Chapter%204%20Indifference%20analysis

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Chapter 4Indifferenceanalysis
2
Indifference analysis
Indifference curves
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Meaning of utility

• Utility is defined in 2 ways
• Ordinal concept of utility
• Utility of each good is not measurable
• It refers to an arbitrary assignment of numbers
  to rank options for the purpose of prediction
  or explaining human behaviour.

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• 2. Cardinal concept of utility
• Utility of each good is measurable
• It refers to the inner level of satisfaction
  experienced by a person in the consumption
  process.
• In HKAL exam, we will only use ordinal utility
  concept.

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I. Basic Assumption of indifference curve
appearance

1. Each individual chooses many goods
2. For each individual, some goods are scare
3. Economic goods are substitutable
4. The more a good one has, the larger the total
   utility, but the lower its MRS or MUV
5. Not all individuals choose the same goods
6. Individuals are consistent

6
II. Meaning of indifference curve

• In a two-good model, an indifference curve shows
  all combinations of two goods that give the same
  total utility to a particular individual.

7
Constructing an indifference curve
Pears
Point
Oranges
a b c d e f g
30 24 20 14 10 8 6
6 7 8 10 13 15 20
Combinations of pears and oranges that Clive
likes the same amount as 10 pears and 13 oranges
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Constructing an indifference curve
a
Pears
Point
Oranges
a b c d e f g
30 24 20 14 10 8 6
6 7 8 10 13 15 20
Pears
Oranges
9
Constructing an indifference curve
a
Pears
Point
Oranges
b
a b c d e f g
30 24 20 14 10 8 6
6 7 8 10 13 15 20
Pears
Oranges
10
Constructing an indifference curve
a
Pears
Point
Oranges
b
a b c d e f g
30 24 20 14 10 8 6
6 7 8 10 13 15 20
c
Pears
d
e
f
g
Oranges
11

• If many indifference curves are drawn together ,
  it is called an indifference map.

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An indifference map
Units of good Y
I1
Units of good X
13
An indifference map
Units of good Y
I2
I1
Units of good X
14
An indifference map
Units of good Y
I3
I2
I1
Units of good X
15
An indifference map
Units of good Y
I4
I3
I2
I1
Units of good X
16
An indifference map
Units of good Y
I5
I4
I3
I2
I1
Units of good X
17
III. Characteristics of indifference

• Why IC curve is downward sloping?
• Explain To increase Qx, one has to
  decrease Qy,
• Since, both entity are defined as good. To keep
  utility constant along the IC curve, as Qx?? Qy?
• there is a negative relationship between the
  consumption of good X and good Y.

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Meaning of MRSxy slope of IC curve

• It is the maximum amount of another good that a
  person is willing to forgo for an extra unit of a
  good.
• Formula

-2
Increase in Qx by one unit, 2 Qy have to forgone
to make a person satisfied with, and indifferent
to both the initial and final baskets of good.
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Deriving the marginal rate of substitution (MRS)
a
b
26
Units of good Y
6
7
Units of good X
20
Deriving the marginal rate of substitution (MRS)
a
MRS 4
DY 4
b
26
DX 1
Units of good Y
6
7
Units of good X
21
Deriving the marginal rate of substitution (MRS)
a
MRS 4
DY 4
b
26
DX 1
Units of good Y
MRS 1
c
d
DY 1
9
DX 1
6
7
13
14
Units of good X
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QUESTION
Combination Good X Good Y MRSxy
A 1 5
B 2 3
C 3 2
D 5 1
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• IC is convex to the origin
• Question
• MRSxy value is diminishing along the
  indifference curve (convex to the origin). Why?
• Explanation
• this is based on the postulate of diminishing
  marginal rate of substitution. if a person is
  consuming more and more of one good (Qx), he or
  she will be less and less willing to sacrifice
  the other good (Qy) for an extra unit of the
  good.
• Value of MRS is MUV two terms refer to the same
  concept

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• the farther the indifference curve represents
  higher utility level.

