3 consumer choice

Learning Outcomes

Upon completing this section, the student should be able to:

• Describe and illustrate the assumptions of indifference curve
analysis
• Illustrate and determine utility functions
• Determine utility maximisation subject to budget constraint
• Distinguish between income and substitution effects
• Apply consumer choice theory to changing prices
• Derive Engel Curves and Compensated demand Curves
• Distinguish between Slutsky and Hicks in terms of their
approach to compensation variation in income.

Consumer Choice

• This section examines consumer decision-making.
• Decisions made at individual level are important.
• How much consumers spend on certain goods and services is of
prime interest to business planners who want to anticipate future
demand levels, but also to governments considering the imposition of
a new tax.
• The approach taken will mainly use the neo-classical framework. This
assumes that individuals are utility maximisers, something that is often
criticised for being unrealistic.
• The theory is not meant to be an accurate description of every situation that
an individual faces.
• What it does provide is an approach that can be used to make predictions
when individual circumstances change.
• First we introduce the analytical tools, indifference curves to represent the
preferences of individuals and 'budget' lines to represent the constraint of a
given amount of income.

Consumer Choice

• We start with a simple way in which we can represent the
preferences of individuals between different combinations of goods
that they might buy.
• We limit ourselves to decisions concerning only two goods.
• One particular individual, Kate, who spends her time drinking coffee.
• She likes both Cappuccino and Espresso, both of which give her
satisfaction or, in the language of economics, utility.
• Figure 5.1 shows alternative combinations that she might drink over a
particular period of time, say each week. Point A shows three cups of
cappuccino and two cups of espresso, points B and C show other possible
combinations.
• The preferences she has in relation to Cappuccino and Espresso can be
represented by an indifference curve.
• This is a graphical way of showing alternative combinations of two goods
that yield a particular level of utility, or satisfaction, to an individual.

Figure 5.1: Indifference Curve

The completeness assumption: The consumer has preferences between all
possible combinations of goods, and these preferences may be ordered. If the
individual is presented with two alternative combinations of goods then he or she can
state which one is preferred (or whether he or she is indifferent between them).

Number of Cappuccinos

6 C
5

4

3
A
2 Kate would be B
willing to give up
1 cappuccino
1 IC0
In exchange for 2 expressos
0

0 1 2 3 4 5 6 Number of Expressos

Figure 5.2: Indifference Map

The assumption of non-satiation: The wants of the consumer are insatiable.
Intuitively the consumer is assumed to prefer-more of a good to less of it. It
follows that indifference curves that are further away from the origin represent
a higher level of satisfaction or utility.

E

D
6
C
5

4

3
IC2
2
IC1
1
IC0
0

Fig 5.4: Diminishing Marginal Rate of Substitution (DMRS).

The rate at which the consumer is willing to exchange one good for another decreases
the more the individual has of the second good. In terms of our example, the more
cappuccino drunk, the greater the willingness to exchange a. cup for an espresso
drink. This is illustrated below where the changing slope of the indifference curve
shows the diminishing marginal rate of substitution.


6
Starting at 5 Cappuccinos
5 Kate would be willing to
give up 3 cappuccinos
4 for 1 additional expresso
Starting at 3 Cappuccinos
Kate would be willing to
3 give up 1 cappuccinos for
2 additional expresso
2
IC0
1

0

Figure 5.5: The Assumption of Transitivity

The assumption of transitivity: The assumption that consumers' preferences are
transitive. This means that consumers are taken to be rational in the sense that their
preferences are consistent. For example, in Figure 5.2, if the individual prefers the
combination of goods associated with point E to that at point D, and also prefers (the
combination associated with) point D to that at point C, then we can say that point E
is preferred to point C.

6

5

4

3
A
2 C
1 IC0
B IC0
0


Note: if indifference curves intersect the assumption of transitivity is violated.

Utility Functions

•Another way of representing consumer preferences is with utility functions. In the case
where the consumer buys just two goods a utility function can be written as:
•U = U(X,Y) where U stands for utility, X and Y represent the quantities of the two goods.

