Samuelson’s revealed preference theory has preference hypothesis as a basis of his theory of demand. The consumer has the option of choosing from the set of bundles belonging to the
feasible consumption set.
The consumer by choosing a bundle of goods over others reveals his preference for that particular bundle, given his budget constraint (determined by his income and prices). The choice of a bundle by a consumer reveals his clear and definite preference for that over all other alternative bundles available under that budget constraint.
The revealed preference for a particular combination of goods implies maximisation of the utility of the consumer, because he is assumed to be rational.
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A consumer decides to purchase a particular combination of commodities, either because he likes it more or it is cheaper. If this combination is not found to be cheaper than others, then, this combination has been revealed preferred to all other alternative combinations, which he could have purchased.
The very fact that in a given price-income situation, he chooses a particular combination implies that all other feasible combinations must have been rejected in favour of this combination. Therefore, according to Samuelson, consumer’s choice reveals his preference.
In the words of William J. Baumol, “if a consumer buys some collection of goods A, rather than any of the alternative collections B, C, D, etc. and it turns out that none of the latter is more expensive than A, we say that A has been revealed preferred to the others or that others have been revealed to be inferior to A)”.
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It is possible to obtain information about the preference scale of the consumer by comparing his preference revealed in different price situations. Before that, it is necessary to find the complete set of combinations which are revealed to be inferior to one particular combination ‘A’.
According to Samuelson, when a consumer prefers to have bundle ‘A’ rather than bundle ‘B’, either he gets more satisfaction from this bundle than another, or, he cannot afford to purchase another bundle, while he can purchase bundle ‘A’.
To quote his lines, “Through any observed equilibrium point A, draw the budget equation straight line with arithmetical slope given by the observed price ratios. Then all combinations of the goods on or within the budget line could have been bought in preference to what was actually bought. But they were not. Hence, they are all ‘revealed’ to be inferior to A”. This may be explained with the help of Fig. 6.2.
In Fig. 6.2, suppose that AB is the budget line with the given income and prices of the two commodities ‘X’ and ‘Y’. Given the price-income situation as represented by this budget line, the consumer can choose any combination of the two commodities lying within or on the triangle OAB (the area of consumer choice).
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In other words, all combinations lying on this budget line AB such as ‘C’, ‘D’, ‘E’ and those lying below this line such as ‘F’, ‘G’, ‘H’ and ‘I’ are alternative combinations open to him, from among which he has to choose.
If the consumer chooses combination indicated by point ‘E’ (laying on budget line AB) out of all options open to him, ‘E’ is said to be revealed preferred to one indicated by equally expensive points, such as ‘F’, ‘G’, ‘H’ and T lying below the budget line, as these points represent smaller amounts of both the commodities than point ‘E’ (points ‘F’ and ‘G’) or than do some other points on the budget lines (points ‘H’ and T in comparison to points ‘C’ and ‘D’ respectively on budget line AB). Thus, such lower points ‘F’, ‘G’, ‘H’ and T are cheaper than point ‘E’.
Point ‘E’ is the equilibrium point representing the actual choice of the consumer. Every point on or below the budget line AB is revealed to be inferior to point ‘A’, since the consumer purchases combination ‘E’ rather than any of these other no more expensive combinations (‘C’ ‘D’, ‘F’ ‘G’, ‘H’ and ‘I’). The consumer’s choice, thus, reveals his preference for combination ‘E’ by rejecting other combinations.
The points above the budget line, such as ‘J’ and ‘K’ are more expensive than point ‘E’. These are beyond the reach of the consumer with the present price-income situation. None of such points can be revealed inferior to point ‘E’. Thus, the chosen bundle is revealed to be preferred to all other alternative bundles available to him under the given budget constraint.
It is clear from the above discussion that the Samuelson’s revealed preference theory is based upon the strong form of preference hypothesis, i.e., strong ordering. Under strong ordering, relation of indifference between various alternative combinations is ruled out. It is different from weak ordering, where the consumer is indifferent between various combinations of the commodities (under indifference curves analysis).
The revealed preference axiom can be translated into index number form. If in two situations, Z1 and Z2 are the combinations of the commodities, P1 and P2 are their respective price vectors, then, the statement that the consumer chooses combination Z1, over combination Z2 can be expressed by the formula that S P1 Z1 > S P1 Z2.
Here, S P1 Z1 implies the total expenditure on the Z, combination of commodities and SP1Z2 implies total expenditure on the Z2 combination of the commodities. The condition indicated by the above formula shows that the consumer could have bought affordable combination Z2, when he actually bought combination Z1 by spending his income on Z2 rather than on Z1. This index number of formulation is convenient, but it does not convey any additional economic sense.