Revealed Preference Theory

Both the Marshalian cardinal utility theory of demand and Hicks-Allen indifference curve analysis provide psychological explanation of consumer’s demand. They derive laws about the consumer’s demand from the consumers reaction psychologically to contain hypothetical changes in price and income but the revealed preference theory which has been put forward by Prof Samuelson seeks to explain consumers demand from his actual behavior in the market at various prices and income situation. 

The basic idea of the revealed preference theory is very simple. Let us suppose that the consumer purchases some commodities either because he likes them more than other commodities or because they happen to be cheaper than other commodities, let us assume that there are two combinations of commodities, there is x and y, the consumer buys combination x and not combination y. From this action of the consumer we should not conclude the combination x is cheaper than combination y nor we should conclude that the combination y is inferior to combination x. If both the combinations are equally good and equally costly even then the consumer buys x combination. The conclusion is obvious, the consumer purchases x combination because he likes it better. By buying the consumer has revealed his preference for it. It can be said that if the consumer purchases x combination rather than y and z combination and that y and z combinations are not more expensive than x combinations, the x combination of good standards reveal the preference to y and z combination. The idea underline the revealed preference theory can be illustrated in the following diagram. 

In this diagram A and B are two commodities the price line N and M reflects given income and price situation for the consumer. The consumer can purchase any combination lying on the price line NM such as DCE or in alternate and he can buy any combination of the two goods lying below the price line. These are alternative combinations and the consumer is free to choose any one of them. The consumer can purchase any combination of the two goods either lying with in or on the triangle NOM known as the consumer choice triangle.


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Substitution, Income and Price Effect

The Substitution Effect 

The substitution effect takes place when the income of the consumer remains constant and the relative prices of the tow commodities changes. Suppose the price of one commodity rises and the other decreases now the consumer is neither better off nor worse off than before. However he will rearrange this purchase to compensate the loss. It means the consumer substitutes relatively cheaper goods for the relatively costlier ones. This can be shown in the following diagram. 

Let us assume the consumer purchases oranges and apples. Suppose if the price of the apple rises and the oranges decreases at this moment the consumer will purchase more oranges and less apples. 

In this diagram the consumer is in equilibrium at point Q because the price line AB touches the IC curve. Here the consumer purchases OM of oranges and ON of apples now the price of apples rises and the oranges decreases. Due to change in price consumer’s budget line will also change from AB to A1B1. At this level the consumer purchases OM1 of more oranges and ON1 of fewer apples. Now the consumer is in equilibrium at the point Q1 because the new budget line A1B1 touches the IC curve at this point. This is consumers new equilibrium point this is the substitution point. 

Income Effect:

The effect of changing consumer’s income on his satisfaction is known as the income effect. Here the consumer will be able to enjoy more or less satisfaction when his income increases or decrease assuming that the prices of the two commodities remain constant. Every increase in income takes him to higher indifference curve. He becomes better off than before. Every decrease in income on the contrary brings him down to the lower indifference curve. He becomes worse off than before. The income consumption curse traces the income effect. 

The income effect can be shown in the following diagram. 

Let us suppose that the consumer wants to purchase apples and oranges. At AB price line the consumer is in equilibrium at point T1 because IC! Curve intersects the price line AB. At this point the consumer purchases 5 oranges and 5 apples. If the income of the consumer increases the price line shifts upwards in the form of A1B1, A2B2, A#B# respectively. The increase in the income enables the consumer to consume more of both the commodities. The equilibrium point 3 will also move towards higher IC curve in the form of T1,T2,T3. If we join all these equilibrium points we obtain the curve known as income curve. The income doesn't trace the effect of a change in income of the consumer on the consumption of commodities. 

The Price Effect: 

The effect of a change in the price of a commodity on its purchase is known as the price effect. We shall now assume that the money income of the consumer remains constant and the prices of orange falls and apples remain unchanged or constant. Now the consumer purchases more oranges. The fall in the price of oranges actually increases the real income of the consumer though his money income remains constant. The cheapness of the oranges induces the consumer into purchasing more and the price line shifts towards right. 

This price effect can be show in the following diagram. 

In this diagram the consumer is in equilibrium at point Q where the IC curve is tangent to AB price line. At this level the consumer purchases 10 oranges and 10 apples. Now the income of the consumer and the price of oranges fall. Now the consumer wants to purchase more of oranges his price line will rotate anti clock wise in the form of AB1. Suppose if the price of orange is still falling the price line will shift towards right in the form of AB2 and the consumer equilibrium point will also changes from Q to Q1. Here the consumer will go on purchasing more and more oranges. There we get new equilibrium points such as Q,Q1,Q2 etc. If we join al these points we get a curve known price consumption curve (PCC). 

Suppose if there is any rise in prices of orange the consumer purchases less of oranges and the price line will be clockwise. 

The price consumption curve shows only various combination of oranges and apples that give maximum satisfaction to the consumer.


