Just an extension to the demand theory for ISC economics, this chapter discusses consumer equilibrium with utility approach. Especially when goods are free, priced and two commodity case.

1. Marginal Utility Analysis
ISC
XII Economics
Chapter 3

2. Utility
• Utility refers to want-satisfying power of a
commodity.
• It is the ability or capacity of a commodity
to satisfy the human want.
• In objective terms, utility may be defined
as the amount of satisfaction derived from
the consumption of a commodity.

3. Characteristics of utility
1. It is subjective
2. It is not measurable
3. It is variable
4. It is different from
usefulness
5. It has no ethical, moral
or legal connotations

4. Total utility
• Total utility refers to the total satisfaction derived
by the consumer from the consumption of a
specific quantity of a commodity, say a number
of mangoes.
• In other words, total utility is the sum total of the
utilities derived ·from all the units consumed of a
commodity.
• For example, the total utility of consuming two
mangoes is the total satisfaction that these two
mangoes provide.

5. Marginal utility
• Marginal utility refers to the additional
utility derived from the consumption of an
additional unit of a commodity
• Marginal utility of consuming third mango
is the increase in total utility as the
consumption of mangoes is increased
from two mangoes to three mangoes.

6. Utility Schedule for Mangoes
Units of
Mangoes
TU (Units) MU (Units)
0 0 Undefined
1 10 10 (10-0)
2 17 7 (17-10)
3 21 4 (21-17)
4 22 1 (22-21)
5 22 0 (22-22)
6 19 -3 (19-22)

7. • Marginal Utility = The addition
made to the total utility by
addition of one more unit of a
commodity.
• Total Utility = The sum total of all
marginal utilities.
• MU nth = TUn – TUn-1
• TUn = MU1 + MU2 + ….MU nth

8. Y
O X
10
1
4
7
654321
No of Mangoes
MarginalUtility
MU
Y
O X
10
22
21
17
654321
TU
MU> 0
M MU= 0
MU< 0
No of Mangoes
TotalUtility
Relationship between TU & MU

9. Explanation
• The total utility cure is concave from above
which indicates declining slope of the curve,
which means declining marginal utility.
• Thus, up to point M, the TU curve has a positive
slope, but the slope goes on decreasing steadily
as quantity consumed is increased.
• So long as total utility increases, marginal utility
is positive. But marginal utility decreases
because total utility increases at a decreasing
rate.
• When total utility is maximum, marginal utility is
zero.
• When total utility declines marginal utility is
negative.

10. The relationship between the total
utility and marginal utility
When TU is Then MU is
Increasing at a
decreasing rate
Decreasing, but
positive
At the maximum Zero
Decreasing Negative

11. Law of Diminishing Marginal
Utility
• H.H. Gossen and Alfred Marshall.
• The law states that as the amount
consumed of a commodity increases, the
utility derived by the consumer from the
additional units, i.e. marginal utility, goes
on decreasing.
• "The additional benefit a person derives
from a given increase of his stock of a
thing diminishes with every 1acrease in
the stock that he already has."

12. Assumptions
1. All the units of a commodity must be same in
all respects - in size, colour, design, quality,
etc.
2. The unit of the good must be standard, e.g., a
cup of water, a bottle of cold drink, a pair of
shoes, a full mango, a glass of water.
3. There should be no change in taste during the
process of consumption.
4. There must be continuity in consumption and if
a break in the continuity is necessary, the time
interval between the consumption of two units
must be short.
5. There should be no change in the prices of
substitute goods.

13. Explanation of the Law
• As more and more quantity of a commodity is
consumed, the intensity of desire decreases, and
therefore, the utility derived from the additional unit
decreases
• If there are many uses of a commodity, the most
urgent requirement will be fulfilled first, followed by
the next important use, and so on. .
• Consumer's Equilibrium
• A consumer will be in equilibrium when he spends
his given income on the purchase of different goods
and services so as to maximise his total utility.
• Equilibrium is the ideal position towards which
consumer will like to move.
• It is the position the household regards as the best
under given circumstances.

14. Consumer Equilibrium
• A consumer will be in equilibrium when he
spends his given income on the purchase
of different goods and services so as to
maximise his total utility.
• Equilibrium is the ideal position towards
which consumer will like to move.
• It is the position which the household
regards as the best under given
circumstances.

15. Assumptions for explaining the
consumer's equilibrium
1. It is assumed that the consumer is rational, i.e. he
aims at maximising the utility from his purchases.
2. Utility can be measured in money terms, i.e. the
utility of one unit , of a commodity equals the
amount of money (price) which a consumer " is
prepared to pay for it.
3. The law of diminishing marginal utility operates.
4. The utility of each unit of money, such as a ten-
rupee note remains constant.
5. Consumer's income is given and remains constant.
6. Prices of other commodities are assumed to be
given.

