Chapter Two :Theory of Consumer Behaviors

Chapter objectives
 After successful completion of this chapter, you will be able to:
 Explain consumer preferences and utility
 Differentiate between cardinal and ordinal utility approach
 Define indifference curve and discuss its properties
 Derive and explain the budget line
 Describe the equilibrium condition of a consumer
 2.1 Consumer preferences

 A consumer makes choices by comparing bundle of goods.

• Strict preference
• Given any two consumption bundles, the consumer either decides that one
of the consumption bundles is strictly better than the other, or decides that
she is indifferent between the two bundles.
• If she always chooses X when Y is available, then it is natural to say that
this consumer prefers X to Y.
• We use the symbol ≻ to mean that one bundle is strictly preferred to
another, so that X ≻Y should be interpreted as saying that the consumer
strictly prefers X to Y.
• Given any two consumption bundles(X1,X2) and (Y1,Y2),if (X1,X2)>(Y1,Y2) or if
he chooses (X1,X2) when (Y1,Y2) is available the consumer definitely wants
the X-bundle than Y.
 2.1 Consumer Preference

• Weak preference
• Given any two consumption bundles(X1,X2) and (Y1,Y2),if the consumer is indifferent
between the two commodity bundles or if (X1,X2) or (Y1,Y2),the consumer would be
equally satisfied if he consumes (X1,X2) or (Y1,Y2)
• Completeness
• For any two commodity bundles X and Y,a consumer will prefer X to Y, Y to X or will be
indifferent between the two.
• Transitivity
• It means that if a consumer prefers basket A to basket B and to basket C, then the
consumer also prefers A to C.
• More is better than less
• Consumers always prefer more of any good to less and they are never satisfied or
satiated. However, bad goods are not desirable and consumers will always prefer less
of them.
 2.2 The concept of utility

 Economists use the term utility to describe the satisfaction or pleasure

derived from the consumption of a good or service.
 In other words, utility is the power of the product to satisfy human wants.
 In defining strict preference, we said that given any two consumption
bundles(X1, X2) and (Y1,Y2) the consumer definitely wants the X bundle

than the Y bundle if (X1, X2) > (Y1,Y2).This means, the consumer preferred

bundle (X1, X2) to bundle (Y1,Y2) if and only if the utility (X1, X2) is larger

than the utility of (Y1,Y2).

 2.2 The concept of utility………

 Utility’ and ‘Usefulness’ are not synonymous. For example, paintings

by Picasso may be useless functionally but offer great utility to art
lovers. Hence, usefulness is product centric whereas utility is consumer centric.
 Utility is subjective. The utility of a product will vary from person to person
 That means, the utility that two individuals derive from consuming the same
level of a product may not be the same.
 For example, non-smokers do not derive any utility from cigarettes.

 Utility can be different at different places and time.

 For example, the utility that we get from drinking coffee early in the morning may be different from the
utility we get during lunch time.
 2.2 The concept of utility………
• A Consumer considers the following points to get maximum utility or level
of satisfaction:
• How much satisfaction he gets from buying and then consuming an
extra unit of a good or service.
• The price he pays to get the good.
• The satisfaction he gets from consuming alternative products.
• The prices of alternative goods and services.
 2.3 Approaches of measuring utility

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

cardinal and ordinal approaches.
 The cardinalist school postulated that utility can be measured objectively.
 According to the ordinalist school, utility is not measurable in cardinal
numbers rather the consumer can rank or order the utility he derives from
different goods and services.
 2.3.1 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.
 For example, 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.
 2.3.1.1 Assumptions of cardinal utility theory

 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. According to the cardinal approach, the
utility or satisfaction of each commodity is measurable.
 Utility is measured in subjective units called utils.
 2.3.1.1 Assumptions of cardinal utility theory……’cont
 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.
 A person at the start of the month where he has received monthly salary gives
equal value to 1 birr with what he may give it after three weeks or so.
 4. Limited Money Income. The consumer has limited money income to spend
on the goods and services he/she chooses to consume.
 4. Diminishing marginal utility (DMU). The utility derived from each
successive units of a commodity diminishes. In other words, the marginal utility
of a commodity diminishes as the consumer acquires larger quantities of it.
 3.3.1.1 Assumptions of cardinal utility theory……’cont
5. The total utility of a basket of goods depends on the quantities of the
individual commodities.
 If there are n commodities in the bundle with quantities X1 , X2 ,...Xn , the
total utility is given by TU = f ( X1 , X2 ......Xn ).
 Utility is also additive, i.e., U (X1) + U (X2) +U (X3) ……… +U
( Xn ) = Total Utility (TU)
 2.3.1.2 Total and marginal utility