X Y U = XY X Y U = XY
25 4 100 50 8 400
20 5 100 40 10 400
10 10 100 20 20 400
5 20 100 10 40 400
4 25 100 8 50 400

Table 3.2: Utility Function U = f (XY), U = f (10XY), U = f (3XY-100),
X Y U = XY U = f (1 0XY) U = 3XY-1 00
25 4 100 1000 200
20 5 100 1000 200
10 10 100 1000 200
5 20 100 1000 200
4 25 100 1000 200

Figure 5.7: Indifference Curves for Perfect Substitutes / Complements

Good Y Good Y
Both Good are Perfect
Both Good are Perfect Complements
Substitutes

Good X Good X

Figure 3.9: The Consumers’ Equilibrium

• Neo-classical theory assumes that consumers are utility maximisers.
• To model this behaviour we need to bring together our representation of the
individual's preferences and the financial constraint faced.
• The utility maximising consumer will attain the highest utility possible given his or her
budget constraint Figure 5.9 shows this as a point of tangency between the
indifference curve, IC0, and the budget line, BL0, marked as point A- At the optimum
point, the individual consumes the quantity Xo of good X, and the quantity Y0 of good
Y.
Good Y
Px
Slope of the Budget line = = −1
M/Py Py

B

A
Y0

C
IC0

BL0

0
0 X0 M/PX Good X

Budget Constraint

Suppose student gets €60 per week of an
allowance

Entertainment
S/he spends on food and/or entertainment
10
units M/Pe = 60/6 = 10
The Price of a typical basket of food is €10 and
the price of the average entertainment unit
(cinema) is €6.

DRAW THE STUDENTS BUDGET LINE M/Pf = 60/10 =6
€60 = P(food)*Quantity of Food + P(entertainment 5
* Quantity of entertainment) - Utility Function

0 1 2 3 4 5 6 units

Food

Budget Constraint

Suppose a student gets €60 per week
of an allowance.
Entertainment

Point A - S/he spends all income 10 A Budget
on entertainment Line

Point B - S/he spends all
income on food C
5

Typically the student will prefer some
combination of Food/Entertainment

Point C - 5 units of entertainment and
B
3 units of food ( This will cost €60) 1 2 3 4 5 6
Food

Consumer Equilibrium - Assume Consumers are Utility Maximisers

All points on the budget line represent
combinations of food/entertainment that
can be purchased for €60. Entertainment
A
All Points on an IC represents equal levels 10 Budget
of satisfaction of utility
Line
WE CAN NOW MODEL INDIVIDUAL
PREFERENCES AND THE
FINANCIAL CONSTRAINT C
5

B
1 2 3 4 5 6
Food

Consumer Equilibrium- Assume Consumers are Utility Maximisers

The tangency between the IC and the
budget line at Point C where the student
can attain the highest possible utility giveEntertainment
a
budget constraint of €60
10 A Budget
This is the highest possible utility given the Line
income available.

This point is referred to as CONSUMER
EQUILIBRIUM
C
5
Higher IC’s are desirable but not attainable
for the given budget constraint

Lower IC’s do not maximise Utility
B
Food
1 2 3 4 5 6

IF THE PRICE OF FOOD INCREASES T0 €12

M = Pf*Qf + Pe*Qe
€60 = €10*3 + €6*5 at Point C Entertainment
Consumption Ration 3F:5E
M = €60, Pf increases to €12, Pe remains 10
A Budget
constant at €6. Line
M/Pf = 60/12 = 5
The Budget Line pivots from the Y axis inward
as the student can only purchase 5 units of
food after the price increase. C
5
The Student cannot now maximise utility
X
at point C and moves to Point X, ICo
4.5 units of E and 2.75 of Food IC1
(less of both goods) B
€60 = €12*2.75 + €6*4.5 at X
New consumption Ratio 2.75F:4.5E 1 2 3 4 5 6
Food

What if the PRICE OF FOOD INCREASES T0 €15

M = P f Q f + P eQe

M = €60, Pf increases to €15, Pe remains Entertainment
constant at €6. A 10 Budget
M/Pf = 60/15 = 4 units of food Line
The Budget Line pivots from the Y axis inward as
PCC
the student can only purchase 4 units of food after
the price increase. Price
Consumption
The Student cannot now maximize utility at
5 C Curve
point X and moves to Point Y, 3.75 units of E X
and 2.5 of Food (less of both goods)
Y
ICo
€60 = €15*2.5 + €6*3.75 at Y IC1

New Consumption Ratio 2.5 F : 3.75 B2 B1 B
E at point Y 1 2 3 4 5 6
Food

Derive a Demand Curve for Food for Kaitlin from Indifferent Curves

Kaitlin has faced three prices for food.
P = €10, P = €12 and P = €15

To Draw a Demand Curve you need Prices & Quantities
You’ve got both P & Q on your IC’s & Budget Constraint for Kate

Derive Kaitlin’s Demand Curve for Food and her Price
Consumption Curve
You Need only 2 Prices/2 Quantities to Draw a Demand Curve.

