Utility Complete Notes

Utility Definition

Utility is the power of a commodity that satisfies the wants of consumer. So, it is the want satisfying power of a commodity. Utility is a psychological phenomenon. It is a feeling of satisfaction, pleasure and happiness or well being which a consumer derives from the consumption, possession or the use of a commodity.

Definitions:

  • According to Jevons, “Utility refers to abstract quality whereby an object serves our purpose.
  • In the words of Hibdon, “Utility is the quality of good to satisfy a want.”
  • According to Mrs. Robinson, “Utility is the quality in commodities that makes individuals wants to buy them”.

Features:

  1. Utility is Subjective: as it deals with the mental satisfaction of a man. A thing may have different utility to different persons. E.g. Liquor has utility for drunkard but for person who is teetotaller, it has no utility.
  2. Utility is Relative: As a utility of a commodity never remains the same. It varies with time and place. E.g. Cooler has utility in summer not during winter season.
  3. Utility has nothing to do with usefulness: A commodity having utility need not be useful. E.g. Liquor and cigarette are not useful, but if these things satisfy the want of addict then they have utility for him. 
  4. Utility is independent of Morality: It has nothing to do with morality. Use of opium or liquor may not be proper from moral point of view, but as these intoxicants satisfy wants of the opium – eaters, drunkards, they have utility

The terms utility and satisfaction are, for the most part, used interchangeably in economics. But Utility is the expected satisfaction where as satisfaction is the realized utility.

Early economists-classical economists, viz. Jeremy Bentham, Leon Walrus, Carl Menger, etc. and Neo-classical Economist, notably Alfred Marshall- believed that utility is cardinally or quantitatively measurable like height, weight, length, and temperature and air pressure. This belief resulted in Cardinal concept.

Cardinal Utility

Cardinal utility is that utility which can be expressed in quantitative terms i.e., utility can be measured in quantitative terms. A measure of utility, or satisfaction derived from the consumption of goods and services that can be measured using an absolute scale. Cardinal utility exists if the utility derived from consumption is measurable in the same way that other physical characteristics–height and weight–are measured using a scale that is comparable between people.

Prof. Fisher has used the term, “Util”, as a unit for the measurement of utility.

A util has a fixed size, making comparisons based on ratios of utils possible.

Analysis of cardinal utility is based on:

  • The law of diminishing marginal utility.
  • The law of Equi- marginal utility.

Assumptions: The cardinal utility approach to consumer analysis makes the following assumptions:-

  1. RATIONALITY – it is assumed that the consumer is a rational being in the sense that he satisfies his wants in the order of their preferences, that is, he or she buys the commodity first which yields the higher utility and that least which gives the least
  2. LIMITED MONEY INCOME – The consumer has a limited money income to spend on the goods and services he or she chooses to consume. Limitedness of income, along with utility maximization objective makes the choice between goods inevitable.
  3. MAXIMIZATION OF SATISFACTION – Every rational consumer intends to maximize his/her satisfaction from his/her given money income.
  4. UTILITY IS CARDINALLY MEASURABLE – The cardinalists have assumed that the commodities that the utility is cardinally measurable and that utility of one unit of a commodity equals the money which a consumer is prepared to pay for it or 1util = 1unit of money.
  5. CONSTANT MARGINAL UTILITY OF MONEY – The cardinal utility approach assumes that the marginal utility of money remains constant whatever the level of a consumer’s income. This assumption is necessary to keep the scale of measuring rod of utility fixed. It is important to recall in this regard that cardinalists used ‘money’ as the measure of utility.
  6. UTILITY IS ADDITIVE – Cardinalists assumed not only that utility is cardinally measurable bit also that utility derived from various goods and services consumed by a consumer can be added together to obtain the total utility. In other words, the consumer has a utility function which may be expressed as:

                                        U= f(X1, X2, X3 …Xn)

      Where X1, X2 …X3 denote total quantities of the various goods consumed.

Given the utility function, total utility obtained from n items can be expressed as:

Un = U1(X1) +U2(X2) + U3(X3) + ……+ Un (Xn) it is the utility function which the consumer aims to maximize.

