Monday, January 18, 2016

Samuelson pointed out a long time ago that, if people like more sugar with their tea than with their coffee and coffee and tea are strong substitutes, coffee and sugar might be substitutes as defined in the usual practically measurable ways (or, alternatively, in terms of the sign of the mixed partial derivative of the cost-of-utility function).  When we talk about "substitutes", we usually have something a bit different in mind, though; something causal, even; coffee and sugar are complements in some direct sense.  (So especially in terms of a smooth, convex cost-of-utility function c(u,pc,ps,pt) where the envelope theorem gives qi=∂ c/∂ pi and you're looking at second partials with respect to prices, it seems likely to me that holding something other than pt fixed might capture this; qt is the obvious alternative, and I'm currently leaning to the idea that that's correct, though not because I think "holding other quantities constant" is the way I'd want to tell the story.)

What makes complements and substitutes a valuable tool in the economic toolbox is that 1) they're relatively intuitive ideas, and 2) they are useful for efficient reasoning in many situations of economic interest; even in the above situation, at least in the hard-to-define sense that coffee and sugar are complements, these both largely hold, as evidenced by the fact that I wrote the first sentence of this email without appeals to detailed algebra or even long-winded explanations --- you understand intuitively that coffee and sugar are complements, and you understand why a price increase in one might yet lead to an increase in demand for the other, with this latter understanding fully driven by a recognition of other complementarities and substitutions.

I think the same is true of supply and demand; if you look at the factors that affect price and quantity, often the important ones can be fairly cleanly categorized as "demand-side" or "supply-side" and you can increase your chances of understanding a market by making that separation.  When you get heavily asymmetric information or liquidity issues or the like, supply-and-demand models become less clean — though, perhaps all the more compelling, are still certainly useful in guiding thought, even as you have to be a bit more attentive to how the whole system is behaving.  Supply-and-demand reasoning is a useful thing to teach to freshmen, not necessarily because there's a deep theoretical reason they would have to work as well as they do, but for the twin reasons that, in our real world, (1) they often work quite well, and (2) many adults young and old have folk-economic ideas for which supply-and-demand reasoning is far more often to lead to fewer mistakes rather than more confusion.