Consumer behaviour and utility analysis

Consumer Behaviour and
Utility Analysis

Meaning
The theory of consumer behaviour
describes how consumers buy
different goods and services.
Consumer behaviour also explains
how a consumer allocates its income
in relation to the purchase of different
commodities and how price affect
his/her decision.

Consumer Choice and Budget
Constraint:
 Rational behavior:
As we know money is scare. Due to this
scarcity of money consumers tend to be
rational in their purchasing decision. A
consumer would spend his money on the
best possible place or product that
guarantees him utility or a sense of
satisfaction. The rational behavior of
consumer also means that buyers only
purchase goods and services only when
needed rather than wasting money on things
that have no immediate use as of now.

Continue
 Preferences :
Each consumer has preferences for
certain of the goods and services that
are available in the market. Buyers also
have a good idea of how much marginal
utility they will get from successive units
of the various products they might
purchase. However, the amount of
marginal & total utility that the people will
get will be different for every individual in
the group because all individuals have
different taste and preferences.

Continue
 Budget Constraint :
The consumer has a fixed, limited
amount of money income.
◦ Every consumer faces a budget constraint
◦ There is infinite demand, but limited
income

Countine
 Prices :
Goods are scarce because of the
demand for them. Each consumers
purchase is a part of the total demand
in a market. However, since
consumers have a limited income,
they must choose the most satisfying
combination of goods based partially
on prices. For producers, a lower price
is needed in order to induce a
consumer to buy more of their
product.

Theories of Consumer
Behavior
 There are two theories that seek to
explain consumer behavior.
 The Cardinal Approach : Which
explains utility is objectively
measurable.
 The Ordinal Approach : Which
explains consumer can rank their
preferences.

The Cardinal Approach
(Utility theory)
The utility theory explains consumer
behavior in relation to the satisfaction
that a consumer gets the moment he
consumes a good. When we speak of
utility, we refer to the satisfaction or
benefits that a consumer derives of his
consumption. This theory assumes
that satisfaction can be measured.
The unit of measures of utility is called
utils.

Two types of Utility
1.Total utility 2. Marginal utility
Total Utility (TU) : It is the total amount of
satisfaction or pleasure a person derives
from consuming some specific.
Marginal Utility (MU) : It is the extra
satisfaction a consumer realizes from an
additional unit of that product. In other
words, it is additional satisfaction that an
individual derives from consuming an
additional unit of a good or services,
MU = Change in total unit / change in
quantity

For example
Quantity Total Utility (TU) Marginal Utility (MU)
0 0 -
1 15 15
2 28 13
3 39 11
4 48 9
5 55 7
6 60 5
7 63 3
8 64 1
9 63 -1

Analysis of the table :
 TU rises, MU falls
 TU at maximum level , when MU = 0
 TU falls, when MU negative
 TU in general increase with quantity.
 If TU increases, MU > 0
 If TU decreases, MU < 0

Utility Maximization
 Explains how consumers allocate their
money incomes among the many
goods and services available for
purchase
 You will be faced with problems that
provide you with a consumer’s MU or
TU derived from purchasing 2 goods.
You will be expected to show how many
of each a rational consumer would
purchase.

Numerical Example:
Find the Utility-Maximizing Combination of
A and B, if you have an Income of $10
(1)
Unit of
Product
(a)
Marginal
Utility,
Utils
(a)
Marginal
Utility,
Utils
(b)
Marginal
Utility
Per Dollar
(MU/Price)
(b)
Marginal
Utility
Per Dollar
(MU/Price)
(2)
Product A:
Price = $1
(3)
Product B:
Price = $2
First
Second
Third
Fourth
Fifth
Sixth
Seventh
10
8
7
6
5
4
3
24
20
18
16
12
6
4
10
8
7
6
5
4
3
12
10
9
8
6
3
2

Utility-Maximizing Combination of Products
A and B Obtainable with an Income of $10
(1)
Unit of
Product
(a)
Marginal
Utility,
Utils
(a)
Marginal
Utility,
Utils
(b)
Marginal
Utility
Per Dollar
(MU/Price)
(b)
Marginal
Utility
Per Dollar
(MU/Price)
(2)
Product A:
Price = $1
(3)
Product B:
Price = $2
First
Second
Third
Fourth
Fifth
Sixth
Seventh
10
8
7
6
5
4
3
24
20
18
16
12
6
4
10
8
7
6
5
4
3
12
10
9
8
6
3
2
Compare Marginal Utilities
Then Compare Per Dollar - MU/Price
Choose the Highest
Check Budget - Proceed to Next Item

