Using the COVID-19 vaccine to teach constrained optimization in Econ 101

When encountering constrained optimization for the first time, students often find the concepts of objective functions, resource constraints, and Lagrangians a far cry from the dynamic world of business that they are eager to enter. This note offers an example of how the classroom teaching of constrained optimization can be made more interesting, relevant, and accessible to students by drawing on the recent experience of COVID-19 and the real problem of allocating vaccine in the initial stages of its rollout. The paper advocates a diagrammatic rather than a technical introduction to constrained optimization for first-year students. It outlines how the problem of vaccine allocation can be framed, simplified, and then dealt with in a series of intuitively appealing cases with associated diagrams. While no formal mathematical solutions are offered, students are nonetheless introduced to mathematical optimization notation so that later treatments of the topic become easier and more natural for them. The paper does not pretend to offer a solution to what in the real world was a very complicated problem. What it does do is to simplify the problem in a way that maintains its main features but makes it tractable for students to understand, and enables them to see the principles of constrained optimization in operation.