The first substantive chapterof Steve Keen’s book Debunking Economics explores the idea that the demand curve for a market does not necessarily slope downwards, as is the norm in economics textbooks. Instead, once you move past the individual level, then according to neoclassical principles a demand curve can have any shape at all, as long as it doesn’t double back or intersect itself.
This idea was first expounded by the (neoclassical) economist William Gorman in 1953. Gorman, on discovering this, went to great lengths to introduce assumptions that nullified the result, but these assumptions effectively amounted to assuming there was only one consumer, what Keen calls a ‘proof by contradiction:’ starting from an analysis of market demand curves, but eventually having to assume the demand curve is not for a market but for an individual. Keen does an impressive job of communicating this argument, which is obscurely and abstractly stated in Gorman’s paper.
Keen starts with the observation that price changes can have many different impacts, due to the interlinked nature of markets. Demand curves depend on the condition that income remains constant, so that we can study changes in price independent of other effects. However, if we consider somebody buying a ‘basket’ of goods, an increase in the price of one good might make another good unaffordable. The resultant boost in income (from not buying the second good) may well increase demand for the good whose price went up. The various interactions between goods depending on whether they are necessities, luxuries and so forth can create some interesting looking demand curves.
Economists are well aware of this problem, and have of course managed to assume it away! This is known as the Hicksian compensated demand function. I won’t go into too much detail here, but this involves adjusting income until utility is the same level as before, then allowing for adjustments in income. This allows us to separate out the ‘income effect’ (the one listed above) and ‘substitution effect’ (the ‘pure’ effect of price on demand).
The problem is that once you introduce more than one party to the economy, it is impossible to separate out changes in income from changes in demand, as one person’s spending is another’s income. This interplay between spending and income brings back all the problems glossed over by the Hicksian demand function. This is well documented, and known as the Sonnenschein–Mantel–Debreu theorem.
Naturally, economists have managed to assume this away, too. But here their assumptions jump the shark. Here is Gorman in his 1953 paper:
The necessary and sufficient condition quoted above is intuitively reasonable. It says, in effect, that an extra unit of purchasing power should be spent in the same way no matter to whom it is given.
Even when stated in this form, this is obviously not a reasonable proposition. If you give Peter money, he’s not going to spend it in the same way as Paul. It’s really that simple. However, Gorman is slightly disingenuous with this statement, as the real conditions are laid bare later on in the paper:
The older work of Allen and Bowley was based on the assumption that the classical Engel curves for difference individuals at the same prices were parallel straight lines, but this has been rejected in the more recent work of Houthakker in favour of a doubly logarithmic form. However, the earlier assumption fits the data remarkably well.
Keen points out that since all utility functions pass through (0,0) (zero consumption yields zero utility), and all parallel straight lines that pass through the same point are the same line, this amounts to an assumption that consumers are all exactly the same – effectively, that there is only one consumer.
In other words: the only way we can make a market demand curve the same as an individual demand curve, is if we assume that it is an individual demand curve. There is an obvious logical problem with this approach.
The funny thing about this chapter is that Keen concludes that, generally speaking, “there are reasonable grounds to expect that…demand will rise as price falls.” So why go to all the trouble?
The first reason is to show that ‘more is different’ – theories should not necessarily be built up from individual behaviour. Keen notes that the assumptions that all consumers are the same is only defensible if one analyses from the classical perspective of different classes, something the neoclassicists were trying to avoid.
The second reason is to show that, despite economist’s assertions to the contrary, it cannot be proved that a market economy will necessarily maximise social welfare, as, even on their own terms, it is logically possible to have multiple equilibria, some of which are more socially desirable.
The third reason is that the SMD conditions also establish that it is impossible to measure these things independent of the distribution of income, highlighting more general problems with neoclassical ceteris paribus analysis.
I myself experienced some cognitive dissonance when Keen came to that conclusion (I don’t know what it is about studying economics that creates this), but the fact is that this kind of logical inconsistency must be exposed, and, contra Friedman, this does not depend on whether the conclusions are completely sound or not. As I noted in my opening, these problems are all well documented by neoclassical economists themselves. So how can they excuse ignoring them?