Read this article to learn about the revealed preference theory of demand:
Professor Samuelson’s Revealed Preference Theory is a behaviourist ordinal utility analysis as distinct from the introspective ordinal utility theory of Hicks and Allen.
It is ‘the third root of the logical theory of demand’, and has been called by Hicks as the Direct Consistency Test under strong ordering. This theory analyses consumer’s preference for a combination of goods on the basis of observed consumer behaviour in the market.
Choice Reveals Preference:
Prof. Samuelson’s theory of demand is based on the revealed preference axiom or hypothesis which states that choice reveals preference. Keeping this fact into view, a consumer buys a combination of two goods either because he likes this combination in relation to others or this is cheaper than others. Suppose the consumer buys combination A rather than combination В. С or D. It means that he reveals his preference for combination A. He can do this for two reasons. First, combination A may be cheaper than the other combinations B, C, D. Seconds combination A may be dearer than others and even then he likes it more than other combinations. In such a situation, it can be said that A is revealed preferred to В, C, D or В, C, D are revealed inferior to A. This is explained in Figure 14.1.
Given the income and prices of the two goods X and Y. LM is the price-income line of the consumer. The triangle OLM is the area of choice for the consumer which shows the various combinations of X and Y on the given price- income situation LM. In other words, the consumer can choose any combination between A and В on the line LM or between С and D below this line.
If he chooses A, it is revealed preferred to B. Combinations С and D are revealed inferior to A because they are below the price-income line LM. But combination E is beyond the reach of the consumer being dearer for him because it lies above his price-income line LM. Therefore, A is revealed preferred to other combinations within and on the triangle OLM.
The Law of Demand:
Prof. Samuelson establishes the law of demand directly on the basis of his revealed preference hypothesis without the use of indifference curves and the restrictive assumptions associated with them.
Samuelson’s law of demand is based on the following assumptions:
(1) The consumer’s tastes do not change.
(2) His choice for a combination reveals his preference for that.
(3) The consumer chooses only one combination at a given price-income line, i.e., any change in relative prices will always lead to some change in what he purchases.
(4) He prefers a combination of more goods to less in any situation.
(5) The consumer’s choice is based on strong ordering.
(6) It assumes consistency of consumer behaviour. If A is preferred to В in one situation, В cannot be preferred to A in the other situation. This is the two-term consistency, according to Hicks which must satisfy two conditions on a straight line curve: (a) If A is left to В, В must be right of A. (b) If A is right of В, В must be left of A.
(7) This theory is based on the assumption of transitivity. Transitivity, however, refers to three-term consistency. If A is preferred to B, and В to C, then the consumer must prefer A to C. This assumption is necessary for the revealed preference theory if the consumer is to make a consistent choice from given alternative situations.
(8) Income elasticity of demand is positive i.e., more commodity is demanded when income increases, and less when income falls.
Fundamental Theorem or Demand Theorem:
Given these assumptions, Samuelson states his “Fundamental Theorem of Consumption Theory,” also known as demand theorem, thus: “Any good (simple or composite) that is known always to increase in demand when money income alone rises must definitely shrink in demand when its price alone rises.” It means that when income elasticity of demand is positive, price elasticity of demand is negative. This can be shown both in the case of a rise and a fall in the price of a good.
Rise in Price:
First, we take a rise in the price of, say, good X. To prove this Fundamental Theorem, let us divide it into two stages. Firstly, take a consumer who spends his entire income on two goods X and Y. LM is his original price-income line where the consumer is observed to have chosen the combination represented by R in Figure 14.2. The triangle OLM is the consumer’s area of choice for the different combinations of V and Y available to him, as given by his price-income line LM. By choosing only the combination R. the consumer is revealed to have preferred this combination to all others in or on the triangle OLM.
Suppose the price of X rises, the price of Y remaining constant so that the new price-income line is LS. Now he chooses a new combination, say, point A which shows that the consumer will buy less of A than before as the price of A” has risen. In order to compensate the consumer for the loss in his real income as a result of rise in the price of X, let us give him LP amount of money in terms of good Y As a result, PQ becomes his new price-income line which is parallel to the LS line and passes through point R. Prof. Samuelson calls it Over Compensation Effect. Mow the triangle 0P0 becomes his area of choice. Since R was revealed preferred to any other point on the original price-income line LM, all points lying below R on the RQ segment of PO line will be inconsistent with consumer behaviour.
