The conclusion that, to assert anything of the real world, it must be considered a synthetic a posteriori statement is a straightforward and logical requirement.
Nevertheless, how is the law of demand “proved” in neoclassical economics?
I review what Steve Keen says in Chapter 3 of Debunking Economics: The Naked Emperor Dethroned? (rev. edn. 2011). pp. 38–73.
The whole point of the law of demand is that the ceteris paribus assumption entails that all other factors except price are held constant: incomes, prices of other goods, fashions, expectations, information, preferences/tastes, population, the weather, etc.
A crucial question arises about the changes in income. Is this nominal income or real income? As Keen notes, a fall in the price of any one good increases real income and the ability to buy other goods (Keen 2011: 47). The important concepts here are the “income effect” and “substitution effect.”
The “substitution effect” is the substitution of one good for another that arises from changes in their relative prices but where the total utility of consumers is left constant (that is, if there were a compensating transfer of income). This is supposed to isolate the impact of a change in relative prices from the income effect. When a good’s price falls, demand for it increases partly because it is cheaper relative to other goods for which it is a substitute. Along with the income effect, this is supposed to explain why demand curves are downward sloping.
“The always negative substitution effect is the phenomenon economists are trying to isolate with the demand curve, to establish what they call the ‘Law of Demand’ – that demand always increases when price falls. This ‘law’ is an essential element of the neoclassical model of how prices are set, which says that in competitive markets, supply will equal demand at the equilibrium price. For this model to work, it’s vital that there is only one price at which that happens, so it’s vital for the model that demand always increases as price falls (and similarly that supply always rises as price rises).But this “proof” seems devoid of any actual empirical demonstration that the law of demand is true. It is a theoretical or purely logical proof. In other words, it seems to be retreating into a world of analytic a priori statements and deduction, which can hardly prove a synthetic a posteriori statement.
However the income effect can get in the way.
Economists thus found it necessary to search for a way to divide the impact of any change in price into the income effect and the substitution effect. If the income effect could be subtracted from a price change, this would leave the substitution effect as the pure impact on consumption of a change in relative prices. The problem is, though, that neither the ‘income effect’ nor the ‘substitution effect’ is directly observable: all we actually see is a consumer’s purchases changing as the price of a commodity changes.
Economists dreamt up a way of at least notionally subtracting the income effect from a price change, using indifference curves. The clue is that, with income fixed and price falling, the lower price lets a consumer enjoy a higher effective standard of living – which in their model was manifested by the consumer reaching a higher indifference curve.
Since, to an economist, the real object of individual behavior is utility maximization, and since any point on a single indifference curve generates the same utility as any other point, then in utility terms the consumer’s ‘psychic income’ is constant along this curve.
The substitution effect of a price fall could thus be isolated by ‘holding the consumer’s utility constant’ by keeping him to the same indifference curve, and rotating the budget constraint to reflect the new relative price regime. This amounts to reducing the consumer's income until such time as he can achieve the same level of satisfaction as before, but with a different combination of biscuits and bananas. Then the budget constraint is moved out to restore the consumer’s income to its actual level and, voile, we have separated the impact of a price change into the substitution and income effects.
The demand curve derived from neutralizing the income effect is known as the ‘Hicksian compensated demand curve,’ after both the person who first dreamed it up (the English economist John Hicks) and the procedure used. It finally establishes the ‘Law of Demand’ for a single, isolated consumer: the demand for a commodity will rise if its price falls. ….
Nonetheless, the end result is that desired by economists: increasing a product’s price will reduce a consumer’s demand for that product: an individual’s demand curve slopes downwards. The ‘Law of Demand’ holds for a single consumer.” (Keen 2011: 48–49).
And, when neoclassical economics moves from an abstract one person, two-commodity world to a two-person, two-community world (and anything even more complex), market demand curves do not necessarily obey the law of demand (Keen 2011: 51–53).
The Sonnenschein-Mantel-Debreu theorem (coined from the surnames of Gérard Debreu, Rolf Ricardo Mantel, and Hugo Freund Sonnenschein) describes the finding of higher-level neoclassical research literature itself that the law of demand does not necessarily apply to market demand curves (Keen 2011: 52; Gorman 1953; Debreu 1974; Sonnenschein 1972; Shafer and Sonnenschein 1982). As noted above, Steve Keen demonstrates how the law of demand can be proven only in the case of a single consumer (Keen 2011: 51). A market demand curve “can take any shape at all – except one that doubles back on itself” (Keen 2011: 52).
Attempts to prove that market demand curves will always behave like individual demand curves fail, and this was demonstrated when neoclassical economists were forced to state the conditions under which the law of demand could govern the behaviour of market demand curves. These conditions are as follows:
(1) that all Engel curves are straight lines;Empirically, we can see these conditions do not apply to any complex, real world economy. Both conditions are unrealistic, and demonstrate that
This is tantamount to saying either that the ratio in which a person consumes goods must be fixed regardless of income, or that there is only one commodity in the economy.
