Technical rambly post.
So last night I started reading MWG on microeconomics. One of the things which struck me was their use of a rather artificial-feeling mathematical framework, with consumption being a function of prices (a vector in an L-dimensional space) and of wealth (a single real number). Various bits of math follow from the statement that consumption is homogenous of degree zero as a function of these two sets of variables, which is just the statement that prices are only meaningful relative to overall wealth.
What’s a bit unnatural is the division of price and wealth into two separate variables, and the equations all reflect this. It seems a great deal more natural to merge these into an L+1-dimensional vector, with “commodity zero” being money. This is nice both mathematically (the equations are suddenly a lot more compact) and conceptually (it makes it a lot easier to think about, say, multiple kinds of money flowing around in a system) The Walras axiom then takes the form that the aggregate consumption of money over time is equal to total wealth, i.e. ultimately people spend all of their money.
But this led me to two questions which I think still need some pondering.
- In this context, the Walras axiom no longer seems so obvious, especially when you consider that there could be multiple “money-like” commodities in the system. What is special about money that causes people to ultimately spend all of it? In a utility model, I could see that money would be a utility-zero commodity, so if there’s anything with positive value to spend it on you would probably do so. (At least, so long as all interactions are linear — but I think that you can prove that they always are) But this non-obviousness suggests that there may be a more interesting way to phrase the axiom which ties more directly to the way that people relate to money.
- Once you start to treat money as Yet Another Commodity, the arbitrariness of using it as the scale for all the other variables seems significantly more obvious. Not in the moral sense, where it was pretty obvious to begin with, but simply mathematically; the choice of a preferred axis in commodity space seems almost perverse. One interesting alternative way to model things (which fits more naturally with choice models) would be to think about pairwise exchange costs rather than overall numerical costs — i.e., to think of everything as barter, with money simply a highly fungible good. What’s interesting is that this is significantly more general than numerical costs, in the same way that choice models are more general than preference models; it lets you model things such as nonfungible goods. (Money can buy time, but can’t necessarily buy loyalty; on the other hand, loyalty can buy loyalty) I suspect that there are some interesting techniques possible here — has this area been explored?