This is because he cannot have more of X when its price has risen. The consumer will, therefore, reject all combinations below R and choose either combination R or ay other combination, say, В in the shaded area LRP on the segment PR of the price-income line PQ. If he chooses the combination R, he will buy the same quantities of X and Y which he was buying before the rise in the price of X. On the other hand, if he chooses the combination В, he will buy less of X and more of Y than before.
In the second stage, if the packet of extra money LP given to the consumer is taken back, he will be to the left of R at point A on the price-income line LS where he will buy less of X, if the income elasticity of demand for X is positive. Since with the rise in the price of X, its demand has fallen ( when the consumer is at point A), it is proved when income elasticity is positive, price elasticity is negative.
With the rise in the price of X, the consumer buys less of X. So price elasticity of demands negative because price and demand move in the opposite directions. But with the rise in the price of X, the real income of the consumer falls and buys less of X. Therefore, his income elasticity of demand is positive because both income and demand move in the same direction.
Fall in Price:
The demand theorem can also be proved when the price of good X falls. It can be defined thus: “Any good (simple or composite) that is known always to decrease demand when money income alone falls must definitely expand in demand when its price alone falls.” This is explained in Figure 14.3. LM is the original price-income line on which the consumer reveals his preference at point R. With the fall in the price of X, the price of Y remaining constant, his new price-income line is LS. The consumer reveals his preference on this line at, say, combination A which shows that he buys more of X than before. The movement from point R to A is the price effect as a result of fall in the price of X which has led to increase in its demand.
Suppose the increase in the real income of the consumer as a result of fall in the price of X is taken away from him in the form of LP quantity of Y. Now PQ becomes his new price-income line which is parallel to LS and passes through R. The new triangle OPQ becomes his area of choice. Since the consumer was revealing his preference at point R on the line LM, all points lying above R on the segment RP of line PQ will be inconsistent with his choice.
This is because on the RP segment he will have less of good X when its price has fallen. But this is not possible. The consumer will, therefore, reject all combinations above R. He will either choose combination R or any other combination, say, В on the segment RQ of the line PQ in the shaded area MRQ. If he chooses the combination R, he will buy the same quantities of X and Y which he was buying before the fall in the price of X. And if he chooses the combination B, he will buy more of X and less of Y than before. The movement from R to В is the substitution effect of a fall in the price of X.
If the money taken from the consumer in the form of LP is returned to him, he will be at the old combination A on the price-income line LS where he will buy more of X with the fall in its price. The movement from В to A is the income effect. So the demand theorem is again proved that positive income elasticity means negative price elasticity of demand.
It is to be noted that Samuelson’s explanation of the substitution effect is different from that of the indifference curve analysis. In the case of indifference curve analysis, the consumer moves from one combination to another on the same indifference curve and his real income remains constant. But in the revealed preference theory, indifference curves are not assumed and the substitution effect is a movement along the price-income line arising from changing relative prices.
Superiority of Revealed Preference Theory:
The revealed preference approach is superior to the Hicksian ordinal utility approach to consumer behaviour.
(i) It does not involve any psychological introspective information about the behaviour of the consumer. Rather, it presents a behaviouristic analysis based on observed consumer behaviour in the market. This approach has helped, according to Samuelson, to divest the theory of demand of the “last vestiges” of the psychological analysis. Thus the revealed preference hypothesis is more realistic, objective and scientific than the earlier demand theorems.
(ii) It avoids the “continuity” assumption of the utility and indifference curve approaches. An indifference curve is a continuous curve on which the consumer can have any combination of the two goods. Samuelson believes that there is discontinuity because the consumer can have only one combination.
(iii) The Hicksian demand analysis is based on the assumption that the consumer always behaves rationally to maximise his satisfaction from a given income. Samuelson’s demand theorem is superior because it completely dispenses with the assumption that the consumer always maximises his satisfaction, and makes no use of the dubious hypothesis like the Law of Diminishing Marginal Utility of the Marshallian analysis or the Law of Diminishing Marginal Rate of Substitution of the Hicksian approach.
