1

INTRODUCTION TO ECONOMICS

Wondesen Mekonnen (MSc.)

Mizan-Tepi University

Email: eyoabwm9620@gmail.com
 2

UNIT 3

Theory of Consumer Behavior

 Introduction 3

 Consumer theory is based on the premise that we can infer

what people like from the choices they make.

 Consumer behavior can be best understood in three steps.

▪ First, by examining consumer‘s preference,

▪ Second, consumers face budget constraints

▪ Third, we will put consumer preference and budget constraint

together to determine consumer choice.
 3.1 Consumer preferences 4

 A consumer makes choices by comparing bundle of goods.

 Given any two bundles, the consumer either decides that ;
▪ One of the consumption bundles is Strictly better than the other, or
▪ Indifferent between the two bundles.

Symbols:
 X ≻Y: Consumer strictly prefers X to Y
 X~Y: Consumer is indifferent between the two bundles of goods
 X ⪰ Y: Indifferent between the two but weakly/slightly prefers X to Y.
 Assumptions of Consumer Theory 5

If Given bundle ‘A’, ‘B’, and ‘C’ to chose

 Completeness: for two bundles, A ≻ B, B ≻ A, or A ~ B

 Transitivity: for three bundles; if A ≻ B and B ≻ C, then A ≻ C

 Themore is the better; if ‘A’ and ‘B’ contain the same

commodities, the consumer prefer the one with more
quantities.
 3.2 The concept of utility 6

Utility:
 Satisfaction or pleasure derived from the consumption of a G&S.
 Power of the product to satisfy human wants.
 The consumer definitely wants the X-bundle than the Y-bundle if and
only if the utility of X is better than the utility of Y.

Important points:
 Utility’
and ‘Usefulness’ are not synonymous: Usefulness is a product
centric whereas utility is consumer-centric.
 Utility is subjective: Vary from person to person. – (Ex. Non-smokers).
 Utility can be different at different places and time. (Ex. Coffee in the morning)
 3.3 Approaches of measuring utility 7

 There
are two major approaches to measure or
compare consumer‘s utility:

1. Cardinal approach: the Cardinalist school postulated

that utility can be measured objectively.

2. Ordinal approach: Consumer can rank or order the

utility he derives from different goods and services.
 The difference between Ordinal and Cardinal Utility

Ordinal Utility Cardinal Utility

✓ Consumption can’t be measured ✓ Consumption can be measured
✓ Ranking of the products depending ✓ Uses utils which help in
on the preferences of the consumer understanding how much utility is
derived from consumption of a
✓ Conceptual and practical product.
✓ Convex function ✓ Concave function
✓ Qualitative measure ✓ Quantitative
 9
3.3.1 The cardinal utility theory
 According to the cardinal utility theory, utility is measurable
by arbitrary unit of measurement called utils in the form of
1, 2, 3 etc.

 Forexample, we may say that consumption of an orange gives

Bilen 10 utils and a banana gives her 8 utils, and so on.

 From this, we can assert that Bilen gets more satisfaction

from orange than from banana.
 3.3.1.1 Assumptions of cardinal utility theory 10

1. Rationality of consumers
▪ The main objective of the consumer is to maximize his/her
satisfaction given his/her limited budget or income.
▪ Thus, in order to maximize his/her satisfaction, the consumer
has to be rational.

2. Utility is cardinally measurable.

▪ The utility or satisfaction of each commodity is measurable.

▪ Utility is measured in subjective units called utils.

Cont’d 11

3. Constant marginal utility of money

▪ A given unit of money deserves the same value at any time
or place it is to be spent.

4. Diminishing marginal utility (DMU)

▪ The marginal utility of a commodity diminishes as the
consumer acquires larger quantities of it.

5. The total utility of a basket of goods depends on the quantities of the

individual commodities. TU = f ( X1 , X 2 Xn ).
 3.3.1.2 Total and marginal utility 12

 Total Utility (TU) is the total satisfaction a consumer gets from

consuming some specific quantities of a commodity at a
particular time.

▪ As the consumer consumes more of a good per time

period, his/her total utility increases.