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Consumer’s Equilibrium Through Indifference Curve

The consumer spends all his income to maximise his satisfaction it is called consumer equilibrium. It s not possible to know the consumer equilibrium by indifference curve only. For this we must know the income of the consumer and price of the goods. Therefore we should consider both indifference map and price line. If we incorporate the price line into indifference map we can get consumer equilibrium. 

Price line or Budget line: 

If the consumer spends all his income on various combinations of two substitutable commodities which consists a line is called price line or budget line. This can be explained by an example. 

Suppose that the consumer has a sum of Rs 20 in his pocket and he want to spend it on two commodities namely coffee and cigarette. The price of coffee is Rs 2 and the price of cigarette is Rs 1. Now consumer can purchase 10 cups of coffee or 20 cigarettes or he can purchase both . 

As per the illustration of the diagram the consumer can spend his entire income on cigarette, he can purchase 20 cigarettes or 10 cups of coffee. If we join A and B points we get the price line. In this diagram the consumer can purchase any combination of both the commodities which comes on AB price line. 

He cannot purchase the point E above the price line because the consumer doesn't have at his disposal the necessary money and this point E and above the price line. Therefore any combination of the two commodities must follow on the budget line. 

In order to explain how the consumer achieves equilibrium or achieves maximum satisfaction we have to bring together he indifference map and the price line. 

In this diagram the consumer reaches his equilibrium at point T because the price line touches the IC3 curve at this point. Accordingly the consumer can purchase OM quantity of coffee and ON quantity of cigarette with his limited income the consumer is able to purchase only on IC3 curve and he will be in equilibrium position.


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Assumptions and Criticisms of Consumer Surplus

Assumptions: 

This concept is based on the following assumptions. 

• Cardinal measurement of utility. 

• Constant marginal utility of money. 

• The commodity in question does not have substitutes. 

Criticisms: 

1)_ This law is based on certain assumptions and critics argue that these assumptions are unrealistic. 

• Utility cannot be measured cardinally; therefore, consumer’s surplus cannot be measured and expressed numerically. 

• Marginal utility of money does not remain constant. 

• If commodities have substitutes, with the rising prices, he will purchase other goods rather than pay a higher price for the same. The concept has no theoretical validity. 

2)_ It is meaningless to apply the doctrine of consumer’s surplus to necessaries as the utility derived from necessaries as the utility derived from necessaries is infinite. 

3)_ The concept is imaginary and illusory. It does not exist in reality. We create surplus out of our imagination. 

4)_ It is of no practical significance. Prof. Little says, "The doctrine of consumer’s surplus is a useless theoretical toy".


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Consumer Surplus

Dupuit originated the concept of consumer’s surplus. But, it was Marshall who popularized it by presenting it in a most refined way. Marshall viewed that when a consumer buys a commodity, his satisfaction derived from derived from it may be in excess of the dissatisfaction he has experienced in parting with money for paying its price. This excess of satisfaction is called” consumer’s surplus”. 

A consumer is willing to pay the price for a commodity upto its marginal utility compared with the marginal utility of money which he has to pay. If the marginal utility of a commodity is high which is actual market price is low, the consumer derives extra satisfaction, that is, consumer surplus. Consumer surplus therefore can be measured as the difference between the maximum price the consumer is willing to pay for a commodity and the actual market price charged for it. As Marshall puts it, “the excess of the price which a consumer would be willing to pay rather than go without the things over that which he actually does pay, is the economic measure of this surplus of satisfaction. It may be called consumer’s surplus.” 

This concept is based on the law of diminishing marginal utility. 

Prof. Marshall applies the phrase’ consumer’s surplus’ to the difference between the sum which measures total utility and that which measures total exchange value(price paid). For, while the price that he has to pay for each unit is equal to the utility of the marginal unit, the utility of each of the earlier units is more than that of the last. Therefore, he gains more utility than he loses by making the payments. His gain is more than the loss. This is the source of his surplus satisfaction. Thus: 

Consumer Surplus = Price Prepared – Actual Price Paid.

Thus, 

      CS = TU – (P x Q) 

                97 - (10 x 4) 

                97 – 40 

                CS = 57 

Where, 

• CS: Consumer surplus 
• TU: Total utility 
• P: Price 
• Q: Quantity 

Consumer Surplus can be Diagrammatically Represented:

If OP is price, OQ is the units purchased MU of OQ = price OP total money paid = OP x OQ therefore, price paid OPQR 

Price prepared to pay = Total Utility OMRQ 

Therefore, OMRQ – OPRQ = MRP (consumer surplus).


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Marginal Rate of Substitution

The concept is the basis of indifference curve and the modern theory of consumer demand. If the consumer exchanges additional unit of one commodity for another commodity it called marginal rate of substation (MRS). In this MRS the consumer reduces the consumption of one commodity and increase the consumption of another commodity if he wants to get same amount of satisfaction. To explain this concept we can consider earlier examples. 