(1)
Unit of
Product
(a)
Marginal
Utility,
Utils
(a)
Marginal
Utility,
Utils
(b)
Marginal
Utility
Per Dollar
(MU/Price)
(b)
Marginal
Utility
Per Dollar
(MU/Price)
(2)
Product A:
Price = $1
(3)
Product B:
Price = $2
First
Second
Third
Fourth
Fifth
Sixth
Seventh
10
8
7
6
5
4
3
24
20
18
16
12
6
4
10
8
7
6
5
4
3
12
10
9
8
6
3
2
Again, Compare Per Dollar - MU/Price
Choose the Highest
Buy One of Each – Budget Has $5 Left
Proceed to Next Item

(1)
Unit of
Product
(a)
Marginal
Utility,
Utils
(a)
Marginal
Utility,
Utils
(b)
Marginal
Utility
Per Dollar
(MU/Price)
(b)
Marginal
Utility
Per Dollar
(MU/Price)
(2)
Product A:
Price = $1
(3)
Product B:
Price = $2
First
Second
Third
Fourth
Fifth
Sixth
Seventh
10
8
7
6
5
4
3
24
20
18
16
12
6
4
10
8
7
6
5
4
3
12
10
9
8
6
3
2
Buy One More B – Budget Has $3 Left
Proceed to Next Item

(1)
Unit of
Product
(a)
Marginal
Utility,
Utils
(a)
Marginal
Utility,
Utils
(b)
Marginal
Utility
Per Dollar
(MU/Price)
(b)
Marginal
Utility
Per Dollar
(MU/Price)
(2)
Product A:
Price = $1
(3)
Product B:
Price = $2
First
Second
Third
Fourth
Fifth
Sixth
Seventh
10
8
7
6
5
4
3
24
20
18
16
12
6
4
10
8
7
6
5
4
3
12
10
9
8
6
3
2
Buy One of Each – Budget Exhausted

(1)
Unit of
Product
(a)
Marginal
Utility,
Utils
(a)
Marginal
Utility,
Utils
(b)
Marginal
Utility
Per Dollar
(MU/Price)
(b)
Marginal
Utility
Per Dollar
(MU/Price)
(2)
Product A:
Price = $1
(3)
Product B:
Price = $2
First
Second
Third
Fourth
Fifth
Sixth
Seventh
10
8
7
6
5
4
3
24
20
18
16
12
6
4
10
8
7
6
5
4
3
12
10
9
8
6
3
2
Final Result – At These Prices,
Purchase 2 of Item A and 4 of B

Algebraic Restatement:
MU of Product A
Price of A
MU of Product B
Price of B=
8 Utils
$1
16 Utils
$2=
Optimum Achieved - Money Income
is Allocated so that the Last Dollar
Spent on Each Good Yields the Same
Extra or Marginal Utility

Given MU, and an income/budget
constraint of $20… find the Utility-
Maximizing Combination of A and B
(2)
Product A:
Price = $2
(3)
Product B:
Price = $5
Unit MU Unit MU
1 20 1 30
2 10 2 20
3 6 3 15
4 3 4 5
5 1 5 -5

The Law of diminishing
marginal utility
The law of diminishing marginal utility
describes a familiar and fundamental
tendency of human behavior.
“The law of diminishing marginal utility
states that, “as a consumer consumes
more and more units of a specific
commodity, utility from the successive
units goes on diminishing”.

Assumptions of the Law:-
 These assumptions are –
 Various units of goods are homogenous.
 There is no time gap between consumption of
the different units.
 Consumer is rational
 (So aims at maximization of utility of the product)
 Tastes, preferences, and fashion remain
unchanged.
 Consumers posses perfect knowledge of the
price in the market
 No price change
 It assumes Law of marginal diminishing Utility
 Utilities of different commodities are independent
of each other

Explanation of the Law:
 Suppose a person is thirsty and the price of
water is zero. He takes one glass of water which
gives him great satisfaction. We can say the first
glass of water has great utility for him.
 He then takes second glass of water. The utility
of the second glass of water is less than that of
first glass of water. The utility declines 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.

For example
Units Total Utility Marginal Utility
1st glass 20 20
2nd glass 32 12
3rd glass 40 8
4th glass 42 2
5th glass 42 0
6th glass 39 –3

Graph of Diminishing Marginal
Uility

The Ordinal Approach
 The Ordinal Approach : Which
explains consumer can rank their
preferences.

Introduction of Indifference curve
The technique of indifference curves
was originated by Francis Y.
Edgeworth in England in 1881. It was
then refined by Vilfredo Pareto, an
Italian economist in 1906. This
technique attained perfection and
systematic application in demand
analysis at the hands of Prof. John
Richard Hicks and R.G.D. Allen in
1934.

Continue
 Professor Hicks introduced the
concept of scale of preferences of a
consumer as the base of indifference
curve technique. The conceptual
arrangement of different goods and
their combinations in a set order of
preferences is called the scale of
preferences.