▪ However, there is a saturation point for that commodity

beyond which the consumer will not be capable of
enjoying any greater satisfaction from it.
 13
Cont’d
 Marginal Utility (MU) is the extra satisfaction a consumer
realizes from an additional unit of the product.

 In other words, MU is the change in total utility that results

from the consumption of one more unit of a product.

 Graphically, it is the slope of total utility.

 Mathematically, marginal utility is:

Δ𝑇𝑈
𝑀𝑈 =
Δ𝑄
 Table: Total and marginal utility
14
Quantity MU TU
0 - 0
1 10 10
2 8 18
3 6 24
4 4 28
5 2 30
6 0 30
7 -2 28

▪ TU first increases, reaches the maximum (when the consumer consumes 6 units) and then
declines as the quantity consumed increases.
▪ MU continuously declines (even becomes zero or negative) as quantity consumed increases.
 TU 15

When TU is TU

increasing,
MU is positive.
0 Q
MU

0
MU
Q
 3.3.1.3 Law of diminishing marginal utility (LDMU) 16

▪ The law states that

“as the quantity consumed of a commodity increases per unit of
time, the utility derived from each successive unit decreases,
consumption of all other commodities remaining constant”

▪ The extra satisfaction that a consumer derives declines as he/she

consumes more and more of the product in a given period of time.

▪ This gives sense in that the first banana a person consumes gives him
more marginal utility than the second and the second banana also
gives him higher marginal utility than the third and so on.
 Assumptions 17

 The law of diminishing marginal utility is based on the

following assumptions.

▪ The consumer is rational

▪ The consumer consumes identical or homogenous product
- similar quality, color, design, etc.
▪ There is no time gap in consumption of the good
▪ The consumer taste/preferences remain unchanged.
 18
3.3.1.4 Equilibrium of a consumer

 The objective of a rational consumer is to maximize total utility.

 As long as the additional unit consumed brings a positive

marginal utility, the consumer wants to consume more of the
product because total utility increases.

 However, given his limited income and the price level of goods
and services, what combination of goods and services should
he consume so as to get the maximum total utility?
a) the case of one commodity 19

 The equilibrium condition of a consumer that consumes a single

good X occurs when the marginal utility of X is equal to its
market price.
MUX = PX
Proof
▪ Given the utility function U = f (X )
▪ If the consumer buys commodity X, then his expenditure will be
Qx Px .
 The consumer maximizes the difference between his utility and
expenditure.
the case of one commodity… 20

 The necessary condition for maximization is equating the derivative

of a function to zero. Thus,

Max (U – Qx Px)
𝑑𝑈 𝑑(𝑄𝑥 𝑃𝑥)
− =0
𝑑𝑄𝑋 𝑑𝑄𝑋

𝑀𝑈𝑥 − 𝑃𝑥 = 0

𝑴𝑼𝒙 = 𝑷𝒙
Figure: Equilibrium condition of consumer with only 21
one commodity
MUx

MUxA A

B
MUxB Px

MUxC C
MUx

QxA QxB QxC Qx

b) the case of two or more commodities 22

 For the case of two or more goods, the consumer‘s equilibrium is

achieved when the marginal utility per money spent is equal for each
good purchased and his money income available for the purchase of
the goods is exhausted. That is,

𝑀𝑈𝑥 𝑀𝑈𝑦 𝑀𝑈𝑛

That is, = = −−− =
𝑃𝑥 𝑃𝑦 𝑃𝑛

and 𝑃𝑥 𝑄𝑥 + 𝑃𝑦 𝑄𝑦 … = 𝑃𝑛 𝑄𝑛 = M

Where, M the income of the consumer

 23
Example:
 Suppose Saron has 7 Birr to be spent on two goods:
▪ Banana and
▪ Bread

 The unit price of Banana is 1 Birr and the unit price of a

loaf of Bread is 4 Birr.