This table shows the five different combinations of apples and oranges which derive the same amount of satisfaction to the consumer because all the five combinations represented by the same indifference curve. Here the consumer increases the purchase of apples and reduces the purchase of purchase of oranges. It means he is substituting apples for oranges. The rate of substitution between apples and oranges goes on diminishing, in the 1st combination 20 oranges and one apple is the 1st stage of satisfaction. In the 2nd stage 15 oranges and 2 apples to get one apples extra the consumer has to forgo 5 oranges. It means 5 oranges were substituted for one apple. The ratio of apples and oranges is 5:1. In the third combination the ratio is 4:1. In the 5th combination the rate of substitution the ratio of substitution will be 2:1. Thus the rate of substitution goes on diminishing. It means if the consumer increase the purchase of apples the stock of oranges on the other hand decreases and the satisfaction of additional unit of orange increases. That’s why the consumer substitutes only 5 oranges for one apple. The rate at which the consumer purchases one commodity by forgoing the other commodity is called marginal rate of substitution. 

In this diagram we have drawn a stair case which descends to the right. The steps of this staircase are equal width but the height of the staircase diminishes from top to bottom. This is due to the fact that the number of apples continues to increase and the number of oranges continues to decrease at a progressively diminishing rate, because of this reason the IC curve is convex to the origin.


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Properties of Indifference Curve

1. IC slopes downwards from left to right:

The IC curve always slopes downwards from left to right, then only we can show the consumer is purchasing one commodity more and the other one less. In our ex the consumer purchases more apples and fewer oranges. 

2. IC curve should not be horizontal:

In this diagram the IC curve is horizontal and it consists of combinations of apples and oranges but they are equally substituted for 5 apples, here the HRS instead of decreasing it is equally substituted. In this case the consumer will not get the same satisfaction from all the combinations. Actually satisfaction may increase. Therefore the IC curve cannot be horizontal. 

3. The IC curve should not slop upwards to the right:

In this diagram the consumer moves upwards along with the curve. It implies he gets more and more of both the commodities. Therefore the total satisfaction increases. At point P the consumer gets OM of apples and ON of oranges. At point Q he gets ON1 of oranges and OM1 of apples, obviously at this point the consumer gets more of both the commodities and the satisfaction will be greater than P. Therefore the IC curve should not move upwards. 

4. The IC curves are Convex at the origin:

The IC curves are convex to the origin, and then only we can show the diminishing marginal rate of substitution. (DMRS).

In this diagram IC is convex to the origin because the consumer purchases more apples and fewer oranges. This indicates the HRS. If the IC curve were to be concave or straight like HRS may not be appropriate, therefore, the IC curve must be always convex to the origin. 

5. Indifference curve cannot intersect each other:

This can be shown in the following diagram;

In this diagram the two indifference curves intersect each other. The satisfaction point A lies on IC2 represents higher satisfaction to the consumer than the point B which lies on IC1 but the point C which lies on both the curve shows the satisfaction point A and B are equal. This is actually impossible therefore IC curve cannot intersect each other. 

6 Every indifference curve to the right represents higher level of satisfaction:

Every indifference curve which comes right derives greater satisfaction because the right side IC2 cure is above the IC1 therefore any combination on IC2 gives more satisfaction than IC1. In the same way IC3 gives more satisfaction than IC2 and so on. 

7 IC curve will not touch any axis:

In indifference curve cannot touch either axis. This can be shown in the diagram. If IC2 touches X axis a point M the consumer will purchase only apples and not oranges. In the same manner if IC1 touches y axis at point L the consumer will purchase only oranges not apples. But the consumer wanted to buy two commodities. Therefore, the IC curve cannot touch any axis.


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Indifference Curve Analysis

The utility analysis lost its popularity because of its assumptions like utility can be measured, marginal utility of money remain constant. To replace these old concepts the modern economists have introduced an indifference curve analysis. This technique was originally developed by F.Y Edgeworth in 1881. Later picked up by Irving Fisher, who tried to give a concrete shape to it in 1892.It was further developed by Pereto. In 1931, I.R Hicks and Allen gave a scientific treatment to this new analysis, Indifference curve analysis is now being used in the analysis of many economic problems.

The indifference curve analysis excludes all the defects of utility analysis. It is based on ordinal utility. Here utility cannot be measured but it can be ranked. It expresses the dissatisfaction in terms of scale of preference. That’s why it is called ordinal approach. 

According to indifference curve analysis utility can’t be measured but it can give preference or ranking for different combinations of two or more goods for ex x and y, which gave the same satisfaction. Therefore the consumer can select any good in the combination. So it is called as preference approach. 

The indifference curve shows the various combinations of commodities which give sane satisfaction to the consumer. The consumer may think of several commodities but for out convenience and simplicity we shall assume two commodities only. An indifference schedule may be defined as a schedule of various combinations of two goods that will be equally acceptable to the consumer. The various combinations of the following two goods give the same satisfaction to the consumer. 