  1. INDEPENDENT UTILITIES:-It is assumed that the utility which a consumer obtains from a good does not depend upon the quantity consumed of other goods; it depends upon the quantity purchased of that good alone.
  2. INTROSPECTION-Introspection is the ability of observer to reconstruct events which go in the minds of another person with the help of self observation. That is by looking into ourselves we see inside the heads of other individuals.

 

TOTAL UTILITY:-

It is the sum of utilities derived by a consumer from various units of goods and services he consumes. Suppose a consumer consumes four units of a commodity, X, at a time and derives utility as U1,U2,U3,U4. His total utility (TUx) from commodity X can be measured as follows.

                                 TUx = U1 + U2 + U3 + U4

If ‘n’ number of commodities he consumes, then his total utility will be-

                                  TUn = Ux + Uy + Uz

Marginal Utility

It is defined as the utility derived from the marginal unit consumed. It may also be defined as the addition to the utility resulting from the consumption (or accumulation) of one additional unit. Marginal utility (MU) thus refers to the change in the total utility obtained from the consumption of additional unit of a commodity. It may be expressed as-

                                    MU=TUn   – TUn-1

Marginal utility can be:

  1. Positive Marginal Utility: If by consuming additional units of commodity, total utility goes on increasing, then marginal utility of these units will be positive.
  2. Zero Marginal Utility: If the consumption of additional unit of commodity causes no change in the total utility, it means the marginal utility of additional unit is zero.
  3. Negative Marginal Utility:If the consumption of an additional unit of a commodity causes fall in total utility, it means the marginal utility is negative.

Relation between Total Utility and Marginal Utility:

Total utility is the summation of the marginal utilities of different units of a commodity.

  • When MU is +ve, TU increases.
  • When MU is 0, TU is max.(Point of Satiety)
  • When MU is -ve, TU decreases.

Table shows that:

a) As more and more units of commodity are consumed, the marginal utility derived from each successive unit goes on diminishing. But the total utility increases up to a limit

b) Marginal utility of the first four units being positive,the total utility goes onincreasin Thus as long as the marginal utility of the commodity remains  positive, total utility goes on increasing.

c) Marginal utility of the fifth unit is zero. In this situation total utility (20) will be This situation also represents pointof saturation.

d) Marginal utility of the sixth unit is negati As aresult of it, total utility of six units of the commodity falls from 20 to 18 units.

The Law of Diminishing Marginal Utility

Law of Diminishing Marginal Utility is the foundation stone of utility analysis. All of us experience this law in our daily life. The law of diminishing marginal utility is universal in character. It is based upon the important fact that human wants are unlimited but a single want can be satisfied at a particular time.

“The additional benefit, which a person derives from a given increase of a stock of a thing diminishes, other things being equal, with every increase in the stock that he already has.”-Prof. Marshall

Definition of ‘Law of Diminishing Marginal Utility’

It is clear from the above definitions that at a given time when we go on consuming additional units of a commodity, the marginal utility from each successive unit of that commodity, other things being equal, goes on diminishing in relation to the preceding unit. It is this diminishing tendency of the marginal utility that has been enshrined in the law of diminishing marginal utility.

Simply put, as the rate of commodity consumption increases, marginal utility decreases. If commodity consumption continues to rise, marginal utility at some point falls to zero, reaching maximum total utility. Further increase in consumption of units of commodities causes marginal utility to become negative; this signifies dissatisfaction.

Suppose, a man is very thirsty. He goes to the market and buys one glass of sweet water. The glass of water gives him immense pleasure or we say the first glass of water has great utility for him. If he takes second glass of water after that, the utility will be less than that of the first one. It is because the edge of his thirst has been blunted to a great extent. If he drinks third glass of water, the utility of the third glass will be less than that of second and so on. The utility goes on diminishing with the consumption of every successive glass of water till it drops down to zero. This is the point of satiety. It is the position of consumer’s equilibrium or maximum satisfaction. If the consumer is forced further to take a glass of water, it leads to disutility causing total utility to decline. The marginal utility will become negative. A rational consumer will stop taking water at the point at which marginal utility becomes negative even if the good is free.

