Utility analysis

What is Utility?
Satisfaction, happiness, benefit
In the words of Hibbdon , “Utility is the Quality of
a good to satisfy a want.”
Thus we can say that wants satisfying power of a
commodity is called utility.

FEATURES OF UTILITY
• UTILITY IS SUBJECTIVE: It is subjective because it deals
with the mental satisfaction of a man.
• UTILITY IS RELATIVE: Utility of a commodity never
remains the same. E.g. Cooler has utility in the summer but not
during winter.
• UTILITY IS NOT ESSENTIALLY USEFUL:A commodity
having utility need not be useful. Liquor and cigarette are not
useful, but to satisfy the want of an addict then they gave utility
for him.
• UTILITY IS INDEPENDENT OF MORALITY: Utility has
nothing to do with morality.

Cardinal Utility vs. Ordinal Utility
Cardinal Utility: Assigning numerical/quantitative
values to the amount of satisfaction
Alfred Marshall, Leon Walrus, and Carl Meneger
Ordinal Utility: Not assigning numerical values to the
amount of satisfaction but indicating the order of
preferences, that is, what is preferred to what
J.R. Hicks
According to this concept, utility cannot be measured
numerically, it can only be ranked as 1, 2, 3, and so
on.

Util
A unit of measure of utility

Initial Utility
• The utility derived from the first unit of a
commodity is called initial utility.
• It is always positive.

Total Utility
The total amount of satisfaction obtained
by consuming specified amounts of a
product per period of time.

Marginal Utility
The change in total utility (TU) resulting from a
one unit change in consumption (X).
MU = TU/ X
Marginal utility can be (i) positive (ii) zero (iii) negative.

Marginal utility is the derivative of total utility.
MU = dTU/dX
Calculating MU from a TU Function
Example: TU(X) = 16 X – X2
MU = dTU/dX = ?

Law of Diminishing Marginal Utility
•It stated that as the consumer goes on consuming more and more
amount of commodity the marginal utility of the commodity goes
on declining becomes zero and finally becomes negative.
•The marginal utility derived from it is declining becomes zero and
negative.
•Total utility is increasing at increasing rate so long as marginal
utility is positive.
•Total utility becomes maximum when marginal utility is zero.
•Total utility starts declining when marginal utility is negative.

Cont.
• Mr. H. Gossen, a German economist, was first
to explain this law in 1854. Alfred Marshal later
on restated this law in the following words:
“The additional benefit which a person derives
from an increase of his stock of a thing
diminishes with every increase in the stock that
already has”.

Total and Marginal Utility
Apple
consumed
Total
Utility,
Utils
Marginal
Utility,
Utils
0
1
0
10
Units consumed per apple
Units consumed per apple
30
20
10
TotalUtility(utils)MarginalUtility(utils)
10
8
6
4
2
0
-2
0 1 2 3 4 5 6 7
1 2 3 4 5 6 7

Apple
consumed
Total
Utility,
Utils
Marginal
Utility,
Utils
0
1
0
10
10
Units consumed
Units consumed
30
20
10
10
8
6
4
2
0
-2
0 1 2 3 4 5 6 7
1 2 3 4 5 6 7

Apple
consumed
Total
Utility,
Utils
Marginal
Utility,
Utils
0
1
2
0
10
18
10
8
Units consumed per Apple
30
20
10
10
8
6
4
2
0
-2
0 1 2 3 4 5 6 7
1 2 3 4 5 6 7

Apple
consumed
Total
Utility,
Utils
Marginal
Utility,
Utils
0
1
2
3
0
10
18
24
10
8
6 0 1 2 3 4 5 6 7
30
20
10
10
8
6
4
2
0
-2
1 2 3 4 5 6 7

Apple
consumed
Total
Utility,
Utils
Marginal
Utility,
Utils
0
1
2
3
4
0
10
18
24
28
10
8
6
4 Units consumed per Apple
30
20
10
10
8
6
4
2
0
-2
0 1 2 3 4 5 6 7
1 2 3 4 5 6 7

Apple
consumed
Total
Utility,
Utils
Marginal
Utility,
Utils
0
1
2
3
4
5
0
10
18
24
28
30
10
8
6
4
2
30
20
10
10
8
6
4
2
0
-2
0 1 2 3 4 5 6 7
1 2 3 4 5 6 7

Apple
consumed
Total
Utility,
Utils
Marginal
Utility,
Utils
0
1
2
3
4
5
6
0
10
18
24
28
30
30
10
8
6
4
2
0
30
20
10
10
8
6
4
2
0
-2
0 1 2 3 4 5 6 7
1 2 3 4 5 6 7

Apple
consumed
Total
Utility,
Utils
Marginal
Utility,
Utils
0
1
2
3
4
5
6
7
0
10
18
24
28
30
30
28
10
8
6
4
2
0
-2
30
20
10
10
8
6
4
2
0
-2
TU
MU
0 1 2 3 4 5 6 7
1 2 3 4 5 6 7

Apple
consumed
Total
Utility,
Utils
Marginal
Utility,
Utils
0
1
2
3
4
5
6
7
0
10
18
24
28
30
30
28
10
8
6
4
2
0
-2
Units consumed per meal
30
20
10
10
8
6
4
2
0
-2
TU
MU
0 1 2 3 4 5 6 7
1 2 3 4 5 6 7
Observe
Diminishing
Marginal
Utility

Assumptions
• Utility can be measures in the cardinal number system.
• Marginal utility of money remains constant.
• Marginal utility of every commodity is independent.
• Every unit of the commodity being used is of same
quality and size.
• There is a continuous consumption of the commodity.
• Suitable quantity of the commodity is consumed.
• There is no change in the income of consumer, price of
the commodity and its substitutes.
• There is no change in the tastes, character, fashion and
habits of consumer.