Indifference Schedule 

The above indifference schedule shows the various combinations of the two commodities which derives same satisfaction. The consumer is indifferent between these combinations which yields same satisfaction. Now we can trace the indifference curve with the help of indifference schedule.

In this diagram the ox axis represents apples and oy axis represents oranges. IC curve is the indifference curve. This curve shows the five combinations of two combinations that is 20 oranges and 1 apple, at point A, 15 oranges and 2 apples at point B. In this way the combinations of the tow commodities continues up to point E. If we join all these points we can get IC curve. It is called indifference curve. 

Indifference Map 

In the above set of indifference curve the consumer is able to derive a particular quality of satisfaction. Suppose if he wanted to get more satisfaction this process of combination must be continued. For this purpose we have to draw another indifference curve which is parallel to the previous indifference curve. This can be shown in the following diagram. 

This indifference maps shows the equal satisfactory combinations of the commodities at each level of total income. There are various terms in this indifference map such as IC1, IC2, IC3, IC4, etc. All the points on any one of the curve give the same satisfaction. 

For example - Point AB on IC give the same satisfaction C and D point on IC2 give the same satisfaction. Suppose if the consumer wanted to get more satisfaction he has to go for higher indifference curve. So every indifference curve which moves upwards in the form of IC2, IC2, IC3, IC4 give higher satisfaction to the consumer. Accordingly IC2 yields greater satisfaction than IC1 and IC3 will be greater than IC3 etc. 

This indifference map represents a collection of indifference curves. Each curve shows certain level of satisfaction to the consumer. The different IC curves are numbered in ascending order, as shown in the diagram. So every IC curve which comes on right side derives greater satisfaction and left side curve gives lesser satisfaction.


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Importance of the Concept of Consumer Surplus

• The concept of consumer’s surplus does emphasize the amenities that we enjoy in a modern society. Much of the consumer’s surplus, we enjoy depends on our surroundings and the opportunities of consumption available to us, example, amenities of life in America as compared to Central Africa. It thus clarifies conjectural importance. The concept enables us to compare the advantages of environment and opportunities or conjectural benefits. The larger the consumer’s surplus, the better off is the people. The concept, thus, serves as an index of economic betterment. 

• It is useful in price policy of a monopoly firm. The monopolist can put a higher price on the goods if consumer’s surplus is high, without causing any reduction in sales. 

• It is of significance to the exchequer in determining indirect taxation. The finance minister can easily levy more taxes where consumer’s surplus is high. 

• By estimating the difference in consumer’s surplus resulting from a change in price, we can know and compare the effects of a given change in the price of any commodity on the different classes of people. It is, therefore, widely adopted in welfare economics. 

• Gains from international trade can be measured in terms of consumer’s surplus obtained in the imported goods.

Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Limitations of the Law of Equi-Marginal Utility

The law has been subject to certain criticisms or limitations. They are as follows: 

• The law is based on unrealistic assumption, being, an extension of the law of diminishing marginal utility, it involves all the unrealistic assumptions and conditions such as homogeneity, continuity, constancy etc. 

• The proportionality rule presumes cardinal measurement of utility, but, it is not an unrealistic phenomenon. 

• The law cannot be applied to indivisible goods. On practical grounds, it looks ridiculous to equate utility of television set to coffee for a rupee. 

• Consumer does not behave rationally all the time quite often; his behaviour is influenced by habit, social customs, fashions advertising, propaganda etc. 

• It has also been pointed out by many critics, that it is; wrong to assume that the marginal utility of money will remain constant. Actually when money is spent, the remaining units of money will tend to have a greater marginal utility. Thus there is a backward operation of the law of diminishing marginal utility. Prof. Friedman however defends Marshall, on this point, stating that Marshall was perfectly right in his assumption, as only a part of a consumer’s income at a time is spent on purchasing a few commodities. This income which is kept for allocation in the family budget can very well be assumed to be as given and will be constant as the marginal utility of money changes very gradually with large changes in the stock of money. 

• Ignorance on the part of the consumer about market prices and utility of different goods and the uncertain scale of preference due to his wavering mind also pose a limitation to the operation of this law. 

Despite all these criticisms, it can, however, be concluded that every rational consumer tends to behave according to the law to derive maximum satisfaction though he may not necessarily be forced to do so. On the theoretical ground, it is an analytical proposition of the law that the consumer can maximize his satisfaction only when the marginal utilities are equalized. Analyzing the behavioral aspect of a consumer the law is thus, merely a statement of tendency that has been a common experience.


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Assumption and Importance of the Law of Equi-Marginal Utility

Assumption of the Law:

The law of equi-marginal utility is based on the following assumptions;

• The consumer is a rational economic man who seeks to maximize his total satisfaction.

• Utility is measurable in cardinal terms. 

• The consumer has a given scale of preference for the goods in consideration. He has perfect knowledge of utility derived. 

• Prices of goods are unchanged. 

• Income of the consumer is fixed. 

• Marginal utility of money is constant.

• Wants and goods are substitutable. 