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Question

• Which IC curve represents highest utility?

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4. IC curve will never intersect

• Question
• Why?

27

• Assume if IC1 and IC2 now intersect, it will
  violate the assumption of consistency in
  consumption behaviour, why?
• Explanation
• if we now make some point on the indifference
  curves.

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• Consider IC1,
• a and c represents
• the combination
• that gives same
• utility level to a
• consumer.
• Consider IC2
• ?b and d refers to the combination that give the
  same utility to a consumer on a higher level than
  IC1.

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• Now if we consider only point a and b. Which one
  refers to higher utility?
• Answer b, because it is on a higher IC.
• if we consider now only point c and d, which one
  refers to higher utility?
• Answer c
• ? since a and c are on the same IC, if c is
  preferred to d ? also, imply a is preferred to d.

30

• but since b and d are on the same IC, it should
  also imply b is preferred to a.
• ? we cannot say in the same time, b is preferred
  to a, but is also inferior to c.
• ? inconsistent

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Indifference analysis
Budget lines
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4. What is a Budget Line

• Definition
• It shows all combinations of two goods that are
  just obtainable, given an individuals money
  income (nominal income, current income) and the
  prices of the two goods (constant).

BL PxQxPyQy
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• Slope of the BL

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Illustrative example

• given income 360, you are require to buy only
  X and Y.
• if Px 10
• Py 20
• How many X will be bought
• how many y will be bought

35

• Draw the budget line

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• case A) if now I increase to 720, Px and Py
  remain unchanged.
• new amount of X bought
• new amount of Y bought
• draw the new budget line on the same diagram

Hence, the BL2 will shift out parallely, if Px
and Py are constant but with I increases?real
income increase (purchasing power ?) ? both Qx
and Qy consume more
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• Case b) if now I decrease to 180, Px and Py
  remain unchanged,
• new amount of X bought 18
• new amount of y bought 9
• Draw the new budget line on the same diagram.
• hence, the BL will shift inward parallely, if Px
  and Py are constant but with I decreases?
  purchasing power ? ? ?? both Qx and Qy
  consume ?.

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• Case C) now, if I double but Px and Py double,
  that is
• now I 720
• new Px 20
• new Py 40
• Draw the new budget line on the same diagram.
• Thus, the budget line remains unchanged with I,
  Px and Py change in the same proportion.

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• Case d) Assume I and Py remain the same,
• I 360
• Py 20
• new px 5
• new amount of X bought 72
• Draw the new budget line on the diagram

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• Hence, if I and Py remain the same BL will rotate
  outwards if Px falls and inwards if Px rises.
• Case e) Assume I and Px now are constant, new Py
  10
• new amount of Y bought 36
• Draw the new budget line.

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Indifference analysis
The optimal level of consumption
consumption equilibrium Postulate budget
constraint and utility maximization
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• Budget Line
• the preferences of a person, which is
  represented by an indifference map or curve
• The choices available to the person, which is
  represented by a budget line.
• A persons behaviour is limited by the choice or
  resources available to him/her. For a consumer,
  constraint on consumption is termed a budget
  constraint.

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Consumption equilibrium

• Consumption equilibrium is equal to Budget line
  tangent to indifference curve
• ?budget line slope IC curve slope
• ? - Px / Py - MRS

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Finding the optimum consumption
Units of good Y
I5
I4
I3
I2
I1
O
Units of good X
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Finding the optimum consumption
Consumption equilibrium Budget line tangent to
IC curve
Units of good Y
Budget line
I5
I4
I3
I2
I1
O
Units of good X
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Finding the optimum consumption
r
Units of good Y
I5
I4
v
I3
I2
I1
O
Units of good X
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Finding the optimum consumption
r
s
Units of good Y
u
I5
I4
v
I3
I2
I1
O
Units of good X
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Finding the optimum consumption
r
s
Units of good Y
t
u
I5
I4
v
I3
I2
I1
O
Units of good X
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Finding the optimum consumption
r
s
Units of good Y
t
Y1
u
I5
I4
v
I3
I2
I1
O
X1
Units of good X
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5. Consumer equilibrium under indifference curve
theory