 The total utility she obtains from consumption of each

good is given below.
 Table 3.2. Utility schedule for two commodities
24
Income = 7 Birr, Price of banana = 1 Birr, Price of bread = 4 Birr

Banana Bread
Q TU MUx 𝑀𝑈𝑥 Q TU MUy 𝑀𝑈𝑦
𝑃𝑥 𝑃𝑦
0 0 - - 0 0 - -
1 6 6 6 11 12 12 3
2 11 5 5 2 20 8 2
3
3 14 3 33 3 26 6 1.5
4 16 2 2 4 29 3 0.75
5 16 0 0 5 31 2 0.5
6 14 -2 -2 6 32 1 0.25
 25
At Equilibrium, 𝑴𝑼𝒙
𝑷𝒙
=
𝑴𝑼𝒚
𝑷𝒚

▪ Utility is maximized when the condition of MU of one commodity divided by its

market price is equal to the MU of the other commodity divided by its market
price

▪ In table 3.2, there are two different combinations of the two goods where the MU
of the last birr spent on each commodity is equal.

▪ Saron will be at equilibrium when she consumes 3 units of banana and 1 loaf of
bread. At this equilibrium,

MUx MUy 𝑀𝑈𝑏𝑎𝑛𝑎𝑛𝑎 𝑀𝑈𝑏𝑟𝑒𝑎𝑑 3 12

= = = = =3 =3
Px Py 𝑃𝑏𝑎𝑛𝑎𝑛𝑎 𝑃𝑏𝑟𝑒𝑎𝑑 1 4
 26
𝑷𝒙 𝑸𝒙 + 𝑷𝒚 𝑸𝒚 = 𝐌
= (𝟏 ∗ 𝟑) + (4*1) = 𝟕
 The total utility that Saron derives from this combination can be given

TU= TUx + TUy

TU= 14 + 12
TU= 26
 Given her fixed income and the price level of the two goods, no combination of
the two goods will give her higher TU than this level of utility
 27
Limitation of the cardinal approach

1. The assumption of cardinal utility is doubtful because utility

may not be quantified.

2. Utility cannot be measured absolutely.

3. The assumption of constant MU of money is unrealistic

because as income increases, the marginal utility of money
changes.
 3.3.2 The ordinal utility theory 28

 Utility is not expressed in absolute terms, like 1 util, 2 utils, or 3 utils but
it is possible to express the utility in relative terms.

 The consumers can rank commodities in the order of their

preferences as 1st, 2nd, 3rd and so on.

 Therefore, the consumer need not know in specific units the utility of
various commodities to make his choice.

 It suffices for him to be able to rank the various baskets of goods

according to the satisfaction that each bundle gives him.
 3.3.2.1 Assumptions of Ordinal utility theory 29

❑ Consumers are rational: they maximize their satisfaction or utility

given their income and market prices.

❑ Utility is ordinal: utility is not absolutely (cardinally) measurable.

Consumers are required only to order or rank their preference for
various bundles of commodities.

❑ Diminishing marginal rate of substitution (DMRS): The MRS is the

rate at which a consumer is willing to substitute one commodity for
another commodity so that his total satisfaction remains the same.
Cont’d 30

❑ The total utility of a consumer is measured by the amount

(quantities) of all items he/she consumes from his/her
consumption basket.

❑ Consumer’s preferences are consistent:

▪ For example, if there are three goods in a given consumer‘s
basket, say, X, Y, Z and if he prefers X to Y and Y to Z, then
the consumer is expected to prefer X to Z.

▪ This property is known as axioms of transitivity.

 3.3.2.2 Indifference set, curve and map 31
 Indifference set/ schedule is a combination of goods for which the
consumer is indifferent.
 It shows the various combinations of goods from which the consumer
derives the same level of satisfaction.
 In table below, each combination of good X and Y gives the
consumer equal level of total utility. Thus, the individual is indifferent
whether he consumes combination A, B, C or D.
Table: Consumption Schedule
Bundle (Combination) A B C D
Orange 1 2 4 7
Banana 10 6 3 1
 32
Indifference curve: When the indifference set/schedule is expressed
graphically, it is called an indifference curve.
An indifference curve shows different combinations of two goods which
yield the same utility (level of satisfaction) to the consumer.
Banana
10 A Bundle A B C D

Orange 1 2 4 7
6 B Banana 10 6 3 1

3 C
D
1 IC

1 2 4 7 Orange
 33
Indifference Map:
❑ A set of indifference curves

Banana

E
B

F C IC 3
D
IC 2
IC 1
Orange
 3.3.2.3 Properties of indifference curves 34

I. Indifference curves have negative slope (downward sloping)

▪ Consumption level of one commodity can be increased only by reducing
the consumption level of the other commodity. In order to keep the utility
of the consumer constant, as the quantity of one commodity is increased
the quantity of the other must be decreased

II. Indifference curves are convex to the origin.

▪ This implies that the slope of an indifference curve decreases (in absolute
terms) as we move along the curve from the left downwards to the right.
The convexity shows the diminishing marginal rate of substitution.