Deriving the Demand Curve

Q of Entertainment M = €60, Pf = €10, Pe = €6
PCC IF Pf ↑ €12
If Pf ↑ €12
M/Pe @ €6
If Pf ↑ €15

IC 1
IC 2
IC 2
IC 3

Q of Food
Price M/Pf @ €15 M/Pf @ €12 M/Pf @ €10

P= 15

P= 12

P= 10 Demand Curve for Food
at 3 different prices
Q

Budget Line & Changes in Income

Entertainment
11
Budget Line when M = €60, Pfood = €10 ; PEnt = €6
10
Budget Line when M = €66, Pfood = €10 ; PEnt = €6
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 6.6
Quantity of Food

Income Consumption Curves (ICC) & Engel Curves

Q Good Y Budget Line when M = €60, Pfood = €10 ; P ent = €6
If you get a 10% pay rise M = €66, Pfood = €10 ; P ent = €6

If you get a 20% pay rise M = €72, Pfood = €10 ; P ent = €6

ICC – Income Consumption Curve

Income Q Good X

M = €72 Engel Curve
M = €66 The Relationship between the level of
demand for good and the level of
M = €60
income is known as an Engel curve

Q Good X

Income & Substitution Effects

A change in Price of a good effects a The income effect of a price change
consumers income. is the adjustment of demand to the
change in real income alone. (Budget
If Kate bought only food and food prices Line)
fell, the max. she can buy is the ratio of
Money Income to the Price of Food - The substitution effect of a price
M/Pfood. change is the adjustment of demand
to the relative price change alone.
(IC’s)
If the Pfood increased it led to a decrease
in purchasing power or real income. This is the effect of a change in the
relative price ratio on the demand for
This income effect can lead to an a good.
increase, decrease or no change in the
demand for food A rise in Pricefood changes the price
The extent of the reduction in real ratio, reducing the demand for food,
for the purchasing power available to
income is affected by the proportion of the individual.
income spent on food.


The Income Effect: (p 78) The Substitution Effect: (p78)
There is an effect on a consumer's income This is the effect of a change in the
when there is a change in the price of one or relative price ratio on the demand for a
other of the goods. For example, suppose the good. If a rise in the price of X lowers
the price ratio and this will reduce the
consumer only bought good X and the price demand for X, for a given level of
of it incresed. The maximum amount that he purchasing power available to the
or she could buy is given by the ratio of individual.
money income to the price of good X, M/PX,
which will drop giving an decrease in The substitution effect is referred to as
purchasing power or real income. being ‘negative’ since the change in the
The income effect can lead to an increase, price ratio and the effect on demand for
decrease or no change in the demand for the X move in the opposite directions. (If
good as the extent of the rise in real income the price goes up the quantity demanded
arising from a fall in the price of good X is goes down and vice versa)
clearly affected by the proportion of the
budget spent on good X.


•Suppose a student gets €90per week of an allowance
S/he spends on food and/or entertainment.
The Price of a typical basket of food is €20 and the price of the average
entertainment unit (night out) is €25.
The student’s budget line can be represented as follows:
M = PXQx+ PYQY.
The student can purchase either 4.5 units of food and zero entertainment,
Good Y - Entertainment
or have 3.6 units of entertainment and zero food, but they generally
M/Py
prefer combinations of both goods.
90/25
=3.6
Point A represents a student’s decision to consume 2 baskets of food
and have 2 nights out. [€90 = €20*2+ 25*2] no saving
The students consumption ratio is 2 Food : 2 Entertainment (A)

Y0 = 2 A

IC0

BL0
0

0 X 0= 2 M/PX=90/20 = 4.5 Good X (food)

Inflation increases the price of food

Following Budgetary changes, the price of food
increased to €30 a basket, whereas the price of
entertainment remained the same. So now, the maximum
the student can consume is 3 baskets of food from the
€90 allowance.
Good Y - Entertainment The student can no longer be in equilibrium at point A,
they do not have enough income.
M/Py The students consumption ratio is now
90/25 1.5 units of Food : 1.8 units of Entertainment

A

Y0 = 1.8
B
IC0
0
BL0

0 X1= 1.5 X0= 2 Good X (food)

Price effect of an increase in the price of Food

Price effect = Income + Substitution Effect

The income effect of a price change is the
adjustment of demand to the change in real
income alone, measured along the Budget
Line.
Good Y - Entertainment The substitution effect of a price change is
The students consumption ratio is now 1.5 Food : 1.8 Entertainment the adjustment of demand to the relative
M/Py price change alone, measured along the
90/25 indifference curve. This is the effect of a
change in the relative price ratio on the
demand for a good.
C

A

Y0 = 1.8
B
IC0

0 BL2

BL1 BL0
0 X1= 1.5 X0= 2 Good X (food)
A-B = Price Effect

A-C = Substitution Effect
C- B = Income Effect

Problem: Decompose a Price increase for food into and Income and
Substitution Effect