Importance of the Law: 

The law has theoretical as well as practical utility. Theoretically it is a useful device for analyzing the behaviour of a rational consumer. Logically it is a convincing tool to describe the conditions of consumer equilibrium. It opens up analytical areas; it serves as a background for the traditional theory of value. 

The law has the following practical usefulness also: 

1. It Applies to Consumption: 

The law indicates how a consumer derives maximum satisfaction with the help of the principal of substitution; the consumer is able to make the best choice of his wants to gain maximum total satisfaction. It serves as a guide to the consumers to bring about the optimum allocation of his income and expenditure. It thus determines the relative demand for different goods. 

2. It Applies to Production: 

To the producer the law is useful because the very principle of substitution lies in the optimum allocation of resources. The producer can have the most economical or optimal combination of factors of production, when the last unit of investment expenditure brings equal productivity to all the factors of production employed. 

3. It Applies to Exchange: 

This principle has an important bearing on the determination of value. The scarcity of a commodity is reflected through rising prices, in an exchange phenomenon- the market. It, thus, helps in readjustment of resources and adjustment of demand and supply by substitution. 

4. It Applies to Distribution: 

The general theory of distribution involves the principle of substitution. In distributing the rewards of the various agents of production, there shares are determined by the principle of marginal productivity. An optimum distribution is one based on the marginal productivity of factors. This is how the law of substitution is applicable here. 

5. It Applies to Welfare and Public Finance: 

Modern states are welfare states and consider the maximization of social benefits in their revenue and expenditure activities. The principle of ‘maximum social advantage’ involves the law of substitution when it proposes that revenues must be distributed in such a way that the last unit of expenditure brings equal welfare and satisfaction to all classes of people.


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Relationship between the Law of Diminishing Marginal Utility and the Law of Equi-Marginal Utility

• The law of equi-marginal utility is an extension of the law of diminishing marginal utility. It considers the satisfaction derived from the number of commodities at a time. the law of diminishing marginal utility is applicable only to a single commodity whereas the law of equi-marginal utility is applicable to several commodities at a time, therefore, it has greater practical value. 

• The law of equi-marginal utility also accepts the basic principle of diminishing marginal utility, that is, as consumption of a commodity increases, its marginal utility decreases. 

• Both the laws advocate the same principle that marginal utility must be proportional to the price to maximize total utility. The law of diminishing marginal utility however deals with a single commodity only and states that no consumer shall pay a price for the commodity greater than its marginal utility. Thus with a single commodity his equilibrium condition is marginal utility equals price. The same logic is extended further by law of equi-marginal utility and states that in the case of several commodities the equilibrium condition is the marginal utility of all commodities should be proportional to their prices. 

Thus, Mua      Mub 

           Pa   =   Pb


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

The Law of Equi-Marginal Utility

The law of equi-marginal utility is an extension of the law of diminishing marginal utility. This law is called the law of substitution or the law of maximum satisfaction. It is obvious that the law of diminishing marginal utility is applicable only to a single want with one commodity in use. But, in reality there may be a number of wants to be satisfied at a time, and, these various wants are to be satisfied with several goods. To analyse, such a situation, one has to extend the law of diminishing marginal utility and such an extended form is called the law of equi-marginal utility. 

The law of equi-marginal utility is based on the three characteristics of wants, that is, wants are comparative, substitutable and complementary. The law takes the following factors as its starting point: 

1. Consumer has limited income or limited stock of a given commodity. 
2. The consumer has more than one want to satisfy. This he can do either by purchasing the required number of commodities out of a given income or putting a given commodity to various uses to satisfy his different wants. 
3. The consumer is rational and seeks to maximize his wants and his satisfaction. 
4. He has no control over the price of the commodity, but the prices are given. 

Under these conditions the law indicates how to acquire maximum satisfaction by spending the given income for purchasing various goods to satisfy a number of wants. 

Statement of the Law: 

The law of equi-marginal utility states that, other things being equal, a consumer gets maximum total utility from spending his given income, when he allocates his expenditure to the purchase of different goods in such a way that the marginal utilities derived from the last unit of money spent on each item of expenditure tends to be equal, that is, to say that the consumer maximizes his satisfaction, which he obtains equi-marginal utility from all the goods purchased at a given time. 

To consider the condition of consumer’s equilibrium with respect to maximum total satisfaction a proportionality rule in terms of equi-marginal utility has been formulated by Marshall. The proportionality rule states that when the ratio’s of marginal utility to prices of different goods are equalized with the given marginal utility of money income of the consumer, total utility so derived would be the maximum and the consumer will be at equilibrium under this condition. So long as the ratios of marginal utility of money are not equalized, the consumer will go on redistributing his expenditure from one commodity to another, buying less of one, and more of another, that is substituting one for the other, till these ratios become equal. In symbolic terms, that proportionality rule may be stated as follows: 

Where, 

• Mu: is marginal utility 
• P: is price 
• M: is the marginal utility of a given money income. 
• a, b, c,: refers to different goods.