Units of Commodity

Total Utility

Marginal Utility

1

3

8

2

14

6

3

16

2

4

16

0

5

14

-2

CAUSES OF OPERATION OF LAW:

The law of diminishing marginal utility is based upon three facts:

First, total wants of a man are unlimited but each single want can be satisfied. As a man consumes more and more units of a commodity, his desire for that good goes on falling. A point is reached when the consumer no longer wants any more units of that good.

Secondly, different goods are not perfect substitutes for each other in the satisfaction of various particular wants. As such the marginal utility will decline as the consumer gets additional units of a specific good. (Prof. Boulding)

Thirdly, the marginal utility of money is constant given the consumer’s wealth.

ASSUMPTIONS OF LAW OF DIMINISHING MARGINAL UTILITY

The law of diminishing marginal utility is true under certain assumptions. These assumptions are as under:

  • Rationality: In the cardinal utility analysis, it is assumed that the consumer is rational. He aims at maximization of utility subject to availability of his income.
  • Constant marginal utility of money: It is assumed in the theory that the marginal utility of money based for purchasing goods remains constant. If the marginal utility of money changes with the increase or decrease in income, it then cannot yield correct measurement of the marginal utility of the good.
  • Diminishing marginal utility: Another important assumption of utility analysis is that the utility gained from the successive units of a commodity diminishes in a given time period.
  • Utility is additive: In the early versions of the theory of consumer behavior, it was assumed that the utilities of different commodities are independent. The total utility of each commodity is additive.

U = U (X) + U (X) + U (X)………. U (X) 

  • Consumption to be continuous: It is assumed in this law that the consumption of a commodity should be continuous. If there is interval between the consumption of the same units of the commodity, the law may not hold good. For instance, if you take one glass of water in the morning and the 2nd at noon, the marginal utility of the 2nd glass of water may increase.
  • Suitable quantity: It is also assumed that the commodity consumed is taken in suitable and reasonable units. If the units are too small, then the marginal utility instead of falling may increase up to a few units.
  • Character of the consumer does not change: The law holds true if there is no change in the character of the consumer. For example, if a consumer develops a taste for wine, the additional units of wine may increase the marginal utility to a drunkard.
  • No change to fashion: Customs and tastes: If there is a sudden change in fashion or customs or taste of a consumer, it can than make the law inoperative.
  • No change in the price of the commodity: there should be any change in the price of that commodity as more units are consumed.

EXCEPTIONS OF LAW OF DIMINISHING MARGINAL UTILITY

There are some exceptions to the law of diminishing utility.

  • Initial units: When the initial units of a commodity in used is less then appropriate quantity, then the marginal utility from the additional units goes on
  • Case of intoxicants: Consumption of liquor defies the low for a short period. The more a person drinks, the more likes it. However, this is truer only initially. A stage comes when a drunkard too starts taking less and less liquor and eventually stops it.
  • Rare collection: If there are only two diamonds in the world, the possession of 2nd diamond will push up the marginal utility.
  • Application to money: The law equally holds good for money. It is true that more money the man has, the greedier he is to get additional units of it. However, the truth is that the marginal utility of money declines with richness but never falls to zero.
  • Hobbies: In case of certain hobbies like stamp collection or old coins, every addition unit gives more pleasure. MU goes on increasing with the acquisition of every unit.
  • Reading: reading of more books gives more knowledge and in turn greater satisfactions.
  • Misers: It seems law does not apply to misers who are out to acquire more and more of wealth. Their desire for money seems to be insatiable.

Summing up, we can say that the law of diminishing utility, like other laws of Economics, is simply a statement of tendency. It holds good provided other factors remain constant.

