Since I have been unable to find a simple mathematical model of monetary disequilibrium, I’ve been interested in putting on together. Mathematical models help people narrow down exactly where disagreements lie and make help make sure that their thinking isn’t confused. Since there’s a lot of disagreement and confusion in macroeconomics, I think simple mathematical models should be especially helpful here.
The model I’ve built consists of a large number of identical agents (I believe this is called a “representative agent” model) in an economy with two goods, backrubs and money. You can’t consume your own backrubs, so they have to be traded in a market, but it still makes sense to have a market for them. In this model, money provides utility by fascilitating trade, the more money agents have relative to the amount they’re buying the more utility they get. The utility of money can vary over time. I’ve described the model more in depth in my write up.
Most macro models I’ve seen start at too high a level, taking aggregate demand/supply, interest rates, etc. as basic concepts instead of utility functions and optimization. To be as clear as possible, I’ve tried to the model start from first principles as much as possible.
If you find an error or want to make a technical or non-technical suggestion, please let me know. Though the model is fairly simple (it uses only simple calculus), I haven’t done much economic modeling before, so I wouldn’t be very surprised to find errors.
I’ve written up the model here (LaTeX source). I also have an excel simulation of the model which I’m working on. I think it’s working right, but I haven’t checked it thoroughly yet (the draft is here). I’ll probably update these a bit in the future.