Illustration of the Law:

The law of equi-marginal utility may be explained with the help of an imaginary example which is as follows: 

Let us assume that: 

1. A consumer has a given income of Rs. 24. 
2. He wishes to spend his entire income on three different goods a, b, and c. 
3. The prices of these goods are Rs.2 per unit of ‘a’, Rs. 3 per unit of ‘b’ and Rs.5 per unit ‘c’. 
4. Consumer is rational and seeks to maximize his satisfaction.
5. The consumer has a definite scale of preference as revealed by the marginal utility schedule given below.

Now the question is how this consumer would spend his Rs.24 so that he derives maximum satisfaction. 

As per the proportionality rule of the law of equi-marginal utility, we, may, solve the problem as under;

Diagrammatic Representation of the Law:

The operation of the law of equi-marginal utility can be explained with the help of a graph. 

In the diagram money expenditure of a given income is denoted on the ‘x’ axis and ‘y’ axis represents marginal utility. Mua, Mub, Muc are the marginal utility curves for the three assumed goods, a, b, c respectively. It can be seen that these curves are drawn in such a way that they show the relative order of preference of the given goods a, b, and c. In graphical terms, now the consumer will allocate his given income in such a way that he will purchase OA goods of unit ‘a’, OB units of good ’b’, OC units of good ‘c’. It is easy to see that by spending his income the consumer equalizes the marginal utilities of each commodity purchased, thus maximizing his total satisfaction.


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Total Utility and Marginal Utility

The concepts of total utility and the marginal utility are the basic concepts used in the cardinal measurement of utility. 

According to Prof. Meir, "Total utility is the amount of satisfaction derived from one unit of that commodity". 

According to Prof. Boulding, "Marginal utility of any quantity of commodity is the increase in the total utility, which results from a unit increase in consumption". 

Prof. Bilas points out that, "Marginal utility is defined as the change in the total utility resulting from one unit change in the consumption of the good in question per unit of time". 

In other words, total utility is the total satisfaction derived from the consumption of all the quantities of the commodity in possession or purchased. Marginal utility is the utility or satisfaction derived in consuming the last unit of that commodity. 

Suppose a consumer, purchases a packet of biscuits, total utility is the satisfaction derived from the consumption of all the biscuits in the packet. In other words, total utility means total satisfaction experience regarding all the units of consumption at a particular point of time, apparently total utility tends to be more with the largest stock and less with the smallest stock. In mathematical terms total utility is a direct function of the number of units of a commodity in consideration. To put it symbolically: 

Total utility of x is the increasing function of its quantity. Where TU is the total utility of the commodity, (Qx), ∆ (delta) refers to a small change. 

This functional relationship of total utility to quantity of a commodity may be illustrated by constructing a utility schedule.

In this schedule, we have assumed a cardinal measurement of utility in terms of so many units expressed in numbers, it can be seen that the consumer in the illustration consumes 5 units of commodity ’x’ he derives 82 units of total satisfaction. Total utility thus, measures the strength of the consumers demand for the entire stock of the given commodity. 

Marginal utility on the other hand refers to successful increment in the total utility made by taking separately each unit of the commodity in a successive manner as an addition to its total stock. Thus, utility of the first unit is measured as the marginal utility at the beginning. Then the utility of the 2nd unit x is measured as the marginal utility of the 2 units on the given stock similarly, the utility derived from the 3rd unit would be marginal utility of the stock 3 units. 

Thus marginal utility may be measured as a difference between the utility of the total units of the stock of consumption of a given commodity minus that of consuming one unit less in the stock.

The computation of marginal utility has been illustrated in the following table: 

It’s easy to see that the marginal utility determines the rate of increase in the total utility with the increase in the units of a commodity. In short marginal utility refers to the utility of marginal unit of consumption. It changes according to the changes in the stock of things. It is the last unit in the sequence of consumption. 

In expounding the marginal utility analysis of the consumers demand behaviour, Prof Alfred Marshall has propounded 2 fundamental laws. 

1. The law of diminishing marginal utility 
2. The law of equi-marginal utility.

Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Measurement of Utility

Utility being an introspective phenomenon cannot be directly measured in a precise manner. Economist however adopted an indirect measurement of utility in terms of ’price’ a consumer is willing to pay for a given commodity. When a consumer is willing to pay a high price for a commodity, it means there is high utility estimated by him for that commodity and vice versa. But, this is just a rough indication it suggests no precise and proportionate measurement of utility. 

From the stand point of theory, however, there are 2 basic approaches to the measurement of utility namely: 

1. Cardinal approach 
2. Ordinal approach 

The cardinal measurement of utility was propounded by prof. Alfred Marshall and his followers. According to them utility of a commodity is quantifiable hence measurable numerically. They assume that for a consumer an apple may yield 10 utils (utils is the term used by Marshall for expressing the measurement of imaginary units of utility or satisfaction) while mango may yield 30 ‘utils’. Thus, utility of a mango is 3 times more in proportion to a utility of an apple. Such a numerical measure is imaginary. When a utility statement is tabulated as a schedule of utility, it is referred to as the cardinal measurement of utility. 