• Given a BL and an indifference map
• ? consumer equilibrium will occur at the
  tangency point of the BL and the indifference
  curve

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• Implication
• At consumer equilibrium point E, the consumer
  will buy Qx of X and Qy of Y ? this combination
  of X and Y gives him the highest utility.
• At tangency point E, slope of BL slope of
  indifference curve

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• Question
• in the following diagram which point is the
  consumer equilibrium point ? point C

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• Comparison the slope of BL and slope of
  indifference curve.
• 1.Which one is greater Slope?
• at point A?
• at point B?
• 2.Why does the consumer not choose point D for
  consumption?
• this present budget line cannot reach this point
• He is limited by the present income constraint
  (Budget constraint).

They are indifference
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• Conclusion
• If X is a normal good, Px ? both substitution
  and income effect are positive on Qd.
• Hence, Px ? Qx ? D is a normal one

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Effect on consumption of a change in income
Units of good Y
B1
I1
O
Units of good X
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Effect on consumption of a change in income
Units of good Y
I2
B2
B1
I1
O
Units of good X
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Effect on consumption of a change in income
Units of good Y
I4
I3
I2
B2
B3
B1
B4
I1
O
Units of good X
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Effect on consumption of a change in income
Income-consumption curve
Units of good Y
I4
I3
I2
B2
B3
B1
B4
I1
O
Units of good X
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• Joining all consumer equilibrium point, we can
  get the ICC.

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6. Nature of goods and the shape of the ICC.

• Different shape of ICC curves implies different
  types of the goods.

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6a. Income Consumption Curve (ICC)

• if I , with Px and Py ,
• BL shift out parallely.
• new consumer equilibrium can be attained

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• As I , Qx and Qy
• X is a normal good
• Y is a normal good.

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Effect of a rise in income on the demand for an
inferior good
Units of good Y (normal good)
a
I1
B1
O
Units of good X (inferior good)
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Effect of a rise in income on the demand for an
inferior good
b
Units of good Y (normal good)
I2
a
I1
B1
B2
O
Units of good X (inferior good)
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Effect of a rise in income on the demand for an
inferior good
Income-consumption curve
b
Units of good Y (normal good)
I2
a
I1
B1
B2
O
Units of good X (inferior good)
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• As I , Qx unchanged, Qy
• X is a necessity
• Y is a normal good

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Deriving an Engel curve from an
income-consumption curve
Bread
I3
I2
I1
B3
B2
B1
CDs
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Deriving an Engel curve from an
income-consumption curve
Bread
Income-consumption curve
I3
I2
I1
B3
B2
B1
CDs
69
Deriving an Engel curve from an
income-consumption curve
Bread
Income-consumption curve
I3
I2
I1
B3
B2
B1
CDs
Income ()
CDs
70
Deriving an Engel curve from an
income-consumption curve
Bread
Income-consumption curve
a
Qb1
I3
I2
I1
B3
B2
B1
Qcd1
CDs
Income ()
CDs
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Deriving an Engel curve from an
income-consumption curve
Bread
Income-consumption curve
a
Qb1
I3
I2
I1
B3
B2
B1
Qcd1
CDs
Income ()
Y1
a
Qcd1
CDs
72
Deriving an Engel curve from an
income-consumption curve
Bread
Income-consumption curve
Qb2
b
a
Qb1
I3
I2
I1
B3
B2
B1
Qcd2
Qcd1
CDs
Income ()
Y2
b
Y1
a
Qcd2
Qcd1
CDs
73
Deriving an Engel curve from an
income-consumption curve
Bread
Income-consumption curve
Qb3
c
Qb2
b
a
Qb1
I3
I2
I1
B3
B2
B1
Qcd2
Qcd3
Qcd1
CDs
Y3
c
Income ()
Y2
b
Y1
a
Qcd3
Qcd2
Qcd1
CDs
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Deriving an Engel curve from an
income-consumption curve
Bread
Income-consumption curve
Qb3
c
Qb2
b
a
Qb1
I3
I2
I1
B3
B2
B1
Qcd2
Qcd3
Qcd1
CDs
Engel curve
Y3
c
Income ()
Y2
b
Y1
a
Qcd3
Qcd2
Qcd1
CDs
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Indifference analysis
Effects of a change in price
76
Price Consumption Curve

