Revealed Preference Theory

Revealed Preference Theory

Revealed preference theory was given by Paul A. Samuelson.  According to him, utility analysis and indifference curve analysis are based on unrealistic assumptions as neither utility can be measured nor preferences of an individual can be obtained.

The main merit of the revealed preference theory is that the 'law of demand' can be directly derived from the revealed preference axioms without using indifference curves and most of the restrictive assumptions. It only records the observed behavior of the consumer in the market. The consumer reveals his behavior by the bundle of goods, that he buys at different prices.

Revealed preference theory is based on observable and testable hypotheses. Thus, there is a shift from the psychological to the behavioristic explanation of consumer behavior.

According to this theory, the consumer is supposed to reveal the nature of his preferences.

Assumptions:

1. Rationality-  The consumer is rational in behavior who prefers a larger basket of goods to the smaller ones.

2. Consistency:  We assume that the consumer's choices are consistent. It means that if a consumer, given his circumstances, prefers A to B, he will not prefer B to A under the same conditions.

3. Transitivity:  If a consumer prefers A bundle of goods to B bundle of goods and also prefers B bundle of goods to C bundle of goods, Then he will also prefer A bundle of goods to C bundle of goods. It means that If A>B and B>C then it implies that A>C.

4. Positive Income Elasticity of Demand:   It refers that consumer's demand for commodity must increase with the increase in income.

Revealed preference Axiom: A distinguishing feature of  Samuelson's theory is that of 'Strong ordering'. In the strong Ordering, each item in a consumer's scheme of purchases is allocated a definite number and at each number, there is only one item so that the consumer definitely reveals his preferences. In other words, choice reveals a preference, by choosing one combination and rejecting others. the consumer shows his definite preference. In a weak ordering, there may be some items that can not be organized in order or preference, so that the consumer is unable to specify which items he prefers to which. In the case of strong ordering, the consumer chooses the most preferred position and reveals his preference strongly. While in the weak ordering, the consumer hesitates and cannot at once reveal his preference. The revealed preference theory can be stated as follows: Given the income of a consumer and prices of two goods, X and Y,  AB is the income price line and triangle AOB is the area of consumer's selection. If a consumer chooses a particular basket, he reveals his preference for the basket. 

The consumer can select any of the combinations C, K, E, H with the help of his given constraint under the price line AB. If the consumer chooses to buy combination K, then K is revealed preferred to others. Once a consumer reveals his preference for a particular combination K, then all other combinations C, E, H are inferior.

In Samuelson's words, he reveals his preference for K over all other positions available to the consumer. This theory is known as the strong ordering hypothesis.

According to Hicks, if a consumer makes his choice for a particular combination K, it doesn't mean that K is preferred to all other positions within or on the budget-line. It is quite possible that some rejected combinations may be as good as K but the consumer may be indifferent between K and some other combinations like C & E. In this case, the combination H is inferior. This is known as the weak-ordering hypothesis.

Demand Theorem with Revealed Preference Hypothesis

 Samuelson has tried to express the inverse relationship between price and the amount demanded by assuming income elasticity of demand to be positive.

Samuelson states the demand-theorem under the title 'Fundamental Theorem of Consumption Theory' thus: 'Any good (simple or composite) that is known always to increase in demand when income alone rises must definitely shrink in demand when its price alone rises.' a

In the above diagram, AB is the price line and consumer's income is shown by  OA in terms of Good Y. It is assumed that the consumer has given his preference to the basket Q on the price line AB as it is giving him the maximum satisfaction.

Suppose that the price of good X rises and the price of good Y remains the same, then the new price line is AC, thus the demand for good X contracts OB to OC. Now Basket Q which put the consumer in equilibrium before becomes now beyond his reach. We give some extra money to the consumer to overcome the higher price resistance in order to enable him to buy the same combination Q.  It is shown by the imaginary line DE parallel to AC by passing through Q. We give the consumer DA more money in terms of Y to enable him to buy Q combination because Q is on the imaginary price line DE. 
Prof. Samuelson calls the extra money as an overcompensation effect and Hicks calls it Cost- difference.

Now Combination Q is again available to the consumer, so he will not choose any other combination to lower than Q i.e lying on QE part of DE. They were available for him before since they lie within the triangle AOB made by the price line AB but were rejected by him in favor of Q. Either he will choose Q or any higher combination lying on QD part of the price line DE. If he chooses any other combination above Q on QD portion of DE, it means he is buying less of X and more of Y. This shows the substitution effect after the price increase as some units of Y have been substituted for some units of X.

Thus, it is obvious, even after giving some extra money to the consumer to compensate for the rise in the price of X, he either buys the original quantity of X or less quantity at a higher price. If extra money were not given to him, he would definitely buy a smaller quantity of good X after the rise in its price. It shows the inverse relationship between the price and quantity demanded.

Thus, the Revealed Preference Theory is an improvement on the Utility analysis and Indifference Curve technique.  This theory relies on the observed behavior of a consumer. It is, therefore, more realistic and scientific. Another advantage of this theory is that it navigates clear of the utility maximization principle and uses the consistency principle to derive the demand theorem which is less restrictive and more realistic.

 In spite of these advantages, it is not free from defects.

It is based on strong ordering and as such does not admit of indifference.  The consumer is sometimes confronted with alternatives that are equally desirable and he is hesitant to choose between them.

Another flaw in this theory arises from the assumption of positive income-elasticity of demand. Therefore, it cannot explain Giffen's paradox in which the income effect is negative.

In conclusion, this theory is superior and applies a scientific and behaviouristic method to consumer's demand.

Dr. Swati Gupta

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