The terms cardinal and ordinal have been taken from mathematics. The numbers 1,2,3,4,5,6, etc are cardinal in the sense that number 6 is twice the size of number 3 and number 4 is twice the size of 2. In the cardinal analysis, the utility contained in commodities are made quantifiable. For example: an orange may yield to a consumer utility of 10 units whereas a mango yields 20 units. From this it is clear that the consumer derives twice as much utility from a mango compared to an orange. The units of measurements are purely imaginary and the cardinal analysis termed the imaginary units of utility of ‘utils’. 

On the other hand Prof Hicks Allen and their followers among the modern economists have suggested an ordinal measurement of utility. In their view utility cannot be quantified so its numerical expression is unrealistic. 

The ordinal measurements are 1st, 2nd, 3rd, 4th, 5th, 6th etc. It is not possible from this ranking to know the actual size of related number. The 2nd need not be twice as that of 1st, the size may be of any pattern. For example: 1st, 2nd, 3rd, could be 10, 15, 25, or 10, 20, 45 or 55, 65, 95 etc. According to ordinalists, utility being subjective and a mental concept cannot be measured and to quantify utility is absurd. 

Ordinal approach contains that the theory of consumer behaviour can be explained or analyzed even without measuring utility as the cardinal approach does. In the all ready stated example the ordinalists say that the consumer prefers a banana to an orange and rank the commodities in the scale of preferences without taking the trouble of measuring the imaginary quantum of utility. This method of ordinal approach is also called’ indifference curve approach’. 

Dr. Alfred Marshall and his followers advocated the cardinal approach to utility, while, the modern economists like Hicks, Allen, supported the ordinal approach. Hence the cardinal approach has come to be known as, ”Marshallian utility analysis” and the ordinal approach is called ‘Hicksian’s indifference approach’.


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Utility and its Meaning

Consumer has a pivotal role in the economic activity. He consumes goods and services for the satisfaction of his wants. Satisfaction of wants is the beginning and end of all economic activity. Thus micro economics analysis always begins with the understanding of the consumer’s behaviour by investigating into fundamental basis of demand. Stanley Jevouns a noted classical economist originated the concept of “utility” as the fundamental basis of consumers demand for a commodity.  The term utility refers to the want satisfying power of a commodity or service assumed by a consumer to constitute his demand for that commodity or service. 

Utility thus is an introspective or subjective term. It relates to the consumers mental attitude and experience regarding a given commodity or service. Thus, utility of a commodity may differ from person to person. Utility is a relative term it depends on time and place. Thus, the consumer may experience a higher or lesser utility for the same commodity at different times and different places. Moreover, utility has no ethical or moral consideration. A commodity that satisfies any type of want whether morally good or bad has utility. Further utility is not necessarily equaled with usefulness. 

 A commodity may have utility, a power to satisfy some want but, it may not be useful to the consumer. For example: a Cigarette has utility to a smoker but it is injurious to his health. Utility is the function of intensity of want. A want which is unsatisfied or greatly intense will imply a high utility for the commodity concerned to a person. But a want is satisfied in the process of consumption it tends to become less intense than before. As such the consumer tends to experience a lesser utility of that commodity than before. Such an experience is very common and it is described as the tendency of diminishing utility experienced with the increase in consumption of a commodity. In other words more of a commodity we have, the less we want it.


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Utility and Satisfaction

The term utility is, however, distinct from satisfaction. Utility implies potentiality of satisfaction in a commodity. It serves as a basis to induce the consumer to buy the commodity. But, the real satisfaction is the end result of the consumption of a given commodity. 

Though utility and satisfaction are psychological, there is a distinctive gap between the two experiences. Utility is anticipation of satisfaction visualized. Satisfaction is the actual realization. Sometimes, satisfaction derived from the consumption of a commodity may be less or more than what is expected in the visualization of utility. For example when a consumer buys a motor car and if it starts giving him trouble his satisfaction so realized from the use of the motor car will be less than what he had estimated about his utility. 

Nonetheless in economic theory for the sake simplicity and convenience in analysis, economist usually assumes utility and satisfaction as synonymous terms.


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Exceptions to the Law of Diminishing Marginal Utility

Under the assumptions of homogeneity, continuity, reasonability, constancy and rationality, the law is deemed to be universal. In certain cases, however, it has been observed that a consumer tends to attain increasing marginal utility with an increase in the stock of a commodity consumed or acquired. Such cases are treated as exception to the law of diminishing marginal utility. These exceptions are: 

1. Hobbies: 

It is often argued that in the case of hobbies like stamp collection, collection of antique goods, collection of old coins etc, every additional unit gives more pleasure, that is, marginal utility, tends to increase. No doubt this is true, but, it is not a genuine exception to the law of diminishing utility, because in such cases, homogeneity condition of the law is violated. Indeed each time a new variety of stamp or coin or antique is collected by a person but not of the same variety. 