 Total Utility (TU) is the total satisfaction a consumer gets from consuming
some specific quantities of a commodity at a particular time.
 if a consumer consumes 4 units of a commodity and derives U1, U2, U3
and U4 from the successive units consumed, then TU = U1+U2+U3+U4.
 In case the number of commodities consumed is greater than one, then
TU= TUx TUy + TUz + ……… TUn
 As the consumer consumes more of a good per time period, his/her total
utility increases.
 2.3.1.2 Total and marginal utility….

 Marginal Utility (MU) is the extra satisfaction a consumer realizes from an

additional unit of the product.
 In other words, marginal utility 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: where, TU is the change
in total utility, and Q is the change in the amount of product consumed.
 To explain the relationship between TU and MU, let us consider the following
hypothetical example.
2.3.1.2 Total and marginal utility….
 2.3.1.2 Total and marginal utility….

 Graphically, the above

data can be depicted
as follows.
 2.3.1.2 Total and marginal utility……

 As it can be observed from the above figure,

  When TU is increasing, MU is positive.
  When TU is maximized, MU is zero.
  When TU is decreasing, MU is negative.
 2.3.1.3 Law of diminishing marginal utility (LDMU)
 The law of diminishing marginal utility 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 law of diminishing marginal utility is based on the following
assumptions.
 The consumer is rational
The consumer consumes identical or homogenous product. The commodity to
be consumed should have similar quality, color, design, etc.
 There is no time gap in consumption of the good
 The consumer taste/preferences remain unchanged
• Limitations or Exceptions
• The law does not apply in the case of rare collections like stamps paintings and coins etc.
In the case of rare collections, the larger the number the collects, the greater will be the
pleasure. Hence, the law does not apply.
• When we discuss the law, we are applying it only to normal persons. But there are some
abnormal persons too e.g., misers, drunkards etc. The more the money a miser has, the
greater is the utility that he derives. The more the drunkard gets pleasure the more he
drinks.
• Importance
A. The law of diminishing marginal utility expresses us a basic principle of man’s
behaviour. It is of great practical value to human beings in every walk of life.
B. The law is applied in the sphere of taxation. A rich man is taxed more, fro the
utility of money to a rich man is less than to a poor man. The principle of
progressive taxation is based on this only.
A. The law can also be applied in determining the prices of goods in the market.
An increase in the stock of a commodity brings a person less satisfaction and
therefore he can be induced to buy more only if the price is lowered. Hence,
the greater the supply, the lower should be the price to clear it and vice-versa.
B. The law regulates our daily expenditure pattern. We know that as we go on
buying more of a commodity, its marginal utility falls. Having only a limited
amount of money at our disposal, we do not want to waste it unnecessarily on
the purchase of the same commodity in large quantity. We, therefore, stop
purchasing it at a point where the utility of money spent is equal to the last
unit of the good purchased. We spend the rest of our money on other goods.
C. The marginal utility analysis of pricing and the diminishing marginal utility can
quickly dispose of the diamond-water paradox with the aid of this analysis we
can now explain that the relative scarcity of diamonds results in high price,
while the relative abundance of water means that its marginal utility and
consequently its price will be low despite its high total utility.
 2.3.1.4 Equilibrium of a consumer