▪ the commodities can substitute one another at any point on an

indifference curve but are not perfect substitutes
 35
Properties of indifference curves…

Y Y
Convex Curve Concave Curve

X
1 2 3 4 5 X 1 2 3 4 5
Cont’d 36

3. A higher indifference curve is always preferred to a lower one.

▪ The further away from the origin an indifferent curve lies, the
higher the level of utility it denotes.

▪ Baskets of goods on a higher indifference curve are preferred by

the rational consumer because they contain more of the two
commodities than the lower ones.

4. Indifference curves never cross each other (cannot intersect).

▪ The assumptions of consistency and transitivity will rule out the
intersection of indifference curves.
Cont’d 37

A
E

B
IC 2

IC 1

X
3.3.2.4 Marginal rate of substitution (MRS) 38

 Marginal rate of substitution is a rate at which consumers are willing to

substitute one commodity for another in such a way that the
consumer remains on the same indifference curve.

 MRS of X for Y is defined as the number of units of commodity Y that

must be given up in exchange for an extra unit of commodity X so
that the consumer maintains the same level of satisfaction.

 Since one of the goods is sacrificed to obtain more of the other good,
the MRS is negative. -usually we take the absolute value of the slope.
Cont’d 39

𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒖𝒏𝒊𝒕𝒔 𝒐𝒇 𝒀 𝒈𝒊𝒗𝒆𝒏 𝒖𝒑 𝜟𝒀

MRSxy = 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒖𝒏𝒊𝒕𝒔 𝒐𝒇 𝑿 𝒈𝒂𝒊𝒏𝒆𝒅
=- 𝜟𝑿

 It is also possible to derive MRS using the concept of marginal

utility. MRSXY is related to MUX and MUY as follows;

𝑴𝑼𝒙
MRSxy=
𝑴𝑼𝒚
Proof 40
 Suppose the utility function for two commodities X and Y is defined as:

U = f (X ,Y)
 Since utility is constant along an indifference curve, the total differential of
the utility function will be zero.
𝑑𝑈 𝑑𝑈
𝑑𝑈 = 𝑑𝑋 + 𝑑𝑌 = 0
𝑑𝑋 𝑑𝑌
𝑀𝑈𝑋 𝑑𝑋 + 𝑀𝑈𝑌 𝑑𝑌 = 0
𝑀𝑈𝑋 𝑑𝑋 = − 𝑀𝑈𝑌 𝑑𝑌

𝑴𝑼𝒙 𝒅𝒀 𝑴𝑼𝒚 𝒅𝑿
𝑴𝑼𝒚
=− 𝒅𝑿
= 𝑴𝑹𝑺𝒙𝒚 Similarly, 𝑴𝑼𝒙
=− 𝒅𝒀
= 𝑴𝑹𝑺𝒚𝒙
To understand the concept, consider the following IC
Quantity
of Banana

14 A The marginal rate of substitution

between Banana and Orange is
MRS = 6
the rate at which the consumer
is willing to give up Banana to
B get more Orange.
8
1

