The pleasure of teaching the Stackelberg model

The Stackelberg model is one of the components of what is called Industrial Organization, the microeconomic study of imperfect competition by oligopolies and monopolies. Its name may not tell much to a random reader, but the students and professionals of economics have probably heard about it. I would not say that it is a very useful model, except to understand some properties of models of market power. However, its two firm version seems to me a masterpiece of rigour and precision. Of course, there are many similar models in economics (probably not all of them are as useless). When one has enough calm to prepare it, it becomes such a pleasure to explain it, bit by bit, slowly (as I did today in a course I'm teaching in Colombia these days). What I do is first to explain the mathematics of it, and next I draw a graph with all the details. Somehow, the graph becomes as complex if not more as the maths. First one has to draw the reaction functions of each firm in a surface where the axes are the quantities of a leader and a follower firm. Then one explains why the profits of the leading firm can be represented by concave curves where the direction of more profits in down to the right, and why these so-called iso-profit curves have their maximum on the reaction function of the leader. Then one has to show that the point of the Stackelberg equilibrium is the point of the follower's reaction function that touches the best possible iso-profit curve. The whole thing does not finish until one shows that unless the quantities are interpreted as capacities, or unless the leader has a way to credibly commit to the Stackelberg quantity, the whole thing collapses to another equilibrium, the Cournot equilibrium, where the leader ends up with less profits. I apologize for not reporting about something that any reader can understand, but other academics will understand the pleasure of teaching slightly complex things that, unlike reality, are clear and precise.