(iv) In the first stage of Samuelson’s demand theorem the ‘over compensation effect’ is more realistic as an explanation of consumer behaviour than the Hicksian substitution effect. It permits the consumer to shift to a higher price-income situation in case of rise in the price of X and vice versa. Thus it is an improvement over Hicks’ substitution effect. Similarly, the second stage of the Samuelsonian Theorem explains the Hicksian ‘income effect in a much simpler way. Hicks himself admits the superiority of Samuelson’s theory when he writes that as a clear alternative to the indifference technique its presentation is the newest and important contribution of Samuelson to the theory of demand.
(v) This theory provides the basis for welfare economics in terms of observable behaviour based on consistent choice.
Defects of the Revealed Preference Theory:
There are, however, certain weaknesses in Samuelson’s revealed preference theory.
1. Neglects Indifference:
It neglects “indifference” in the consumer behaviour altogether. It is, of course, true that the consumer does not reveal his indifference in a single-valued demand function in or on the budget line when he chooses a particular set of goods at point R on the budget line LM. But it is possible that there are points like A and В on every side of a given point R, shown within the circle in Figure 14.4, towards which the consumer is indifferent. If this criticism by Armstrong is accepted, then Samuelson’s fundamental theorem breaks down. Suppose the price of X rises.
As a result, his new budget line is LS. Now give the consumer some extra money to enable him to buy the same combination R on the line PQ. In this new price- income situation, suppose he chooses point В below R towards which he is indifferent. This is based on Armstrong’s assumption that the consumer is indifferent between points around the chosen point.
But the choice of В on the PQ line means that the consumer buys more of X when its price has risen.
This breaks down the Samuelson theorem because with the rise in the price of X, its demand has expanded instead of shrinking.
2. Not Possible to Separate Substitution Effect:
Samuelson’s Fundamental Theorem is conditional and not universal. It is based on the postulate that positive income elasticities imply negative price elasticities. Since the price effect consists of the income and substitution effects, it is not possible to isolate the substitution effect from the income effect on the level of observation. If the income effect is not positive, price elasticity of demand is indeterminate. On the other hand, if the income elasticity of demand is positive, the substitution effect following a change in price cannot be established. Thus, the substitution effect cannot be distinguished from the income effect in the Samuelsonian Theorem.
3. Excludes Giffen Paradox:
Samuelson’s revealed preference hypothesis excludes the study of the Giffen Paradox, for it considers only positive income elasticity of demand. Like the Marshallian Law of Demand, the Samuelsonian Theorem fails to distinguish between negative income effect of a Giffen good combined with a weak substitution effect and a negative income effect with a powerful substitution effect. Samuelson’s Fundamental Theorem is, therefore, inferior to and less integrated than the Hicksian price effect which provides an all inclusive explanation of the income effect, the substitution effect and of Giffen’s Paradox.
4. Consumer does not choose only one Combination:
The assumption that the consumer chooses only one combination on a given price-income situation is incorrect. It implies that the consumer chooses something of everything of both the goods. But it is seldom that anybody purchases something of everything.
5. Choice does not reveal Preference:
The assumption that “choice reveals preference” has also been criticised. Choice always does not reveal preference. Choice requires rational consumer behaviour. Since a consumer does not act rationally at all times, his choice of a particular set of goods may not reveal his preference for that. Thus the theorem is not based on observed consumer behaviour in the market.
6. Fails to derive Market Demand Curve:
The revealed preference approach is applicable only to an individual consumer. Negatively inclined demand curves can be drawn for each consumer with the help of this approach by assuming ‘other things remaining the same.’ But this technique fails to help in drawing market demand schedules.
7. Not Valid for Game Theory:
According to Tapas Majumdar, the revealed preferences hypothesis “is invalid for situations where the individual choosers are known to be capable of employing strategies of a game theory type.”
8. Fails in Risky or Uncertain Situations:
The revealed preference theory fails to analysis consumer’s behaviour in choices involving risk or uncertainty. If there are three situations, A, B, and C, the consumer prefers A to В and С to A. Out of these, A is certain but chances of occurring В or С are 50-50. In such a situation, the consumer’s preference for С over A cannot be said to be based on his observed market behaviour.
It appears from the above discussion that the revealed preference approach is in no way an improvement over the indifference curve analysis of Hicks and Allen. It is unable to isolate the substitution effect from the income effect, neglects Giffen’s Paradox and fails to study market demand analysis. But the fact is that in a single-valued demand function, the indifferent behaviour is replaced by the observed market behaviour of the consumer. This makes the revealed preference theory somewhat more realistic than the indifference curve technique.