Completed what I wanted about monopoly and launched into imperfect competition and introduced the nash equilibrium. I follow the set up in the chapter of pricing from my pricing book with Lakshman Krishnamurthi. The novelty, if any, is to start with Bertrand competition, add capacity and then differentiation. I do this to highlight the different forces at play so that they are not obscured by the algebra of identifying reaction functions and finding where they cross. We’ll get to those later on. Midterm Day, 12. I am, as Enoch Powell once remarked in another, unattractive context,
…. filled with foreboding. Like the Roman, I seem to see “the River Tiber foaming with much blood”.
Much of my energy has been taken up with designing homework problems and a midterm exam on monopoly. Interesting questions are hard to come by. Those lying around make me want to make gnaw my feet off. I started with the assumption, which I may live to regret, that my students are capable of the mechanical and have good memories. The goal, instead, is to get them to put what they have learnt in class to use. Here is an example. Two upstream suppliers, A and B, who each supply an input to a Retailer. The Retailer is characterized by a production function that tells you how much output it generates from the inputs supplied by A and B as well as a demand curve for the final product. Fix the price set by B to, w, say. Now compute the price that A should charge to maximize profit. Its double marginalization with a twist. Suppose the inputs are substitutes for each other. If B raises its price above w what effect will that have on A’s profits? There are two effects. The retailers costs will go up of course, so reducing its output. However, A will retain a larger share of the smaller output. Which will be bigger? Its a question that requires them to put various pieces together. I’ve had them work up to it by solving the various pieces under different guises in different problems. Am I expecting too much? I’ll find out after the midterm. Yet, I cannot see anyway around having questions like this. What is the point of the mathematics we require them to use and know if we don’t ask them to apply it when blah-blah alone is insufficient?
I now have a modest store of such problems, but coming up with them has been devilish hard. Working out the solutions is painful, because it involves actual algebra and one cannot afford errors (on that account I’m behind the curve). To compound matters, one is unable to recycle the exam and homework problems given various sharing sites. I begin to regret not making them do just algebra.