2. Alcoholics: 

The law seems to be inapplicable to alcoholics as intoxicants increases with every successive dose of liquor. This is true, but the rationality condition of the law is violated. The introspective behaviour of an alcoholic at that time is irrational or abnormal. 

3. Misers: 

In the case of a miser, it is pointed out that greed increases with every additional acquisition of money. Hence, the marginal utility of money does not diminish for him with more and more money. But, when the miser spends his money his utility of the commodity will be diminishing perhaps more rapidly than in the case of others. Hence, a miser’s behaviour cannot be a significance exception to the law of diminishing marginal utility. 

4. Music and poetry: 

In the case of music and poetry it’s commonly experienced that a repeat gives a better satisfaction than the first one. Hence, it is thought that the law of diminishing marginal utility may not be applicable here. But there is a limit to repeated hearing of the same music and poetry because, it will become monotonous and yields dis-utility  so it is not a genuine exception to the law. 

5. Reading: 

Since more reading gives more knowledge a scholar would get more and more satisfaction with every additional book. But, here we may point out that it is not a real exception to the law as the condition of homogeneity is violated here. Knowledge and satisfaction increases by reading different books and not the same book over and over again.


Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Importance of the Law of Diminishing Marginal Utility

The law of diminishing marginal utility has great economic significance, theoretical as well as practical. From the theoretical point of view the law is important because, 

• The law explains the behaviour and the equilibrium condition of a rational consumer with respect to a single want and commodity. 

• The law of diminishing marginal utility is the basic law of economics. It provides the foundation for various laws of consumption. The law of demand is the outcome of the law of diminishing marginal utility. The law of demand states that larger quantities are purchased at a lower price. The reason is that as more units of a commodity are purchased its marginal utility to the consumer becomes less and less and so he gives lesser importance to additional units of a commodity. Therefore, he will buy additional units of a commodity only at a lower price. 

• The law explains the paradox of value. The value-in-use and value-in-exchange for a commodity are different. Diamonds have great value-in-exchange, as they are scarce in supply, they have greater marginal utility, and therefore, value is high. On the other hand, water is in abundant supply and its marginal utility is very low. Therefore, it commands no price even though its total utility is high. Thus water has great value in use but no value in exchange. Diamonds have great value in exchange though they are less useful than water. The price of a commodity is thus, related to its marginal utility. 

• Prof. Marshall has built up his theory of taxation and public expenditure on the basis of the law of diminishing marginal utility. The principle of progression has been deduced in the theory of taxation by the application of this law, to money. Further, it is argued that there should be equitable distribution of wealth because the utility derived by the rich from money is much less than what could accrue to the poor. If Rs. 100 deducted from the rich man’s income, means only a small sacrifice of comparatively little utility, while the addition to the amount to the poor man’s income, will increase his satisfaction by more than what a rich man has lost, therefore, methods should be devised to redistribute the national income on a more equitable basis.

The law has the following practical significance as well; 

• To the producer, the law serves as a guide to promote sales by reducing prices. Because, when the price falls, to attain equilibrium the consumer has to decrease the marginal utility to that extent. To do this he has to purchase more goods as the marginal utility diminishes only when the stock increases. 

• The law is useful to the finance minister in formulating an appropriate tax policy. He can justify progressive taxation on higher income on the ground that rich people will feel relatively lesser impact of the tax burden as the marginal utility of money is lower with the increase in income. 

• Similarly socialists can agitate for a redistribution of wealth to promote welfare on the ground that the transfer will cause more gain to the poor and less sacrifice to the rich.

Notes provided by Prof. Sujatha Devi B (St. Philomina's College)

Criticism of the Law of Diminishing Marginal Utility

Though the law expresses a universal tendency of consumer’s introspective behaviour, its traditional exposition has been criticized on various counts. 

• The traditional or Marshallian explanation of the law presumes the cardinal measurement of utility. The law assumes that utility can be numerically measured added or subtracted. This is rather not convincing because utility being a subjective or introspective phenomena cannot be measured numerically. It is a feeling experienced by the consumer. We cannot therefore have a objective measure of a subjective feeling. 

• The law is based on unrealistic assumptions or conditions. The condition assumed like homogeneity, continuity, constancy and rationality all together present at a time is very difficult to find in practice. 

•  The application of the law to the indivisible bulky commodity seems to be absurd. Because no one would normally buy at a time more than one unit of good like television set, refrigerator, scooter, motor car etc. It would be absurd to talk of increase in the stock of such goods and marginal utility thus derived. 

• The law unrealistically assumes constant marginal utility of money, which is highly unsatisfactory, with the increase in purchase of goods, for consumption, the marginal utility of money will increase due to the diminishing stock of purchasing power.

Notes provided by Prof. Sujatha Devi B (St. Philomina's College)