Hicks’s Revision of Demand Theory

2 years ago

Atiqur Rahman

16 minutes

Introduction

Hicks presented his demand theory in his work “Value and Capital“. He revised his demand theory and brought out a book, “A Revision of Demand Theory” in 1956. The main reason behind the revision of demand theory by Hicks is the emergence of the “Revealed Preference Approach” by Samuelson, the rise in the econometrics analysis, mathematical theories of weak and strong ordering and the discovery of more reasoned derivation of demand from a few simple propositions of logic.

Hicks was influenced by the revealed preference approach and the logic of strong ordering by Samuelson and his followers, i.e. Arrow, Little and Houthakar. To quote Hicks, ”All this I owe to Samuelson and the Samuelsonians, though I can hardly count myself of their number since I retain a considerable scepticism about the “revealed preference approach”.

Hicks, in his “A revision of demand theory”, again rejects the concept of the hypothesis of independent utilities and cardinal utility. He still assumed utility to be purely ordinal. Hicks, who popularized the use of the indifference curve in demand theory, has given them up in his revision of demand theory.

In his book, he has explained all the concepts without the usage of the indifference curve though there are positions which are equally preferred by the consumer. He also explained the concept of consumer surplus without using the indifference curve. He explained the disadvantages of the indifference curve techniques.

First, he points out that the graphical method of indifference curve analysis is fully effective and useful for representing cases where there are only two goods are involved. When the indifference curve analysis is extended towards three commodity cases, complicated three-dimensional diagrams need to be plotted. The situation becomes more difficult when the analysis is extended to more than three commodities.

The second disadvantage of the indifference curve is that it forces us to make an assumption of continuity. Hicks gave up this assumption in his revision of demand theory. To quote Hicks,” The consideration which decides me in favor of the new method, at least as an essential complement to the old, if not as a substitute, is its greater effectiveness in clarifying the nature of the preference hypothesis itself”.

Preference Hypothesis and Logic of Ordering

Hicks assumes the preference hypothesis as a principle which governs the behaviour of the ideal consumer. The behaviour according to the scale of preferences is known as the preference hypothesis.

According to Hicks, the ideal consumer chooses the alternative which he prefers most out of the various alternatives open to him. The ideal consumer is affected only by the current market condition. In one set of market conditions, he makes one choice; in others, another choice, but all the choices he makes under these market conditions express the same order and must be consistent with one another.

We have seen that the demand theory that was presented by Hicks under “Value and Capital” was also based upon the preference hypothesis. But under “Value and Capital”, the scale of preferences was given in the form of a set of indifference curves. But indifference curve analysis was given up because of its disadvantages in the revision of demand theory.

Hicks, in the revision of demand theory, started from the logic of ordering itself rather than its geometric application. According to him, the demand theory, which is based on the preference hypothesis, turns out to be an economic application of the logical theory of ordering. Before proceeding with the derivation of demand theory using the preference hypothesis, Hicks explained the “logic of order”.

Let us proceed with the logic of order by first explaining the difference between strong and weak ordering and then followed by demand theory based on weak ordering.

Difference Between Weak and Strong Ordering:

The difference between weak and strong ordering is explained as follows:

Strong Ordering: A set of items is strongly ordered; if each item has a place of its own in the order, and each item could then be given a number, and to each number, there would be one item and only one item which would correspond.

Weak Ordering: A set of items is weakly ordered if the items are clustered into groups, but none of the items within a group can be put ahead of the others. Thus, weak ordering consists of a division into groups, in which the sequence of groups is strongly ordered but in which there is no ordering within the groups.

We have seen that consumer is indifferent on an indifference curve as all the points lying on it give the same level of satisfaction. It implies that the indifference curve shows weak ordering as all the points lying on it give the same level of satisfaction and hence occupy the same place in the order.

On the other hand, the revealed preference approach shows strong ordering as it assumes that any chosen combination reveals its preference for it over all the available alternative combinations. Weak ordering implies that the consumer chooses a combination and rejects all other alternatives open to him, then the rejected combinations need not be inferior to the position actually chosen but may have been indifferent to it. The strong and weak ordering is shown in Figure 1.