Importance of the law of DMU

  1. Basic of economic law and concepts: This law of DMU forms the basis of law of demand, law of Equi-marginal utility, elasticity of demand and concept of consumer surplus.
  2. Variety in production and consumption: It is because of the operation of the law of diminishing marginal utility that variety in production and consumption is Continuous consumption of one commodity will yield less and lessmarginal utility to the consumers. So every prudent consumer stops theconsumption of that good after a particular limit and shift to other commodity.
  3. Difference between value in use and value in exchange: According to Adam Smith goods having more value in use command low price and those having more value in exchange command high price. It can be explained on the basis of diminishing marginal utility as there is abundant supply of water air etc and the same can be used in large quantity, consequently there marginal utility falls rapidly and so is the price. Thus goods having more value in use have less marginal utility.
  4. Price determination: Price of every commodity is determined by its demand and supply. Demand for a commodity depends upon its marginal utility. The consumer buys more units only when the price per unit falls. 
  5. Basis of progressive taxation: Progressive taxation system refers to that system of taxation under which rate of taxation increases as the income of person increases. It is so because with increase in income marginal utility of money goes on diminishing
  6. Advantage to the consumer: According to this law, in order to get maximum satisfaction from the consumption of a good a consumer should buy only that many units of it whose marginal utility is equal to its price.
  7. Basis of redistribution:According to this law the fundamental reason of redistribution of income is that marginal utility of money to the rich is less then to poor. So it wealth is redistributed in favor of poor, total welfare of society would increase.

Criticism:

  1. Cardinal measurement of utility is not possible.
  2. Marginal utility of money is not constant.
  3. Every commodity is not an independent commodity.

 No commodity is independent, as the marginal utility of one commodity has no effect on the consumption of other commodities. It is very difficult to make precise estimate of marginal utility.

  1. Marginal utility cannot be estimated in all conditions

Marginal utility of only those commodities can be estimated which are divisible, but in real life many commodities are not divisible.

  1. Unrealistic assumption: This law is based on many unrealistic assumptions. It is applicable only when the tastes, habits, fashion, income etc. of the consumer remains constant. But in actual life all these are ever changing.

Law of Equi Marginal Utility

“The utility will be maximised, when the marginal unit of expenditure in each direction brings in the same increments of utility.”

-Prof. J.R. Hicks

Thus, the law of Equi-marginal utility explains that wants of every consumer are unlimited, but the resources available with him to satisfy these wants are limited, that too having alternative uses. Therefore, he spends these resources in a manner that he may get maximum satisfaction.

According to this, a consumer is in equilibrium when he distributes his given money income among various goods in such a way that marginal utility derived from the last rupee spent on each good is the same.

The income at his disposal at any time is limited. The consumer is therefore, faced with a choice among many commodities that he can and would like to pay. He therefore, consciously or unconsciously compares the satisfaction which he obtains from the purchase of the commodity and the price which he pays for it.

As he buys more and more of that commodity, the utility of the successive units begins to diminish. He stops further purchase of the commodity at a point where the marginal utility of the commodity and its price are just equal.

If he pushes the purchase further from his point of equilibrium, then the marginal utility of the commodity will be less than that of price and the household will be a loser. The consumer will maximize total utility from his given income when the utility from the last rupee spent on each good is the same

The law of Equi marginal utility is simply an extension of the law of diminishing marginal utility to two or more than two commodities.

The law of Equi marginal utility is known, by various names. It is named as the Law of Substitution, the Law of Maximum Satisfaction, the Law of Indifference and the Proportionate Rule.

This law has been illustrated with the help of table given below.

Units

MU of Apples

MU of Oranges

1

10

7

2

8

6

3

6

5

4

4

2

5

2

0

6

0

-2

7

-2

-4

8

-4

-6

Suppose apples and oranges are the commodities to be purchased suppose we have Rs. 5to spend. Let us suppose that price of both the goods is Rs.1 per unit. We will spend first rupee on apple for it gives us highest utility.

First Rupee – Apple

Second Rupee – Apple

Third Rupee – Orange

Fourth Rupee – Apple

Fifth Rupee – Orange

Now the MU of last rupee spent on both oranges and apples is the same i.e. 6. This arrangement yields maximum satisfaction. Thus,

Total utility of 2 oranges would be 7+6=13

Total utility of3 apples would be 10+8+6=24

Total utility from both goods is 37.

Thus, it can be concluded that we obtain maximum satisfaction when we equalize marginal utilities by substituting some unit of the more useful for the less useful commodity.

Any other combination will result in decreased TU.

Assumptions: The main assumptions of the law of Equi-marginal utility are as under:

(1) Independent utilities. The marginal utility of different commodities is independent of each other and diminishes with more and more purchases.

 (2) Constant marginal utility of money. The marginal utility of money remains constant to the consumer as he spends more and more of it on the purchases of goods.

(3) Utility is cardinally measurable.

(4) Every consumer is rational in the purchase of goods.

