• Bilateral oligopoly theory (the math)

    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.

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    • I appreciate your efforts to deconstruct the components of health care cost with this post and prior posts on pricing.
      However, I fear that you are going to be frustrated in the same way that nutritionists are when they discover “vitamins” or “fats” and try to explain human health in terms of these components. These are very complex systems and I fear that attempts to deconstruct them into components to explain cause and effect will be difficult.
      I would prefer to take a systems view where we look at other complex systems which have approached this problem more successfully. We can look at the health system of all of the other OECD “developed” countries as well as a few “developing” countries for examples of how to achieve better health at much lower cost.
      For instance, Switzerland has a health system that is similar to what we are trying to create in the US. They have mandatory coverage through private insurers. However, they also have strong regulation of prices and services which keeps their costs at less than half of ours with much better access and quality. Your current discussion of hospitals and insurers does not include the effects of government regulation which could squash the entire curve down to something we could afford.

    • If Republicans ever decide to pass their plan for selling across state borders, this is pretty important stuff to work out.


      • @steve – It’s possible to have theory that can’t be put into tractable mathematical form without overly simplistic assumptions. This may be an example. In that case, we just have qualitative, stylized facts that are generally agreed upon. If they’re supported by empirical work, they’re of some use. After all, the whole point is to make the math come out as we expect given our qualitative ideas about what we think is right (informed by observation and data, of course). The only thing lacking when it can’t be put into math is the ability to use mathematics to make additional predictions and to inform empirical work. That is a loss.

        Perhaps this is an area for computational theory: using computers to simulate outcomes given certain assumptions and presumed dynamics.