Introductory Microeconomics EC10006

1
Introductory Microeconomics (EC10006)

• Topic 2 The Theory of Consumer Choice

2
I. Introduction

• We have seen how demand curves may be used to
  represent consumer behaviour.
• But we said very little about the nature of the
  demand curve why it slopes down for example.
• Now we go behind the demand curve
• i.e. we investigate how buyers reconcile what
  they want with what they can get

3
I. Introduction

• N.B. We can use this theory in many ways - not
  simply as household consumer buying goods.
• For example
• Modelling decision of worker as regards his
  supply of labour (i.e. demand for leisure)
• Allocation of income across time (saving and
  investment)

4
II. Theory of Consumer Choice

• Four elements
• (i) Consumers income
• (ii) Prices of goods
• (iii) Consumers tastes
• (iv) Rational Maximisation

5
III. The Budget Constraint

• The first two elements define the budget
  constraint
• The feasibility of the consumers desired
  consumption bundle depends upon two factors
• (i) Income
• (ii) Prices
• Note We assume, for the time being, that both
  are exogenous (i.e. beyond consumer's control)

6
III. The Budget Constraint

• Example (N.B two goods)
• Two goods - films and meals
• Student grant 50 per week (p.w.)
• Price of meal 5
• Price of film 10

7
III. The Budget Constraint

• Thus student can consume maximum p.w. of 10
  meals or 5 films by devoting all of his grant to
  the consumption of only one of these goods.
• Alternatively, he can consume some combination of
  the two goods
• For example, giving up one film a week (saving
  10) enables student to buy two additional meals
  (costing 5 each)
• .

8
III. The Budget Constraint
9
Figure 1 Budget Constraint
Films
5

A
4


B
1

Meals
0

2 8
10
10
III. The Budget Constraint

• The budget constraint defines the maximum
  affordable quantity of one good available to the
  consumer given the quantity of the other good
  that is being consumed.
• N.B. Trade-off!
• Trade-off is represented slope of budget
  constraint.

11
III. The Budget Constraint

• Intercepts
• Determined by income divided by the appropriate
  price of the good
• Define maximum quantity of a particular good
  available to an individual
• Slope
• Independent of income
• Determined only by relative prices
• .

12
III. The Budget Constraint

• If consumer is devoting all income to films (qf
  50/10 5), then 1 meal can only be obtained by
  sacrificing consumption of some films.
• How many films must consumer give up?
• pm 5 thus to obtain that 5, the consumer
  must give up 1/2 a film

13
III. The Budget Constraint

• The slope of the budget constraint in this
  example is thus

14
Figure 2 Slope of Budget Constraint
Films
?qm 1
5
?qf - 0.5


4.5



Meals
0

1
10
15
III. The Budget Constraint

• More generally
• Two goods (x,y), prices (px, py) and money income
  (m)
• m pxx pyy
• Slope of budget constraint - px/py

16
III. The Budget Constraint

• Proof

17
III. The Budget Constraint

• Thus
• Such that

18
Figure 3 Budget Constraint y m/py - (px/py)x
y
m/py
?x
A

?y -(px/py) ?x
B


x
0


m/px
19
III. The Budget Constraint

• Intuition
• If additional units of x costs px
• Then their purchase requires a change in
  consumption of y of (px/py) (i.e. a sacrifice of
  y) in order to maintain the budget constraint.

20
IV. Preferences

• Consider now the consumer preferences
• Given what consumer can do, what would he like to
  do?
• Four assumptions
• (i) Completeness
• (ii) Consistency
• (iii) Non-satiation
• (iv) Diminishing Marginal Rate of Substitution

21
IV. Preferences

• Completeness
• Consumers can rank alternative bundles according
  to the satisfaction or utility they provide
• Thus given two bundles a and b, then a gt b, a lt
  b or a b
• Preferences assumed only to be ordinal, not
  cardinal i.e. consumer simply has to be able to
  say he prefers a to b, not to say by how much.