16. Explanation of Consumer's Equilibrium
• How much quantity X should the consumer purchase at its
given price so as to reach the equilibrium?
• A utility-maximising consumer will be in equilibrium when he
purchases that much quantity of the commodity where the
marginal utility of the commodity equals its price.
• Since money (price) which the consumer has to spend to
purchase a unit of the commodity and the commodity both,
gives him same utility.
• Explanation of Consumer's Equilibrium
• If Marginal utility of X is greater than the price of X (i.e. MUx>
Px), the consumer can increase his total utility by purchasing
more units of X.
• If marginal utility of X is less· than its price
• (i.e. MUx < Px), the consumer can increase his total utility by
consuming less units of X
• He will maximise total utility when marginal utility of a
commodity equals its price.
• (i.e. MUx = Px)

17. Consumer Equilibrium in Single
Commodity Case
Units of shirts in
Rs.
Marginal Utility
1 700
2 650
3 600
4 500
5 350

18. O
Y
X
54321
MU
Units of Shirts
MarginalUtility/Price(Rs)
350
500
600
650
700
P
E

19. • This is called the law of equi-marginal
utility, since maximum satisfaction is
obtained only be equating marginal
utilities.
• It’s called as the Law of substitution (Since
consumer can substitute one commodity
for another), Law of maximum satisfaction
(since the consumers aim at maximum
satisfaction)
Consumer’s Equilibrium in Two
Commodity Case

20. Now, MU of a rupee spent on a
good is equal to the MU of the
good divided by its price.
• Symbolically,
• MUm = MUx/Px = Utility obtained by spending
one unit of money on X.
where, MUm = Marginal utility of money.
MUx = Marginal utility of good X.
Px = Price of good X.
Similarly,
MUm = MUy/Py = Utility obtained by spending
one unit of money on y.
where MUm = Marginal utility of good y.
Py = Price of good y.

21. • The consumer will be in equilibrium when
he is spending his money income on two
goods in such a way that MU of last rupee
spent on the two goods is the same.
• That is in equilibrium where

22. Graphical Analysis
Consumer’s Equilibrium in case of two commodities.

24. Numerical Analysis:
Let the prices of goods X and Y be Rs. 2 and Rs. 3
respectively and the consumer has Rs. 19 to spend on the two
goods. MU of the money is 6 units.

25. Utility maximization principles
• Optimization Rule 1:
When only one good is consumed and is
available for free, consume till
MUx = 0
• Optimization Rule 2:
When only one good is consumed and is
available for a price:
Consume till MUx = Pricex
• Optimization Rule 3:
When more than one good is consumed and
the goods’ prices are different:
Consume till MUx/Px = MUy/Py = MUz/Pz

26. The law of Equi-Marginal Utility
• "The consumer maximising his total utility will
allocate his income among various commodities
in such a way that the marginal utility of the last
rupee spent on each commodity is equal.“
• The consumer will spend his money income on
different goods in such a way that marginal utility
of each good is proportional to its price.
• The consumer will be in equilibrium while
MUx = MUY
Px PY

27. Utility schedule for X and Y
Units MUx MUy MUx
Px
MUy
Py
1 50 80 10 8
2 45 70 9 7
3 40 60 8 6
4 35 50 7 5
5 30 40 6 4
6 25 30 5 3

28. Expenditure on purchase of X and Y
Combinations Total expenditure
3 units of X + 1 unit of Y Rs.25(3*5+1*10=15+10=25)
3 units of X + 1 unit of Y Rs.40(4*5+2*10=20+20=40)
5 units of X + 3 unit of Y Rs.55(5*5+3*10=25+30=55)
6 units of X + 4 unit of Y Rs.70(6*5+4*10=30+40=70)

29. Limitations of Law of Equi-
Marginal Utility
1. It is difficult for the consumers to know the
marginal utilities from different commodities
because utility cannot be measured.
2. Consumers are in many cases governed by
habits and customs.
3. Many consumers are ignorant, and, therefore,
they may not be able to arrive at equilibrium
position due to their ignorance.
4. In case of expensive and indivisible
commodities such as cars and refrigerators
etc., it is absurd to talk of marginal utility of a
rupee spent.

30. Prepare a Figure from given
Schedule
Number
Purchased
Total Utility Marginal Utility
0 0 0
1 4 4
2 7 3
3 8 1
4 8 0
5 7 -1

31. Ans:

32. Prepare a
Schedule from
the figure

33. Ans:
Units Total Utility Marginal Utility
1 20 20
2 32 12
3 40 8
4 42 2
5 42 0
6 39 –3