• Definition
• It shows how consumption of the two goods changes
  as the price of one (e.g. Good X) changes. The
  price of the other good (e.g. Good Y) and the
  consumers money income are assumed to be
  constant.

77
Effect of a fall in the price of good X
Assumptions PX 2 PY 1 Budget 30
Units of good Y
j
I1
B1
Units of good X
78
Effect of a fall in the price of good X
Assumptions PX 1 PY 1 Budget 30
k
Units of good Y
j
I2
I1
B1
B2
Units of good X
79
Effect of a fall in the price of good X
Price-consumption curve
k
Units of good Y
j
I2
I1
B1
B2
Units of good X
80
Deriving a demand curve from a price-consumption
curve
a
Expenditure on all other goods
I1
B1
Units of good X
81
Deriving a demand curve from a price-consumption
curve
Fall in the price of X
a
b
Expenditure on all other goods
I2
I1
B1
B2
Units of good X
82
Deriving a demand curve from a price-consumption
curve
Further falls in the price of X
a
b
Expenditure on all other goods
c
d
I4
I3
I2
I1
B4
B3
B1
B2
Units of good X
83
Deriving a demand curve from a price-consumption
curve
a
Price-consumption curve
b
Expenditure on all other goods
c
d
I4
I3
I2
I1
B4
B3
B1
B2
Units of good X
84
Deriving a demand curve from a price-consumption
curve
a
Price-consumption curve
b
Expenditure on all other goods
c
d
I4
I3
I2
I1
B4
B3
B1
B2
Units of good X
a
P1
Price of good X
Q1
Units of good X
85
Deriving a demand curve from a price-consumption
curve
a
Price-consumption curve
b
Expenditure on all other goods
c
d
I4
I3
I2
I1
B4
B3
B1
B2
Units of good X
a
P1
Price of good X
b
P2
Q1
Q2
Units of good X
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Deriving a demand curve from a price-consumption
curve
a
Price-consumption curve
b
Expenditure on all other goods
c
d
I4
I3
I2
I1
B4
B3
B1
B2
Units of good X
a
P1
Price of good X
b
P2
c
P3
Q1
Q2
Q3
Units of good X
87
Deriving a demand curve from a price-consumption
curve
a
Price-consumption curve
b
Expenditure on all other goods
c
d
I4
I3
I2
I1
B4
B3
B1
B2
Units of good X
a
P1
Price of good X
b
P2
c
P3
d
P4
Q1
Q2
Q3
Q4
Units of good X
88
Deriving a demand curve from a price-consumption
curve
a
Price-consumption curve
b
Expenditure on all other goods
c
d
I4
I3
I2
I1
B4
B3
B1
B2
Units of good X
a
P1
Price of good X
b
P2
c
P3
d
P4
Demand
Q1
Q2
Q3
Q4
Units of good X
89
Indifference analysis

• Income and substitution effects
• of a change in price
• normal good/ superior good
• inferior

90
Effects of a price change

• Price effect of good X has 2 effects on
  consumption
• substitution effect (S.E)
• Income effect (I.E)

Price Effect substitution effect Income Effect
91
Price effect S.E I.E

• Case 1
• X is a normal good / superior good
• Substitution effect
• if Px decrease assume nominal income real
  income is keep constant (utility constant)
• people substitute cheaper good for more expensive
  good (Increase Qx )
• substitution effect is -ve on Qx. (Px??Qx?)
• means P and Qd is negatively related

92

• X is a normal good or superior good
• Income effect (real income)
• if Px decrease assume nominal income is
  constant, holding the relative price of good x is
  constant.?
• ?that will Increase real income of the consumer
• ? Increase Qx superior
• ? income effect is the ve on superior or normal.
  (Px?--real income??Qx?)