C
4 D
MRS = 1
3
1
Indifference
curve

0 2 3 6 7 Quantity
of Orange
 42
Example: Suppose a consumer’s utility function is given by U(X, Y) = 𝑿𝟒 𝒀𝟐 .
Find 𝑴𝑹𝑺 𝒙𝒚
Solution: 𝟒𝑿𝟑 𝒀𝟐 𝟐𝑿𝟑 𝒀
𝑀𝑈𝑥 𝑀𝑅𝑆 𝑥𝑦 = =
𝑀𝑅𝑆 𝑥𝑦 = 𝟐𝑿𝟒 𝑌 𝑿𝟒
𝑀𝑈𝑦
𝜕𝑈
𝑀𝑈𝑥 = 𝜕𝑋
= 𝟒𝑿𝟑 𝒀𝟐 = 𝟐𝑿𝟑−𝟒 𝒀 = 𝟐𝑿−𝟏 𝒀
𝜕𝑈 1
𝑀𝑈𝑦 = = 𝟐𝑿𝟒 𝒀 = 2 𝑌
𝜕𝑦 𝑋
𝑀𝑈𝑥 𝟒𝑿𝟑 𝒀𝟐
Hence, 𝑀𝑅𝑆 𝑥𝑦 = = 𝟐𝒀
𝑀𝑈𝑦 𝟐𝑿𝟒 𝑌
𝑴𝑹𝑺 𝒙𝒚 =
𝑿
 3.3.2.5 The budget line or the price line 43

 Indifference curves only tell us about consumer preferences

 In reality, the consumer is constrained by his/her income and prices

of the two commodities.

 This constraint is often presented with the help of the budget line.

 The budget line is a set of commodity bundles that can be

purchased if the entire income is spent.

 It is a graph that shows the various combinations of two goods that a

consumer can purchase given his/her limited income and the prices
of the two goods.
Cont’d 44

 In order to draw a budget line facing a consumer, we

consider the following assumptions.
1. There are only two goods bought in quantities, say, X and Y.

2. Each consumer is confronted with market determined

prices, PX and PY.

3. The consumer has a known and fixed money income (M).

4. The consumer spends all his/her income on the two goods

(X and Y)
Cont.. 45

 Assuming that the consumer spends all his/her income on the two
goods (X and Y), we can express the budget constraint as M = PX.X +
PY.Y.
 By rearranging the above equation, we can derive the
following general equation of a budget line;
PX.X+ PY.Y = M

𝑀 𝑃𝑥
𝑌= - X
𝑃𝑦 𝑃𝑦

 – PX/PY is the slop of the budget line, M/PY is Y-intercept while M/PX is
X-intercept
Note that: 46
 Any combination of the two goods within the budget line (such as point A) or along the
budget line (point B) is attainable.
 Any combination of the two goods outside the budget line (such as point C) is
unattainable (unaffordable).
Y
The Budget Line
M/PY

C
A: Possible but under utilization of M
B
B: Possible and full utilization of M
A C: Impossible M

M/PX X
 Example:
A consumer has birr100 to spend on two goods X and Y with prices birr 3 and
birr 5 respectively. Derive the equation of the budget line and sketch the graph.

Solution: The equation of the budget line can be derived as 3𝑥

0 = 20 -
follows: 5

PX. X + PY.Y =M 3𝑥
= 20
5
3X+5Y= 100
3𝑥
5Y=100 - 3X 5( ) = (20)5
5
100 3
Y= - x
5 5 3𝑥 = 100
3𝑥
Y= 20 -
5 𝑥 = 33.33
When X is 0, Y= 20
Example… 48

▪ When the consumer spends all of her income on good Y, we get

the Y- intercept (0,20).

▪ Similarly, when the consumer spends all of her income on good X,

we obtain the X- intercept (33.3, 0).

▪ Using these two points we can sketch the graph of the budget line.

▪ Recall that a budget is drawn for given prices and fixed consumer‘s
income changes in prices or income will affect the budget line.
– PX/PY = -3/5 is the slop of the budget line, M/PY = 20 is 49

Y-intercept while M/PX = 100/3 is X-intercept

M/PY= 20

M/PX = 33.3 X
 Change in INCOME 50

o If the income of the consumer changes (keeping the prices of the

commodities unchanged), the budget line also shifts.

o Increase in income causes an upward/outward shift in the budget

line that allows the consumer to buy more goods and services

o Decreases in income causes a downward/inward shift in the BL

that leads the consumer to buy less quantity of the two goods.

 The slope of the budget line does not change as income

changes.
 51
Effects of increase (right) and decrease (left) in income on the budget line

Good Y

𝑀ൗ
𝑃𝑦

𝑀ൗ Good X
𝑃𝑥
 52
Change in PRICES:
 An equal increase in the prices of the two goods shifts the budget
line inward.