Draw M construction line parallel to new budget line
a = €60
Entertainment Pf up €15
and at= €10 to original indifference curve IC1
Pf tangent
10
10

The parallel line
9
8
7
6
5
4

A - B = Price Effect on Food
3

holds the Pe = €6
2
1

9
0

consumption ratio
constant A - C = Substitution Effect
8
As it is at tangent B - C = Income Effect
7
to original IC – you
get the same level 6 C
of utility as you A
had before the 5
price increase.
4 B
IC1
3
2 IC2
1
0
B
0 1 2 C 3 A 4 5 6 Food

Income and Substitution Effects
Entertainment
Decompose a – b (price effect) into income & substitution effect
a to b = price
effect on the 10 The parallel line holds the
Draw a construction line parallel to B2 –
quantity new budget line and at tangent to constant
consumption ratio original
9
demanded of indifference curve it is at tangent to original
As IC1
food as a result 8 IC – you get the same level of
of an increase in utility as you had before the
price of food 7
price increase.
6 B
A
5
C IC1
4
3 IC2
2
1

a – c = substitution 0 b a B2 B1
effect 0 1 2 c 3 4 5 6 Food
c – b = income effect

Hicks versus Slutsky
You are a Business Manager Manager – You are a Business Manager Manager –
The Consumer Price Index indicates
The Consumer Price Index (CPI) Price Increases (Inflation) –
indicates Prices Increase (Inflation) –
You want to know how much Money – You want to know how much Money –
Income must you compensate them for
Income must you compensate the
the price increase to keep them on their
workers for the price increase to original Bundle of Goods
keep them on their original level of
Utility
Use Slutsky Compensation Variation in
Use Hicks Compensation Variation Income
in Income

Compensation Variation in Income - Price Increase Good X
Slutsky r
Y/Py vs Hicks The Income decrease is called the
s welfare loss at the new relative prices
How much do have to compensate
money income so that you can
purchase original bundle after price
t increase - Slutsky?
Slutsky How much do have to compensate money
C income so that you can attain original level
of utility after price increase- Hicks?
Hicks A
B
IC0
IC1

Y/Px1 Y/Px

Originally at point A on original IC maximising utility at Point A, P x increases, budget line pivots
inward to Y/Px1 . Consumer moves to Point B consuming less of good x, and relatively more of
good y. Draw new budget line parallel to new BL at tangent to original indifference curve IC 0.

Hicksian Income Effect

The students consumption ratio is now 1.5 Food : 1.8 Entertainment

M/Py
90/25

C

A

Y0 = 1.8
B
IC0
0
BL2

BL1 BL0
0 X1= 1.5 X0= 2 Good X (food)
A-B = Price Effect


Slutsky and Hicksian Income Effect

The students consumption ratio is now 1.5 Food : 1.8 Entertainment

M/Py
90/25

C
Slutsky Income Effect

A

Y0 = 1.8

B
0 IC0
BL3
IC1

BL1 BL0
0 X1= 1.5 X0= 2 Good X (food)
A-B = Price Effect


Sample Question

C2.A typical student maximises their utility function U = U (F,E) subject to an income
constraint (M). M = PF QF + PE QE., where M = money income, F = Food and E =
Entertainment, P = price and Q = Quantity. The student has an income of €60, the
price of food is €10 per basket and the price of entertainment is €6 per unit.

(a)Illustrate the student’s budget line showing consumer equilibrium at 5 units of
entertainment and 3 baskets of food.

(b) If the price of food increases to €12 per basket, illustrate a typical consumer
equilibrium after the price increase. Identify both the income and substitution effect
resulting from the increase in the price of food.

(c)Derive the student’s demand curve for food at both €10 and €12 per basket, while
maximising utility subject to the budget constraint.

(d) You are the manager of a firm. The staff representative has cited the consumer price
index (CPI) to demonstrate that prices have risen in excess of the recent pay
increase in the document Towards 2016. The minimum the staff will accept is
compensation that will allow then to purchase the bundle of goods that maximised
their utility before the price increases. Demonstrate how you would determine the
level of income necessary to compensate your staff for the price increase clearly
differentiating between the Hicksian and Slutsky compensation variation in income.

Recall our Learning Outcomes

You should now be able to:

• Describe and illustrate the assumptions of indifference curve
analysis
• Illustrate and determine utility functions
• Determine utility maximisation subject to budget constraint
• Distinguish between income and substitution effects
• Apply consumer choice theory to changing prices
• Derive Engel Curves and Compensated demand Curves
• Distinguish between Slutsky and Hicks in terms of their
approach to compensation variation in income.

3 consumer choice

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3 consumer choice