Despite the apparent science behind the construction of indifference curves, there was a fundamentally non-scientific aspect to them: they were no more observable than were the angels dancing on the heads of medieval pins. Samuelson once more came to the rescue with the concept of “revealed preference”. Firstly, using the condition of non-satiation, a bundle A is inferior to any bundle with as much of most commodities, and more of one or more, as shown in Figure 7.
Figure 2.7 Revealed Preference: All points in the square are preferred to A
Secondly, if the consumer is then shown any other bundle B which has less of some commodities than A but more of others, it would be possible to show the consumer these bundles and ask “do you prefer A to B, B to A, or are you indifferent between them?” (see Figure 8).
Figure 2.8 Constructing an indifference curve from revealed preferences
Thirdly, if a consumer choose a particular combination of commodities at a given income and price ratio–say, three bananas and ten biscuits when the price ratio was four biscuits per banana–then this chosen combination was “revealed preferred” to any other combination which the consumer could have purchased, but did not purchase, at the same income and price ratio. The actual bundle purchased must therefore lie on a higher indifference curve than all bundles not purchased, as shown in Figure 9. A rational consumer should therefore prefer bundle A to bundles B or C at all price ratios, and not just the one used in this comparison.
Figure 2.9 Bundle A lies on a higher indifference curve than B or C because the consumer buys it when both B and C are also affordable
By laboriously considering all these alternatives, the consumer’s “indifference map” could finally be drawn, as originally shown in Figure 6. Thus though indifference curves were inherently unobservable, they could at least be inferred from observations of actual consumer choices–though the history of attempts to put Samuelson’s procedure into practice and actually derive someone’s “indifference map” has been less than auspicious.
Metaphysics was thus turned into apparent science. Revealed preference theory enabled economists to–in their terms–prove that an individual’s observed purchases resulted from that individual maximising his/her utility in accordance with the economic definition of rationality. As a consequence, it was now possible to construct an individual’s unobservable utility map from his/her observable purchases.
This two-way mapping between individual commodity choices and individual utility is embodied in several axioms with the acronyms of WARP, SARP and GARP (for the Weak, Strong and Generalized Axioms of Revealed Preference). Their basic meaning is that economists are confident that the choices a consumer makes because of a change in price reflect utility-maximising behaviour.