✓ Since the two goods become expensive, the consumer can

purchase the lesser amount of the two goods.

 An equal decrease in the prices of the two goods shifts the

budget line out ward.

✓ Since the two goods become cheaper, the consumer can

purchase the more amounts of the two goods.
 Changes in the PRICE of one of 53

the two Goods

❑ A change in the price of one of the two goods, keeping the price
of the other good and income constant, changes the slope of the
budget line by affecting only the intercept of the commodity
that records the change in the price.

▪ For instance, if the price of good X decreases while both the

price of good Y and consumer‘s income remain unchanged, the
X-intercept moves outward and makes the budget line flatter.
The reverse is true if the price of good X increases.
 54
Cont’d

▪ On the other hand, if the price of good Y decreases while

both the price of good X and consumer‘s income remain
unchanged, the Y-intercept moves upward and makes the
budget line steeper.

▪ The reverse is true for an increase in the price of good Y.

 55
Effect of decrease in the price of only good X on the budget line

Number of Movies A decrease in the price of concerts

per Month (Y) rotates it rightward.
30

15

5 15 Number of Concerts
per Month (X)
 56
Effect of Increase in the price of only good X on the budget line

Number of Movies
per Month (Y)

An Increase in the price of 30

concerts rotates it leftward.

15

2 5 Number of Concerts
per Month (X)
 57
3.3.2.6. Equilibrium of the Consumer
 The preferences of a consumer are indicated by the IC.
 The budget line specifies different combinations of two goods (say X
and Y) the consumer can purchase with the limited income.
A rational consumer tries to attain the highest possible IC, given the BL.
 This
occurs at the point where the indifference curve is tangent to the
budget line
 The slope of the IC is equal to the slope of the BL;
𝒑𝒙
𝑴𝑹𝑺𝑿𝒀 =
𝒑𝒚
 58
Consumer Equilibrium
Y ▪ The equilibrium of the
consumer is at point “E” where
the budget line is tangent to
M/Py the highest attainable
indifference curve (IC2).
D
Consumer ▪ Mathematically, consumer
C Equilibrium optimum (equilibrium) is attained
at the point where:
F at point E
Slope of indifference curve =
Ye E
Slope of the budget line
B
A IC 3 𝑴𝑹𝑺𝑿𝒀 =
𝑴𝑼𝒙
=
𝒑𝒙
𝑴𝑼𝒚 𝒑𝒚
IC 2
Xe M/Px IC 1 X
 59
Optimal Choice
Example:
A consumer consuming two commodities X and Y has the utility
function U (X ,Y ) =XY + X . The prices of the two commodities
are 4 birr and 2 birr respectively. The consumer has a total income of
60 birr to be spent on the two goods.

a) Find the utility maximizing quantities of good X and Y.

b) Find the MRS XY at equilibrium.
 60
Solution
a) The budget constraint of the consumer is given by: 𝑃𝑥 𝑋 + 𝑃𝑦 Y = M
𝟒𝑿 + 2Y = 60 −−−−−−−−−−− − (1)
Moreover, at equilibrium

𝑀𝑈𝑥 𝑝𝑥
=
𝑀𝑈𝑦 𝑝𝑦

𝑌+2 4
=
𝑋 2
𝑌+2
=2
𝑋

𝒀 = 2x −2 −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− (2)
Cont’d

To get the utility maximizing quantities of good X 4𝑋 + 2Y = 60

and Y, substitute equation (1) into (2), 4(8) + 2Y = 60
32 + 2Y = 60
4𝑋 + 2Y = 60
2Y = 28
4𝑋 + 2(2x−2) = 60
Y= 14
4x+4x- 4 = 60
Utility maximizing quantities of good Y is 14
8x- 4 = 60
8x = 64
𝑀𝑈𝑥 𝑌+2 14+2
b) 𝑴𝑹𝑺𝑿𝒀 = = = =𝟐
𝑀𝑈𝑦 𝑋 8
X= 8

(At the equilibrium, MRS can also be calculated as the

So, the Utility maximizing quantities of good X is 8 ratio of the prices of the two goods)
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