In Figure 1, commodity X is an individual good and is measured on X-axis, and commodity Y (money) is a composite good representing all goods and services other than commodity X. Given the income and price of commodity X and Y, the price income situation of the ideal consumer is shown by line DD. The consumer can choose any combination on line DD or inside triangle ODD. The actual choice of the consumer is shown by point A.

Now the question is how to interpret the choice of the consumer from among the various alternatives available to him. If all the available alternatives are strongly ordered, then the choice of combination A by the consumer shows his preference over all other alternative combinations. Under strong ordering, a consumer shows a definite preference for the chosen combination, and there is no question of any indifferent positions to the selected one.

Hicks criticized the logic of strong ordering on the basis of two grounds.

The strong ordering form under Samuelson’s version of the preference hypothesis, it cannot be assumed that all the geometrical points, which lie within or on the price income line, represent effective alternatives. A two-dimension continuum point cannot be strongly ordered.
According to Hicks, if commodities are assumed to be available in discrete units such that the diagram is to be conceived as being drawn on a square paper. The only effective alternatives are the points on the corner of the square. As the selected point would also lie at the corner of the square, so strong ordering hypothesis is accepted. But the situation is entirely different in the real world because of the use of money. Thus in making a choice between commodity, which is available in discrete units and the divisible commodity money, the strong ordering has to be given up.

Logic of Weak Ordering:

Hicks used a weak ordering hypothesis in his demand theory. To quote Hicks, “If the consumer’s scale of preferences is weakly ordered, then his choice of a particular position A does not reveal that A is preferred to any rejected combination within and on the triangle ODD: all that is shown is that there is no rejected position which is preferred to A. It is perfectly possible that some rejected positions may be indifferent to A; the choice of A instead of that rejected position is then a matter of chance.

If the weak ordering hypothesis is adopted, then the choice of a particular combination does not show the preference for that particular combination over other available alternatives but it only shows that all other possible alternative combinations cannot be preferred to the chosen combination. There is a possibility that some rejected combinations may be indifferent to the chosen bundle. If this weak ordering hypothesis is adopted, then with this little information, the demand theory cannot be derived.

Professor Hicks introduced an additional hypothesis along with a weak ordering hypothesis so as to derive the basic proposition of demand theory. Under the additional hypothesis, the consumer will always prefer a large amount of money to a smaller amount of money, provided that the amount of good X at his disposal remains unchanged. But here, it is noteworthy that it is not necessary to adopt this additional hypothesis if a strong ordering form of preference hypothesis is adopted.

Direct Consistency Test:

Following Samuelson, Professor Hicks also assumed the consistency of choice behaviour by the ideal consumer, who revealed unchanged scales of preferences. According to Hicks, this consistency test is known as the direct consistency test. The term direct consistency is the economic expression of the two-term consistency condition on the theory of the logic of order.

Hicks had proved the hypothesis not for the consistency of the consumer choices but for the inconsistency as well. As before, there are assumed to be two commodities- commodity X and Commodity Y (money). The alternative combinations that are available to the consumer are represented by the points on or under the triangle ODD. Point A shows the actually chosen combination. The strong and weak preferences are the same as we have studied in the last section.

Now let us take a new situation, i.e. a new price income situation. The alternative combinations that are available to the consumer are represented by the points on or under the triangle shown by the new price income line. Suppose B is the actually chosen combination in this new price income situation.

We have also assumed that the consumer is acting according to the unchanged scale of preferences in both situations, new and old. The preferences of the consumer in both situations must be consistent with each other. The consumer behaviour is said to be inconsistent if he reveals his preference for combination A over combination B in A situation, while in situation B, he prefers combination B over combination A when both combination A and B are available to consumer in both situations. But under the weak preference hypothesis, the possibility of indifference has to be taken into account.

Derivation of Law of Demand Through Logical Weak Ordering Approach

Professor Hicks developed his revised theory of demand on the basis of weak preference ordering along with additional hypotheses and the direct consistency test. He initially derives the theory of demand for a single commodity.