22
IV. Preferences

• Consistency
• Preferences are also assumed to be consistent
• Thus if a gt b and b gt c, then we would infer
  that
• a gt c
• We assume consumer is logically consistent

23
IV. Preferences

• Non-satiation
• Consumers assumed to always prefer more goods
  to less.
• We can accommodate economics bads (e.g.
  pollution) in this assumption by interpreting
  then as negative goods
• We can illustrate the first three assumptions
  graphically as follows

24
Figure 4a Preferences
y

a




b

c



x
0

25
Figure 4b Preferences
y
d

a


e
g

b
c



f
x
0

26
Figure 4c Preferences
y
d

h
a

e
g

b
c

i


f
x
0

27
Figure 4d Preferences
y
d

h
a

e
g

b
c

i


Indifference Curve
f
x
0

28
IV. Preferences

• Marginal Rate of Substitution (MRS)
• The quantity of y (i.e. the vertical good) the
  consumer must sacrifice to increase the quantity
  of x (i.e. the horizontal good) by one unit
  without changing total utility.
• We generally assume (smooth) diminishing MRS
• To hold utility constant, diminishing quantities
  of one good must be sacrificed to obtain
  successive equal increases in the quantity of the
  other good.

29
IV. Preferences

• Diminishing MRS derives from underlying
  assumption of diminishing marginal utility
• Marginal utility of a good is defined as the
  change in a consumers total utility from
  consuming the good divided by the change in his
  consumption of the good
• Diminishing MRS assumes that the increase in
  utility from consuming additional units of a good
  is declining

30
IV. Preferences

• Non-satiation implies downward sloping
  indifference curves increases in one good
  require sacrifices in the other good to hold
  total utility constant.
• However, we can go further diminishing MRS
  implies that indifference curves are convex to
  origin, becoming flatter as we move to the right.
• Indeed, the MRS of x for y is simply the slope of
  the indifference curve

31
Figure 5 Indifference Curves
y



I0
x
0
32
Figure 5 Indifference Curves
y
A

B


I0
x
0
33
Figure 5 Indifference Curves
y
A
A

B

I0
B
x
0
34
Figure 5 Indifference Curves
y
?x 1
A
?y
A
?x 1

B
?y

I0
B
x
0
35
IV. Preferences

• Diminishing MRS implies consumers prefer
  consumption bundles containing mixtures of goods
  rather than extremes
• i.e. Bundle C (5, 5) preferred to both Bundle A
  (2, 8) and Bundle B (8, 2)
• Diminishing MRS (i.e. diminishing marginal
  utility)

36
Figure 6 Indifference Curves
y
A


B

I0
x
0
37
Figure 6 Indifference Curves
y
A
8


B

2
I0
x
0
2 8
38
Figure 6 Indifference Curves
y
A
8
C
5


I1
B

2
I0
x
0
2 5 8
39
IV. Preferences

• Note
• (i) Any point on the indifference map must lay
  on an indifference curve.
• (ii) indifference curves cannot cross
• Thus every point on the indifference map must lay
  on one and only one indifference curve.

40
Figure 7 Indifference Curves
y
I2

I1

I0
x
0
41
Figure 8 Indifference Curves Cannot Cross
y
a ? b and a ? c ? b ? c But b gt c
a
b
I1
c

I0

x
0
42
V. Utility Maximisation

• Budget line shows the consumers affordable
  bundles given the market environment.
• The indifference map shows the consumers desired
  bundles
• To complete the model we assume rational
  maximisation - i.e. the consumer chooses the
  affordable bundle that maximises his utility.

43
V. Utility Maximisation

• This is a non-trivial point. We are implicitly
  assuming that the consumer only derives utility
  from the consumption of x and y.
• Moreover, rational maximisation implies consumer
  processes huge amount of information before
  choosing his most preferred bundle
• In reality, perhaps we satisfice

44
V. Utility Maximisation

• The optimal choice bundle will be that point at
  which an indifference curve just touches the
  budget line
• That is, where an indifference curve is tangent
  to the budget line
• In words, where the consumers marginal rate of
  substitution (MRS) and economic rate of
  substitution (ERS) are in accord

45
V. Utility Maximisation

• Marginal Rate of Substitution (MRS)
• Amount of y consumer willing to sacrifice for
  one extra unit of x
• Slope of indifference curve
• Economic Rate of Substitution (ERS)
• Amount of y the consumer is obliged to sacrifice
  for one extra unit of x
• Slope of budget line

46
Figure 9 Equilibrium (MRS ERS)
y
E1
y1
I2

I1

I0
x
0
x1
47
Figure 10 Disequlibrium (MRS ? ERS)
y
?x
E0
?yERS
?yMRS



I0
x
0
48
V. Utility Maximisation

• Since preferences are unique, individuals will
  not choose identical bundles, even when
  confronted by same market environment
• But they will all move to point where MRS ERS
• Even with different preferences, since ERS is the
  same for everyone (i.e. we all face same relative
  prices), it must be the case that in equilibrium
• MRS1 ERS MRS2