Definition
 An indifference curve is the locus of
points representing all the different
combinations of two goods which yield
equal level of utility to the consumer.
Assumptions
 Rational behavior of the consumer
 Utility is ordinal
 Diminishing marginal rate of substitution
 Consistency in choice
 Transitivity in choice making
 Goods consumed are substitutable

Indifference Schedule
Indifference schedule is a list of various
combinations of commodities which are equally
satisfactory to the consumer concerned.
Combinations Apples Mangoes
A 15 1
B 11 2
C 8 3
D 6 4
E 5 5

Graph of Indifference curve
E
D
C
B
A
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
Mangoes
Apples
IC

Indifference Map
A graph showing a whole set of
indifference curves is called an
indifference map. All points on the
same curve give equal level of
satisfaction, but each point on higher
curve gives higher level of satisfaction.

Graph of Indifference Map
0
5
10
15
20
25
0 1 2 3 4 5
Mangoes
Apples
IC1
IC2
IC3

Marginal Rate of Substitution
(MRS)
 Marginal rate of substitution (MRS) - The
maximum amount of one good a consumer will
sacrifice to obtain one more unit of another good.
 Marginal rate of substitution (MRS) can be defined
as “the ratio of exchange between small units of
two commodities, which are equally valued or
preferred by a consumer”.
 The marginal rate of substitution is the rate of
exchange between some units of goods X and Y
which are equally preferred. The marginal rate of
substitution of X for Y (MRS)xy is the amount of Y
that will be given up for obtaining each additional
unit of X.
Formula :
 MRS = ∆Y / ∆X or Change in y / change in x

For example
Combination Good X Good Y MRS of X for Y
1 2 13 -
2 3 9 4:1
3 4 6 3:1
4 5 4 2:1
5 6 3 1:1

Properties of indifference
curve
1. Indifference curves are negatively
sloped
Given a combination of commodity X
and commodity Y, with every increase
in X, the amount in Y should fall in
order that the level of satisfaction from
every combination should remain the
same.

2. Indifference curves are
convex to the origin
Indifference curves are not only
negatively sloped, but also are also
convex to the origin. The convexity of
the indifference curves implies that not
only the two commodities are
substitutes for each other but also the
fact that the marginal rate of
substitution (MRS) between the goods
decreases as a consumer moves
along an indifference curve.

3. Indifference curves can never intersect
each other
 Indifference curve cannot intersect each other
because an intersection would indicate two
difference levels of satisfaction, which is impossible.

4. Higher indifference curve
represent higher levels of satisfaction
The consumer is better off when he moves
to a higher indifference curve

5. Indifference curve must have a
negative slope
 An indifference curve has a negative slope, which
denotes that if the quantity of commodity (y)
decreases, the quantity of the other (x) must
increase, if the consumer is to stay on the same
level of satisfaction (a necessary consequence of
the non satiety postulate).

6. Indifference curves do not touch the
horizontal or vertical axis

7. Indifference curve for substitute and
complementary goods
 The indifference curve for perfect
substitutes will be a straight line
because the marginal rate of
substitution remains constant.
Different brands of beer or petrol and
gas are perfect substitutes. The
preferences for two goods that are
perfect substitutes are convex, but not
strictly convex.

Indifference graph of Substitutes
good

 When two goods must be used always
together in a fixed proportion, as in the
case of right and left shoes, or cup
and saucer, they are said to be perfect
complements. If the consumer is
deprived of his left foot shoe, no
number of additional right foot shoes
will compensate him. This is the case
of cups and saucers.

Indifference graph of
Complement goods

Budget Line
Meaning
 The budget line shows all the different
combinations of the two commodities
that a consumer can purchase, give
his or her income and the price of the
two commodities.
 In other words, it is the limit on the
consumption bundles that a consumer
can afford.

For example:
 The income consumer is 40$ which he
wants to spend on two goods X and Y.
The price of good X is 2$ per unit and
Good Y is 1$ per unit. The consumer can
spend on any of the alternatives
combinations of good X and Y. However,
if spend his total income only on good X
or Y, he can buy only 20 or 40 units
respectively. But this is not possible
because he has to buy only a
combination of two goods. So he will buy
any other combination.

Numerical Example of Budget
Line
Combinations Units of Good X (2 $ per
unit)
Units of Good Y (1 $ per
unit)
B 0 40
Q 5 30
R 10 20
S 15 10
L 20 0

Explanation of Graph
 In table 1 the various combinations of the
table are shown by the BL line. This is the
price or budget line given 40$ with the
consumer, he can buy any one combination
Q,R or S of good X and Y. But he cannot
obtain any point beyond this line such as
combination A because it is out of reach of
his income. On the other hand, he can not
obtain the combination even inside the BL
line such as combination N because he
cannot spend all income 40$ on both good X
and Y. Thus consumer’s budget line is his
budget limit or budget constraint line.