In the derivation of a single commodity, the consumer is confronted with a market situation where there is a change in the price of one commodity, only keeping the prices of other goods constant. He derived the law of demand by decomposing the price effect into the substitution effect and income effect.

Hicks has used two methods to separate the substitute effect from the income effect:

(i) The method of compensating variation and
(ii) the method of Cost difference.

Let us proceed with the derivation of the law of demand by the method of compensating variation.

Let us suppose that there are two commodities-commodities X, and composite good commodity Y. Commodity X is measured on X-axis and commodity Y on Y-axis. Given the price of the commodity and the income of the consumer, the price income line is shown as CE. The chosen combination by the consumer on price income line CE is A.

Suppose that there is a reduction in the price of commodity X with no change in the money income. As a result of this reduction in the price of commodity X, the price income line would pivot right to CD. The vertical intercept would not change as there is no change in commodity Y. Now consumers would choose a combination of this new price income line. The consistency test reveals that as long as the quantity of commodity X is consumed, any combination on line CD must be preferred to combination A.

In other words, it does not matter whether the new combination B on line CD lies to the right of A or to the left of A or exactly above A; it would be preferred to A. This happens because combination A lies within the triangle of OCD. When combination B lies to the right (left) of A, it means that the quantity demanded of good X rises (falls) due to a fall in its price. And if combination B lies exactly above combination A, then the quantity demanded remains unchanged even with the fall in price.

The important question that arises here is whether the quantity consumed of commodity X remains unchanged, falls or rises due to a fall in the price. The answer to this question cannot be deduced from a consistency test.

Derivation of Law of Demand through Hicks Logical Ordering Approach

If the fall in the price of commodity X is associated with a reduction in income, then with the help of the consistency test, it can be shown that the quantity demanded of commodity X remains the same or must rise, but it cannot fall. With the fall in price, if the income is also reduced by an appropriate amount, the remaining effect of the change in price on the quantity demanded of commodity X will be due to the substitution effect. It is clear from the consistency test that due to the substitution effect of the fall in the price of commodity X, the consumption of the commodity must rise or remain unchanged, but it cannot fall.

The price effect is decomposed into the substitution effect and income effect. The residual change in price effect is explained by the income effect. The income effect of a change in the price of commodity X can also be explained with the help of a consistency test. In order to show the influence of the substitution effect on the demand for a commodity, we have to make a suitable reduction in income along with a fall in the price of commodity X.

The movement from A to B represents the price effect. In order to separate the substitution effect, income has to be reduced by compensating variation. The income of the consumer is reduced such that he chooses combination T at a lower price. At this lower price and lower income, this combination is indifferent to combination A. The substitution effect measures the effect of the change in relative prices with real income constant.

On the other hand, the income effect measures the effect of the changes in real income. It is shown in Figure 2. When the income is reduced by compensating variation, the new price income line GH intersects the CE line below combination A. On the new price income line GH, the actually chosen combination is T. The movement from A to T represents the substitution effect and would result in an increase in the quantity demanded of commodity X.

Let us see the income effect. Now let the money that has been taken away from the consumer is restored to him. With this increase in income, whether the consumer will buy more of commodity X or less at T cannot be explained with the help of a consistency test. But empirical evidence shows that in most cases, the consumption of a commodity increases with the rise in income. Thus, when a consumer is at combination A, and his income is increased by the amount that had been taken away from him, he will still increase his consumption of good X. That’s why combination B lies to the right of T. The movement from combination T to B shows the income effect.

To sum up, the demand for a commodity increases with a fall in price due to both substitution and income effects. It is proved that the law of demand holds, i.e. there exists a negative relationship between price and quantity demanded.

Hicks’s Revision of Demand Theory

Introduction

Preference Hypothesis and Logic of Ordering

Difference Between Weak and Strong Ordering:

Logic of Weak Ordering:

Direct Consistency Test:

Derivation of Law of Demand Through Logical Weak Ordering Approach

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Introduction

Preference Hypothesis and Logic of Ordering

Difference Between Weak and Strong Ordering:

Logic of Weak Ordering:

Direct Consistency Test:

Derivation of Law of Demand Through Logical Weak Ordering Approach

Read More- Microeconomics

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