 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
• Suppose the consumer’s utility function is given as
• U =f (X)
• his/her total income spent (expenditure) on commodity X
• Total Expenditure would be: TE = QxPx
• where Qx is amount of commodity x and Px is price of good X.
 2.3.1.4 Equilibrium of a consumer
Suppose the consumer’s utility function is given as U =f (X)
his/her total income spent (expenditure) on commodity X –Total
Expenditure would be: TE = QxPx
• where Qx is amount of commodity x and
• Px is price of good X.
• The consumer would like to maximize the difference between
the utility (satisfaction) and expenditure (sacrifice).
• The problem is a simple maximization of the function.
 2.3.1.4 Equilibrium of a consumer
• 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.
Proof
Given the utility function U  f (X)
• If the consumer buys commodity X, then his expenditure
• the consumer would like to maximizes the difference between his utility and
expenditure.
• Max U – TE or
• U – Px Qx
• The problem is a simple maximization of the function.
• Two conditions must be fulfilled
• Necessary Condition (F.O.C)
• Sufficient Condition (S.O.C)
• The necessary condition (First Order Condition) for maximum,
require that the derivative of the function with respect to
independent variable (Qx) must be equal to zero.
 dU d (Q X PX )
 0
dQ X dQ X

 MUx - Px =0

 MU X  PX
MUx
1
Px 24
 2.3.1.4 Equilibrium of a consumer

• At any point above point C (like point A) where MUX > PX, it pays the consumer
to consume more.

• When MUX < PX (like point B), the consumer should consume less of X.

• At point C where MUX = PX the consumer is at equilibrium.

Consumers Equilibrium: The General Case: (The law of equi-
marginal Utility)
• In reality, however, a consumer consumes a large number of
goods.
• The MU schedules of different commodities may not be the
same.
• A utility maximizing consumer consumes commodities in order
of their utilities.
• He picks up the commodity, which yields the highest utility
followed by the commodity yielding the second highest utility
and so on.
• He switches his expenditure from one commodity to another in
accordance, with their marginal utility.

26
 Cardinal Utility (cont…)
• He continues to switch his expenditure from one commodity to the
other till he reaches a stage where MU of each commodity is equal
per unit of expenditure
• Therefore, the consumer optimum follows the law of equi-marginal
utility.
• We can use a single commodity case to determine the general case.
• For commodity X, equilibrium occurs when MUx = Px
• MUx = Px and this can be written as
• MUx / Px = 1

27
• if the consumer consumes a bundle of n commodities i.e X1, X2
X3…… Xn , he/she would be in equilibrium or utility is maximized if
and only if:
i. when the marginal utility per money spent is equal for each good purchased
MU X 1 MU X 2 MU X n
  ......... 
PX 1 PX 2 PX n

ii. his money income available for the purchase of the goods is exhausted.

In genral
 b) the case of two or more commodities

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.

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.
 Cont………………………………
• Exercise: Consider a consumer having only birr 7 in his
pocket to buy bread and banana
If the Price of banana is birr 4/kg and price of bread is birr
one per unit determine.
i. His marginal utility schedule for the two commodities
ii. Determine his optimum consumption of these two goods
iii. The total utility at optimum consumption
 Bread, Price=birr 1/unit Banana, Price=4birr/kg
Quantity TU MU MU/P Quantity TU MU MU/P
of
0 0 0 0

1 6 1 12
2 11 2 20

3 14 3 26

4 13 4 29

5 13 5 32

6 11 6 31
 Solutions
Bread , Price=birr 1/unit Banana, Price=4birr/kg
Quantity TU M MU/P Quantity TU MU MU/P

0 0 - - 0 0 - -
1 6 6 6 1 12 12 3
2 11 5 5 2 20 8 2
3 14 3 3 3 26 6 1.5
4 13 1 1 4 29 3 0.75
5 13 0 0 5 32 2 .5
6 11 -2 -2 6 31 -1 -0.25
 2.3.1.6. Deriving Cardinalist Demand
• The marginal utility is the slope of the total utility function.
• The derivation of demand curve is base don the concept of diminishing
marginal utility.
• If the marginal utility is measured using monetary units the demand curve for a
commodity is the same as the positive segment of the marginal a
utility curve.
P1
Price b
P

c
P2
MUX
O Quantity

PriceP1

P
Demand
P2 Curve
O Quantit
Q1 Q Q2 y
Quantity of Y Deriving Cardinalist Demand
E3 P3
E2
P2
E1 P1

X1
1 X2 MU X Quantity of X

Price
a
P3
P2 b

P1 c
Demand Curve

X1 X2 X3 Quantity of X
 2.3.1.5. Cardinal Utility (cont…)
Limitation of the Cardinal approach
a) The assumption that utility is a cardinal concept (utility is
objectively measurable) is doubtful.
• Utility is a subjective concept, which cannot be measured objectively.
b) The assumption of constant marginal utility of money is also
unrealistic..
c) The psychological law of diminishing marginal utility has been
established from introspection
d) The cardinal utility approach is on the basis of Ceteris Paribus
assumption.
• As a result it ignores the substitution and income effect.

