as how to use the surface of the balloon to model economic concepts such as marginal product, the economic region of production, and marginal rate of technical substitution (and their consumer side counterparts). Instructions show students how to find and interpret a point where x is more valuable than y and to compare that with the reverse situation. This protocol concludes with instructions allowing students to analyse constrained optimisation visually including what the tangency condition implies regarding the marginal tradeoffs inherent in the constrained optimal solution.