(5) Limited money income. A consumer has limited amount of money income to spend.

Limitations of the Law

Firstly, the utility derived from commodities is not measurable in cardinal numbers.

Secondly, the marginal utility of money cannot be constant. As the money you possess depletes, the marginal utility of money increases.

Thirdly, even a rational economic individual does not allocate his or her income according to the law. Usually, people tend to spend in a certain rough fashion. Therefore, the applicability of the law is doubtful.

Finally, the law assumes that commodities and their marginal utilities are independent. However, in real life, we see many substitutes and complements. In this case, the law loses its credibility.

Practical Importance of Law of EMU:

  1. Consumption: A wise consumer acts on this law while arranging his expenditure and obtains maximum satisfaction.
  2. Production: To obtain maximum net profit, he must substitute one factor of producing to another so as to have most economical combination.
  3. Exchange: Exchange implies substitution of one thing to another and hence this law is important.
  4. Distribution: It is on the principle of the marginal productivity that the share of each factor of production is determined.
  5. Public finance: The Govt. is also guided by this law in public expenditure. The Govt. can expend its revenue (money) in such a way that it will secure maximum welfare of the people.

Consumers Equilibrium Utility Analysis

A consumer is said to be in equilibrium, when he does not intend to change his level of consumption, i.e., when he derives maximum satisfaction.

Consumer’s Equilibrium refers to the situation when a consumer is having maximum satisfaction with limited income and has no tendency to change his way of existing expenditure. The consumer has to pay a price for each unit of the commodity. So, he cannot buy or consume unlimited quantity.

As per the Law of DMU, utility derived from each successive unit goes on decreasing. At the same time, his income also decreases with purchase of more and more units of a commodity.

So, a rational consumer aims to balance his expenditure in such a manner, so that he gets maximum satisfaction with minimum expenditure. When he does so, he is said to be in equilibrium. After reaching the point of equilibrium, there is no further incentive to make any change in the quantity of the commodity purchased.

Consumer’s Equilibrium in case of Single Commodity

The Law of DMU can be used to explain consumer’s equilibrium in case of a single commodity. Therefore, all the assumptions of Law of DMU are taken as assumptions of consumer’s equilibrium in case of single commodity.

A consumer purchasing a single commodity will be at equilibrium, when he is buying such a quantity of that commodity, which gives him maximum satisfaction. The number of units to be consumed of the given commodity by a consumer depends on 2 factors:

  1. Price of the given commodity;
  2. Expected utility (Marginal utility) from each successive unit.

To determine the equilibrium point, consumer compares the price (or cost) of the given commodity with its utility (satisfaction or benefit). Being a rational consumer, he will be at equilibrium when marginal utility is equal to price paid for the commodity.

We know, marginal utility is expressed in utils and price is expressed in terms of money However, marginal utility and price can be effectively compared only when both are stated in the same units. Therefore, marginal utility in utils is expressed in terms of money.

Marginal Utility in terms of Money = Marginal Utility in utils/ Marginal Utility of one rupee (MUM)

MU of one rupee is the extra utility obtained when an additional rupee is spent on other goods. As utility is a subjective concept and differs from person to person, it is assumed that a consumer himself defines the MU of one rupee, in terms of satisfaction from bundle of goods.

Equilibrium Condition:

Consumer in consumption of single commodity (say, x) will be at equilibrium when:

Marginal Utility (MUx) is equal to Price (Px) paid for the commodity; i.e. MU = Price

  1. If MUX> Px, then consumer is not at equilibrium and he goes on buying because benefit is greater than cost. As he buys more, MU falls because of operation of the law of diminishing marginal utility. When MU becomes equal to price, consumer gets the maximum benefits and is in equilibrium.
  2. Similarly, when MUX< Px, then also consumer is not at equilibrium as he will have to reduce consumption of commodity x to raise his total satisfaction till MU becomes equal to price.

Let us now determine the consumer’s equilibrium if the consumer spends his entire income on single commodity.