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• Conclusion
• If X is a normal good/ superior good,
• Decrease Px ? both substitution and income effect
  are increase on Qx superior.
• Hence, decrease Px ?increase Qx ?
• Price eff Substitution eff Income eff

Px??Qx?
Real Income? ? Qx superior?

?Qx ?
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Original BL1 Final BL3------- is
hypothetical BL2
If Px decrease what will be the effect on
superior or normal?
P.E(a ?c) S.E(a?b) I.E (b?c)
Y Superior
Two IC curve only
a
C
b
IC2
IC1
X Superior
BL3
S.E
I.E
BL2
95
Indifference analysis
Income and substitution effects of a change in
price (b) inferior good (c ) Giffen good is a
kind of inferior good
96

• Case II
• If good X is an inferior good,
• a) Substitution effect
• ?Px decrease assume nominal real income keep
  constant
• ? people will sub cheaper goods than expensive
  goods. (Px??Qx??-ve S.E)
• Income effect
• ? Px decrease? real income increase ?Qx
  inferior decrease
• ?Px ? ?(real income??Qx inferior ??-ve I.E)

97

• Conclusion
• If X is an inferior good
• P.E Substitution eff Income effect
• Px ? ?Qx? Ir??Qx Inferior?
• -ve S.E -ve I.E
• price effect may increase or decrease Qx,
  depends on the relative strengths of S.E or I.E.

98

• Situation 1
• If -ve S.E gt -ve I.E
• Px ? ? Qx ? gt Ir ??Qx inferior?
• Final conclusion Px ? ?Qx ?
• Demand is still a normal case.

99
Original BL1 Final BL3------- is
hypothetical BL2
If Px decrease what will be the effect on
inferior good? P.E(a ?c) S.E(a?b) I.E (b?c)
Y Superior
Two IC curve only
C
a
b
IC2
I.E
IC1
X inferior
BL3
S.E
BL2
100
Indifference analysis
Income and substitution effects of a change in
price (c) Giffen good
101

• Situation 2
• if -ve sub effect lt -ve income effect
• Final conclusion
• decrease Px ? decrease Qx ? Demand will be an
  abnormal curve.
• ? the good is called a Giffen good.

102
Original BL1 Final BL3------- is
hypothetical BL2
If Px decrease what will be the effect on Giffen
good? P.E(a ?c) S.E(a?b) I.E (b?c)
Y Good
Two IC curve only
C
a
b
IC2
I.E
IC1
X Giffen
BL3
S.E
BL2
103
Ans

• Giffen paradox
• In the case of positive price effect, a change
  in relative price leads quantity demanded to
  change in the same direction.

Suppose a is the original consumption equilibrium
with IC1 BL1.
Good Y
Px? BL1 with shift outward to BL2
a
IC1
Good X
BL2
BL1
104
Ans
Holding real income constant means the income
effect is not taken into account.
With ? in Px/Py, consumer is held on his original
IC.
The hypothetical BL3 with shift parallel inwards
to the tangency of original IC.
Good Y
If real Income is constant, only S.E. occurs
which always? Qx when Px?
a
Demand is always downward sloping
b
IC1
Good X
BL2
S.E
BL3
105
C
Holding nominal income constant means we will
take the I.E. into account
a
b
IC2
I.E
IC1
BL3
BL2
S.E
P

• Giffen paradox occurs when
• ve I.E. gt S.E.

D
?Demand will be sloping upward.
Qx
106
Conclusion

• Giffen paradox will only occur when nominal
  income is held constant