Slope of Budget Line
Formula
Slope of BL = Price of good X / Price of good Y

Changes in budget line
There are two reasons :
 Changes in Price
 Change in Income

Changes in Price
If the consumer’s income does not
change but the prices of good X and Y
change, the slope of his budget line
will change.

For example
 Suppose that consumer’s income is
40 $ and the prices of good Y (1$)
remain constant and the price of good
X falls from 2$ to 1$, his budget line
will rotate outwards from point B to the
line L2. He can now purchase the
maximum 40 units of as shown in
figure 2. If the price of X increase from
2$ to 4$ his budget line will rotate
inwards from point B to the line L1 and
he can purchase to units of X.

For example
The consumer’s income and prices of X
being constant, with a fall in the price
of Y his budget line LB will rotate
outwards from point L to LB2. This is
because he buys more quantity of Y
than before with the fall in its price.
Conversely, with the increase in its
prices, his price income line LB will
rotate to LB1 because he purchases
less quantity of Y than before.

Change in Income
The price of X and Y remaining
constant, if the consumer’s income or
budget increases or decreases, his
income or budget line will also
change. If income increases, the
budget line will shift outwards.

Consumer’s Equilibrium or Utility
Maximization given their Budget Constraint
A consumer is in equilibrium when
given his tastes and prices of the two
goods, he spend a given money
income on the purchase of two goods
in such a way as to get the maximum
satisfaction.

Assumptions
1. The consumer’s indifference map for the two goods X
and Y is based on his scale of preferences for them
which does not change at all in this analysis.
2. His money income is given and constant. It is 10$
which he spends on the two goods.
3. Prices of the two goods X and Y are also given and
constant. X is priced 2$ per unit and Y at 1$ per unit.
4. The goods Z and Y are homogeneous and divisible.
5. There is no change in taste and habits of the
consumer throughout the analysis.
6. There is perfect competition in the market from where
he makes his purchases of the two goods.
7. The consumer is rational and thus maximizes his
satisfaction from the purchases of the two goods.

For example
Consumer can buy 5 units of X by
spending the entire sum of 10$ on
good X or on 10 units of Y. It shows
that some of the possible
combinations on which 10$ can be
allocated.

Consumer’s Equilibrium
Combinations Units of Good X (2 $ per
unit)
Units of Good Y (1 $ per
unit)
Q 5 0
N 4 2
T 3 4
S 2.5 5
K 1.5 7
R 1 8
P 0 10

Explanation
These seven combinations indicated by
points P,R,K,S,T,N and Q. The line PQ shows
combinations of good X and Y, given their
prices, when he spends his income on his
income on them. This is because,
algebraically I=Px*X + Py*Y,
where I represents the consumer’s income,
Px and Py the prices of goods X and Y,
respectively.
This budget equation is the equation of the
line connecting the points Q and P, where
Q= I/Px and P= I/Py thus PQ is the budget
line.

On this budget line, the consumer can have
any combination. Out of the possible seven
combinations P,R,K,S,T,N or Q. Combination
P or Q is out of question for in either case he
would have only Y or only X. He would not
take combination R or N on a lower
indifference curve I1 because combination K
or T is also available to him on a higher
indifference curve I2. But there is another
combination S which is on the highest
indifference curve I3 on this budget line PQ.
Since all other combinations lie on lower
indifference curves, they represent lower
levels of satisfaction than combination S
which is the consumer’s equilibrium point. We
may thus enumerate the conditions of
consumer’s equilibrium.

 The consumer is in equilibrium when
his budget line is tangent to an
indifference curve. PQ is tangent to
curve I3 at S. At point S, he is also
satisfying the budget equation
 I (10$) = OA*Px + OB*Py
 = 2.5 units of X *2$ + 5 *1$
 = 5 + 5
 = 10 $

Income effect:
Given the taste and preferences of the
consumer and the prices of the two
goods, if the income of consumer
changes, the effect it will have on his
purchases is known as the income
effect. If the income of the consumer
increases his budget line will shift
upwards to the right, parallel to the
original budget line. On the contrary, a
fall in his income will shift the budget line
inward to the left. The budget lines are
parallel to each other because relative
parallel to each other because relative
prices remain unchanged.

The Substitution Effect
Substitute effect measures the effect
of change in the relative prices of a
good with real income constant. The
increase in the real income of the
consumer as a result of fall in the price
of good X, is so withdrawn that he is
nether better off nor worse off than
before.

Consumer behaviour and utility analysis

Consumer behaviour and utility analysis

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