Assumptions:-
a) Utility can be measured in terms of units.
b) Consumer is rational and wants maximum satisfaction.
c) Independent utility
d) MU of money is constant. MU of money is known as worth of a rupee.
e) Law of Diminishing Marginal Utility is applied here

Schedule: – Suppose a consumer is buying X and the price of each unit of orange is Rs.10, hypothetical MU of orange is given as:

In Fig. 2.3, MUX curve slopes downwards, indicating that the marginal utility falls with successive consumption of commodity x due to operation of Law of DMU. Price (Px) is a horizontal and straight price line as price is fixed at Rs. 10 per unit. From the given schedule and diagram, it is clear that the consumer will be at equilibrium at point ‘E’, when he consumes 3 units of commodity x, because at point E, MUX = Px

  1. He will not consume 4 units of x as MU of Rs. 4 is less than price paid of Rs. 10.
  2. Similarly, he will not consume 2 units of x as MU of Rs. 16 is more than the price paid.

So, it can be concluded that a consumer in consumption of single commodity (say, x) will be at equilibrium when marginal utility from the commodity (MUJ is equal to price (PJ paid for the commodity.

Consumer’s Equilibrium in case of Two Commodities:

In real life, a consumer normally consumes more than one commodity. In such a situation, ‘Law of Equi-Marginal Utility’ helps in optimum allocation of his income.

Law of Equi-marginal utility is also known as:

(i) Law of Substitution;

(ii) Law of maximum satisfaction;

(iii) Gossen’s Second Law.

As law of Equi-marginal utility is based on Law of DMU, all assumptions of the latter also apply to the former. Let us now discuss equilibrium of consumer by taking two goods: ‘x’ and ‘y’. The same analysis can be extended for any number of goods.

In case of consumer equilibrium under single commodity, we assumed that the entire income was spent on a single commodity. Now, consumer wants to allocate his money income between the two goods to attain the equilibrium position.

According to the law of Equi-marginal utility, a consumer gets maximum satisfaction, when ratios of MU of two commodities and their respective prices are equal and MU falls as consumption increases. It means, there are two necessary conditions to attain Consumer’s Equilibrium in case of Two Commodities:

  • Marginal Utility (MU) of last rupee spent on each commodity is same
  • MU falls as consumption increases

 

We know, a consumer in consumption of single commodity (say, x) is at equilibrium when MUx/Px =MUM. Similarly, consumer consuming another commodity (say, y) will be at equilibrium when MUY/PY =MUM

We get: MUX/PX = MUY/PY = MUM

What happens when MUX/PX is Not Equal to MUY/PY

(i) Suppose, MUX/ PX>MUY/PY. In this case, the consumer is getting more marginal utility per rupee in case of good X as compared to Y. Therefore, he will buy more of X and less of Y. This will lead to fall in MUX and rise in MUY. The consumer will continue to buy more of X till MUX/PX = MUY/PY

(ii) When MUX/PX<MUY/PY, the consumer is getting more marginal utility per rupee in case of good Y as compared to X. Therefore, he will buy more of Y and less of X. This will lead fall in MUY and rise in MUX. The consumer will continue to buy more of Y till MUX/PX = MUY/PY.

It brings us to a conclusion that MUX/PX = MUY/PY is a necessary condition to attain Consumer’s Equilibrium.

The consumer equilibrium is found by comparing the marginal utility per dollar spent (the ratio of the marginal utility to the price of a good) for goods 1 and 2, subject to the constraint that the consumer does not exceed her budget of $5.

The marginal utility per dollar spent on the first unit of good 1 is greater than the marginal utility per dollar spent on the first unit of good 2(12 utils > 9 utils). Because the price of good 1 is $2 per unit, the consumer can afford to purchase this first unit of good 1, and so she does. She now has $5 − $2 = $3 remaining in her budget.

The consumer’s next step is to compare the marginal utility per dollar spent on the second unit of good 1 with marginal utility per dollar spent on the first unit of good 2. Because these ratios are both equal to 9 utils, the consumer is indifferent between purchasing the second unit of good 1 and first unit of good 2, so she purchases both.

She can afford to do so because the second unit of good 1 costs $2 and the first unit of good 2 costs $1, for a total of $3.

At this point, the consumer has exhausted her budget of $5 and has arrived at the consumer equilibrium, where the marginal utilities per dollar spent are equal. The consumer’s equilibrium choice is to purchase 2 units of good 1 and 1 unit of good 2.

 

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