35
 2.3.2 The ordinal utility theory

 In the ordinal utility approach, it is not possible for consumers to express the
utility of various commodities they consume 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.
 3.3.2.1 Assumptions of ordinal utility theory

 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: The marginal rate of substitution

is the rate at which a consumer is willing to substitute one commodity for
another commodity so that his total satisfaction remains the same.
 3.3.2.1 Assumptions of ordinal utility theory……
• Non-Satiation: In any two consumption bundle A and B, A is
preferred to B, if A contains, at least more of one commodity.
That is, more is preferred to less under normal condition.
• Limited money income.
Generally, ordinalist school simply argue that,
• individual tends to make consistent choice,
• that the law of preference represents a good approximation of actual
behavior of consumer
• and thus, the law of preference are rules of rational choice.

• 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.

• The ordinal utility approach is explained with the help of indifference curves.

• Therefore, the ordinal utility theory is also known as the indifference curve
approach.
 3.3.2.2 Indifference set, curve and map
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.
Consider a consumer who consumes two goods X and Y (table 3.3).
 3.3.2.2 Indifference set, curve and map
• Indifference curve: An indifference curve shows different combinations of
two goods which yield the same utility (level of satisfaction) to the consumer.
• A set of indifference curves is called indifference map.
 3.3.2.3 Properties of indifference curves

1. Indifference curves have negative slope (downward sloping to the right).

• Indifference curves are negatively sloped because the consumption level of

one commodity can be increased only by reducing the consumption level of
the other commodity.

2. Indifference curves are convex to the origin. The convexity of indifference

curves is the reflection of the diminishing marginal rate of substitution.
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.
 3.3.2.3 Properties of indifference curves
• 4. Indifference curves never cross each other (cannot intersect).
• The assumptions of consistency and transitivity will rule out the intersection of
indifference curves. Figure 3.4
 3.3.2.4 Marginal rate of substitution (MRS)

• Marginal rate of substitution 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 scarified to obtain more of the other good, the MRS
is negative.
 3.3.2.4 Marginal rate of substitution (MRS)…….
•
 From the above graph, MRSX,Y associated with the
movement from point A to B, point B to C
and point C to D is 2.0,1.6, and 0.8 respectively.
 3.3.2.4 Marginal rate of substitution (MRS)
• It is also possible to derive MRS using the concept of marginal utility. MYS is XY ,

related to MUX and MUY as follows.

• Proof: 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.
•
 3.3.2.4 Marginal rate of substitution (MRS)…

• Example: Suppose a consumer‘s utility function is given by U(X,Y)  X4 Y2 .

42

Find MRSX,Y.
Exceptional Indifference Curves
• indifference curves are convex to the origin and downward sloping
• However, the shape of the indifference curve reflects the degree of
substitution between the two commodity
• The shape of an indifference curve might be different if the
relationship between two commodities is unique
• Perfect substitutes: perfect substitutes are goods which can be
replaced for one another at a constant rate.

48
 Exceptional IC (Cont …)
• Perfect substitutes

Total
IC3

IC2

IC1

Mobile
49
 Exceptional IC (Cont …)
• Perfect complements: perfect complements are goods which are
to be consumed jointly at a constant rate
• If two commodities are perfect complements the indifference
curve takes the shape of a right angle (L –shape)
• Graphically it is shown as follows.

