As promised, this post presents the math that follows from the bilateral oligopoly theory set-up I provided in an earlier post. Actually, it’s too much trouble to get the math into HTML so I’m providing it in a PDF file.
As I wrote in that prior post, you’ve got to really love this stuff to read the math. I hope those of you who fancy yourselves as theorists will read it. I really hope a professional economics theorist will read it and want to work on it, to do it right. If that doesn’t sound like you, skip the PDF and keep reading this post. For those who feel equipped to dig into the PDF, note that my treatment is very poor and assumes away the most interesting parts. I just can’t do any better because theory is not what I do.
In bending over backwards to convey how awful my theory is, I’m reminded of a passage from Surely You’re Joking, Mr. Feynman!, which is reproduced on Wikipedia:
While in Kyoto I tried to learn Japanese with a vengeance. I worked much harder at it, and got to a point where I could go around in taxis and do things. I took lessons from a Japanese man every day for an hour. One day he was teaching me the word for “see.” “All right,” he said. “You want to say, ‘May I see your garden?’ What do you say?” I made up a sentence with the word that I had just learned. “No, no!” he said. “When you say to someone, ‘Would you like to see my garden? you use the first ‘see.’ But when you want to see someone else’s garden, you must use another ‘see,’ which is more polite.” “Would you like to glance at my lousy garden?” is essentially what you’re saying in the first case, but when you want to look at the other fella’s garden, you have to say something like, “May I observe your gorgeous garden?” So there’s two different words you have to use. Then he gave me another one: “You go to a temple, and you want to look at the gardens…” I made up a sentence, this time with the polite “see.” “No, no!” he said. “In the temple, the gardens are much more elegant. So you have to say something that would be equivalent to ‘May I hang my eyes on your most exquisite gardens?” Three or four different words for one idea, because when I’m doing it, it’s miserable; when you’re doing it, it’s elegant.
With that, go ahead and glance at my lousy theory. Then, please make it better with your exquisitely beautiful theory upon which I would be honored to hang my eyes.
UPDATE: Another post on this follows.