Exceptions
• Curious and Rare Things: Law does not these things.
Those persons who collect old and rare coins ,postage
stamps etc derive increasing marginal utility as the stock of
these rare articles goes on increasing.
• Misers: It seems as if the law does not apply to misers, who
are out to acquire more and more of wealth. Their desire for
money seems to be insatiable.
• Good Book or Poem: Reading a good book or listening to a
melodious song or beautiful poem again and again, one gets
more utility than before so these also exceptions to this law.
• Drunkards: When drunkards takes more and more pegs of
liquor his desire to have more of it goes on increasing.

Consumer’s Equilibrium
Consumer’s equilibrium refers to a situation
wherein a consumer gets maximum satisfaction
out of his limited income and he has no
tendency to make any change in his existing
expenditure.

Cont.
• A rational consumer will consume the
commodity up to a point where the MU of the
final unit of the commodity is equal to the MU of
money (in terms of price) paid for it.
• The consumer will get maximum satisfaction and
will be in equilibrium. (where MU =price)

Consumer’s Equilibrium in case of one
commodity with one use
Unit of ‘x’ (1) M.U. of ‘x’ (2) Utility of ‘x’
sacrificed in
terms of Price of
‘x’ (3)
surplus( 2-3)
1 50 20 30
2 40 20 20
3 30 20 10
4 20 20 0
5 10 20 -10

Law of Equi-Marginal Utility
• Law of Substitution OR
• Law of Maximum Satisfaction OR
• Law of Indifference OR
• Proportion Rule OR
• Gossen's Second Law.

Cont.
• The law of equi-marginal utility is simply an
extension of law of diminishing marginal utility to
two or more than two commodities.
• We know that human wants are unlimited whereas
the means to satisfy these wants are strictly
limited. It, therefore’ becomes necessary to pick
up the most urgent wants that can be satisfied
with the money that a consumer has.

A consumer has number of wants. He tries to
spend limited income on different things in such
a way that marginal utility of all things is equal.
When he buys several things with given money
income he equalizes marginal utilities of all such
things.
Marshal- “if a person has a thing which he can
put to several uses, he will distribute it among
these uses in such a way that it has the same
marginal utility in all”.
Cont.

Schedule:
Units of Money MU of Tea MU of Cigarettes
1 10 12
2 8 10
3 6 8
4 4 6
5 2 3
$5 Total Utility = 30 Total Utility = 39

• A rational consumer would like to get maximum satisfaction
from $5.00. He can spend money in three ways:
• (i) $5 may be spent on tea only.
• (ii) $5 may be utilized for the purchase of cigarettes only.
• (iii) Some rupees may be spent on the purchase of tea and
some on the purchase of cigarettes.
• If the consumer spends $5 on the purchase of tea, he gets
30 utility. If he spends $5 on the purchase of cigarettes, the
total utility derived is 39 which are higher than tea. In order
to make the best of the limited resources, he adjusts his
expenditure

• i) By spending $4 on tea and $1 on cigarettes, he gets 40 utility
(10+8+6+4+12 = 40).
• (ii) By spending $3 on tea and $2 on cigarettes, he derives 46
utility (10+8+6+12+10 = 46).
• (iii) By spending $2 on tea and $3 on cigarettes, he gets 48 utility
(10+8+12+10+8 = 48).
• (iv) By spending $1 on tea and $4 on cigarettes, he gets 46 utility
(10+12+10+8+6 = 46).
The sensible consumer will spend $2 on tea and $3 on cigarettes and
will get maximum satisfaction. When he spends $2 on tea and $3 on
cigarette, the marginal utilities derived from both these commodities
is equal to 8. When the marginal utilities of the two commodities are
equalizes, the total utility is then maximum, i.e., 48 as is clear from
the schedule given above.

Curve/Diagram of Law of Equi-Marginal Utility:
The law of equi-marginal utility can be explained with the help of diagrams.

Limitations/Exceptions of
Law of Equi-Marginal Utility
(i) Effect on fashions and customs: The law of equi-marginal utility may become
inoperative if people forced by fashions and customs spend money on the purchase
of those commodities which they clearly knows yield less utility but they cannot
transfer the unit of money from the less advantageous uses to the more advantageous
uses because they are forced by the customs of the country.
(ii) Ignorance or carelessness: Sometimes people due to their ignorance of price or
carelessness to weigh the utility of the purchased commodity do not obtain the
maximum advantage by equating the marginal utility in all the uses.
(iii) Indivisible units: If the unit of expenditure is not divisible, then again the law
may become inoperative.
(iv) Freedom of choice: If there is no perfect freedom between various alternatives,
the operation of law may be impeded.

Criticism of Cardinal Utility Analysis
• Utility is Subjective.
• Consumer is assumed may not be rational all time.
• Fixed price and Income.
• Tastes are constant.
• Perfect knowledge
• Cardinal measurement of utility is not possible.
• Every commodity is not an independent commodity.
• Marginal utility cannot be estimated in all conditions.
• Marginal utility of money does not remain constant .
• Utility analysis breaks down in an under- developed
Planned Economy.
• Consumer is regarded as a computer.

Utility analysis

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