(2) that the Engel curves of all consumers are parallel;
This is tantamount to saying either that all consumers have identical tastes, or that there is only one consumer. (Keen 2011: 54–55).
“… the real meaning of these two conditions [sc. is]: the Law of Demand will apply if, and only if, there is only one commodity and only one consumer. But in such a situation, the very idea of a ‘Law of Demand’ makes no sense. The whole purpose of the Law of Demand is to explain how relative prices are set, but if there is just one commodity and one consumer, then there can be no relative prices. We have a contradiction: we start from assuming that the Law of Demand applies, and then find that for this to be true, there can be only one commodity and one consumer – a situation in which the Law of Demand has no meaning.” (Keen 2011: 55).Alternatively, one could also say that the law of demand is an analytic a priori statement that is informationally vacuous, and tells us nothing necessarily true of the real world, because it is a tautology.
Keen goes on to note that much of the literature on the law of demand and market demand curves:
“… was developed not to explain an empirically observed phenomenon, but to examine the logical coherence of an utterly abstract, non-empirical model of consumer behavior. Downward-sloping demand curves were therefore not an empirical regularity for which a theory was needed, but a belief that economists had about the nature of demand that the vast majority of them took for granted. Most of them continue to hold this belief, unaware that mathematically erudite economists have shown that it is false. Since the underlying discipline is non-empirical, there is no disconnect between theory and reality that might warn them that something is wrong with the theory.” (Keen 2011: 63).The role of mathematics in neoclassical economics should be stressed here: pure mathematics is an analytic a priori system. So what we have is an unrealistic analytic a priori mathematised economics that assumes reality fits its theory – when the opposite is the case.
Finally, the finding that the aggregation of the demand curves of isolated consumers does not create a well-behaved market demand curve is an important instance of the concept of emergent properties and the fallacy of strong reductionism:
“despite its adherence to strong reductionism, neoclassical economics provides one of the best examples of emergent phenomena ever: the ‘Sonnenschein-Mantel-Debreu conditions’ … . This research proved that a market demand curve derived from the preferences of individual consumers who in isolation obeyed the Law of Demand – i.e., they had ‘downward-sloping demand curves’ – will not obey the Law of Demand: a market demand curve can have any shape at all.” (Keen 2011: 208).In the end, the only satisfactory formulation of the “law of demand” is as a general empirical principle, or synthetic a posteriori statement, to the effect that for many goods (but not all), when the price falls, demand increases (though there are important exceptions).
And for many goods (but not all), when the price rises, demand falls (though there are important exceptions). But, at that point, one wonders why it should be called “a law” at all.
An equally important consequence is that there is no reason to assume equilibrium prices can be found in all markets, which further undermines the basis of neoclassical general equilibrium theory and the Austrian economic notion of effective economic coordination by flexible prices.
The technical “law of demand,” with its ceteris paribus condition, seems to remain a strange analytic a priori statement of marginal relevance to the real world, given that its proof consists in inventing an imaginary world with only one consumer and one commodity.
Syll, Lars P. 2012. “Please say after me – Sonnenschein-Mantel-Debreu,” Lars P. Syll, 21 July.
“‘Debunking Economics,’ Part I: Demand Curves Can Have Any Shape,” Unlearning Economics, June 25, 2012.
“Debunking Economics, Part XVII: Response to Criticisms (1/2),” Unlearning Economics, December 3, 2012.
Robert Vienneau, “Response to Comments on Steve Keen’s Work,” Thoughts on Economics, July 25, 2006.
Steve Keen, “Neoclassical Economists don’t understand Neoclassical Economics,” Debtdeflation.com, July 13th, 2011.
Debreu, G. 1974. “Excess Demand Functions,” Journal of Mathematical Economics 1: 15–21.
Gorman, W. M. 1953. “Community Preference Fields,” Econometrica 21.1: 63–80.
Keen, Steve. 2011. Debunking Economics: The Naked Emperor Dethroned? (rev. and expanded edn). Zed Books, London and New York.
Mantel, R. 1976. “Homothetic Preferences and Community Excess Demand Functions,” Journal of Economic Theory 12: 197–201.
Shafer, W. and H. Sonnenschein. 1982. “Market Demand and Excess Demand Functions,” in K. Arrow and M. Intriligator (eds.), Handbook of Mathematical Economics (vol. 2). Elsevier, Amsterdam. 671–693.
Sippel, R. 1997. “An Experiment on the Pure Theory of Consumer Behaviour,” Economic Journal 107: 1431–1444.
Sonnenschein, H. 1972. “Market Excess Demand Functions,” Econometrica 40: 549–563.