50
 Exceptional IC (Cont …)
• Perfect complements
IC3
IC2
IC1
Right shoe

Left shoe 51
 Exceptional IC (Cont …)
• A useless good: This shows the relationship between useless
good and another normal good.
• A good example is outdated book and food.
• since the outdated books are totally useless, increasing their
purchases does not increase utility.
• The person enjoys a higher level of utility only by getting
additional food consumption
• The indifference curve in this case will have a vertical one

52
 Exceptional IC (Cont …)
• Fig.
IC1 IC2 IC3
Out dated
books

Food 53
 3.3.2.5 The budget line or the price line
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 the commodity bundles that can be purchased if the
entire income is spent.
It is a graph which shows the various combinations of two goods that a
consumer can purchase given his/her limited income and the prices of the two
goods
In order to draw a budget line facing a consumer, we consider the following
assumptions.
 There are only two goods bought in quantities, say, X and Y.
 Each consumer is confronted with market determined prices, PX and PY.
 The consumer has a known and fixed money income (M).
 3.3.2.5 The budget line or the price line
• Assuming that the consumer spends all his/her income on the two goods (X
and Y), we can express the budget constraint as:
• M  P X P Y
X Y By rearranging the above equation, we can derive the
following general equation of a budge t line.

• Graphically,
 3.3.2.5 The budget line or the price line
• Note that:The slope of the budget line is given is by (the ratio of the prices
of the two goods).
 Any combination of the two goods within the budget line (such as point A) or
along the budget line is attainable.
•  Any combination of the two goods outside the budget line (such as point B)
is unattainable (unaffordable).

• Example: A consumer has $100 to spend on two goods X and Y with prices $3
and $5 respectively.
• Derive the equation of the budget line and sketch the graph.
 3.3.2.5 The budget line or the price line
Solution: The equation of the budget line can be derived as follows.

 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.
 Change in Income
If the income of the consumer changes (keeping the prices of the commodities
unchanged), the b udget line also shifts (changes).

Increase in income causes an upward/outward shift in the budget line that

allows the consumer to buy more goods and services and decreases in income
causes a downward/inward shift in the budget line that leads the consumer to
buy less quantity of the two goods.

It is important to note that the slope of the budget line (the ratio of the two
prices) does not change when income rises or falls.
 Change in Income

Figure 3.7: Effects of increase (right) and decrease (left) in income on the
budget line
 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, one the other hand, shifts the
budget line out ward.

 Since the two goods become cheaper, the consumer can purchase the more
amounts of the two goods.
 Change in prices:
Figure 3.8: Effect of proportionate increase (inward) and decrease (out ward)
in the prices of both goods
 Change in prices:
Figure 3.9: Effect of decrease in the price of only good X on the budget line
 3.3.2.6 Equilibrium of the consumer
The preferences of a consumer (what he/she wishes to purchase) are indicated by
the indifference curve.

 The budget line specifies different combinations of two goods (say X and Y) the
consumer can purchase with the limited income.

Therefore, a rational consumer tries to attain the highest possible indifference

curve, given the budget line.

This occurs at the point where the indifference curve is tangent to the budget line
so that the slope of the indifference curve (MRS XY ) is equal to the slope of the
 3.3.2.6 Equilibrium of the consumer……
Figure 3.10: Consumer equilibrium under indifference curve approach

 Mathematically, consumer optimum

(equilibrium) is attained at the point where:
 Slope of indifference curve
= MRSxy = MUx/Muy
 Slope of the budget line = Px/Py
 Slope of indifference curve = Slope of the
budget line, then
 3.3.2.6 Equilibrium of the consumer
The preferences of a consumer (what he/she wishes to purchase) are indicated by
the indifference curve.

 The budget line specifies different combinations of two goods (say X and Y) the
consumer can purchase with the limited income.

Therefore, a rational consumer tries to attain the highest possible indifference

curve, given the budget line.

This occurs at the point where the indifference curve is tangent to the budget line
so that the slope of the indifference curve (MRS XY ) is equal to the slope of the
 3.3.2.6 Equilibrium of the consumer
Example: A consumer consuming two commodities X and Y has the utility
function U(X,Y) =XY + 2X . 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 MRSX,Y at equilibrium.

 3.3.2.6 Equilibrium of the consumer

• Solution
• a) The budget constraint of the consumer
is given by:
• PX.X+ PY.Y = M
• 4X+2Y= 60 …………….…………. (i)

• Substituting equation (ii) into (i), we obtain Y =14 and X = 8.

 3.3.2.6 Equilibrium of the consumer

• Solution

• (At the equilibrium, MRS can also be calculated as the ratio of the prices of the two
goods)
 End of the Chapter

•.

! ! !
n d fo r
e E u n
h
T k y o tio
a n e n
h
T rA tt
o u
y