49
VI. Comparative Statics

• We now consider how the consumer responds to
  changes in his market environment
• That is, to changes in
• (i) Endowment income
• (ii) Prices.
• N.B, Comparative Statics / Dynamics

50
VI. Comparative Statics

• Changes in Income
• An increase in endowment income causes a parallel
  shift out of the budget constraint
• A decrease in endowment income causes a parallel
  shift in of the budget constraint

51
Figure 11 Increase in Income m? gt m
y




x
0



52
Figure 12 Increase in Income m? gt m
y
A

I1
x Normal y Normal
B

E1
C
E0


D
I0
x
0

53
Figure 12 Increase in Income m? gt m
y
x Inferior y Normal
A

E1
I1
B

C
E0


D
I0
x
0

54
Figure 12 Increase in Income m? gt m
y
A

B

I1
C
E0
x Normal y Inferior
E1


D
x
0

55
Figure 12 Increase in Income m? gt m
y
x Inferior y Normal
A

B

x Normal y Normal
C
E0

x Normal y Inferior

D
I0
x
0

56
VI. Comparative Statics

• Changes in Prices
• An increase in price causes a pivot inwards of
  the budget constraint
• An decrease price causes a pivot outwards of the
  budget constraint.

57
Figure 13 Fall in Price
y




x
0



58
VII. Income Substitution Effects

• Price changes affects the optimal choice bundle
  in two distinct ways
• First, there is a change in relative prices as
  represented by a change in the slope of the
  budget constraint.
• Second, there is a change in purchasing power
  (i.e. real income). The same level of money
  income is now worth more to the consumer in terms
  of its ability to purchase both goods.

59
Figure 13 Fall in Price
y




x
0



60
Figure 14 Effects of Fall in Price
y
Fall in price of good x reduces slope of budget
constraint (ERS) - i.e. fall in the relative
price of good x

Fall in price of good x increases consumers
real income - i.e. expansion of the budget set



x
0



61
Figure 15 Effects of a Fall in Price
y


E1
E0


x
0



62
Figure 15 Effects of a Fall in Price
y


E0


E1
x
0



63
Figure 15 Effects of a Fall in Price
y

E1

E0


x
0



64
Figure 15 Effects of a Fall in Price
y
A
Good x is Giffen


B
Good x is Non-Giffen
E0


C
x
0



65
VII. Income and Substitution Effects

• We decompose total effect of price change into
• (i) Income Effect
• (ii) Substitution Effect
• The income effect is the adjustment of demand to
  the change in real income.
• The substitution effect is the adjustment of
  demand to the change in relative prices.

66
Figure 14 Income and Substitution Effects (Fall
in px)
y
A


E0


I0
x
0
A

67
Figure 14 Income and Substitution Effects (Fall
in px)
y
A


E0
E1

I1
I0
x
0
A
B

68
VII. Income and Substitution Effects

• We decompose the overall change in demand into
  income and substitution effects by
  (hypothetically) adjusting the consumers income
  to restore him to the level of real income he
  enjoyed before the price change
• Given the fall in px and the subsequent increase
  in real income, we therefore reduce the
  consumers real income mechanically, we drag the
  new budget line back until it is just tangent to
  the original indifference curve.

69
Figure 14 Income and Substitution Effects (Fall
in px)
y
A


E0
E1

I1
I0
x
0
A
B

70
Figure 14 Income and Substitution Effects (Fall
in px)
y
A


C
E0
E1
E2

I1
I0
x
0
A C B

71
Figure 14 Income and Substitution Effects (Fall
in px)
y
A


C
E0
E1
E2

I1
I0
x
0
A C B

72
Figure 14 Income and Substitution Effects (Fall
in px)
y
E0-E1 Total Effect (x0-x1) E0-E2 Substitution
Effect (x0-x2) E2-E1 Income Effect (x2-x1)
A


E0
E1
E2

I1
I0
x
0
A
B
x0 x2 x1

73
VIII. Inferior and Giffen Goods

• In a two good model, a price change always
  induces a substitution effect in the opposite
  direction of the change in price
• i.e a rise (fall) in px induces a substitution
  away (towards) good x ceteris paribus
• We usually say that the own price substitution
  effect is always negative.

74
VIII. Inferior and Giffen Goods

• The income effect, however, can be positive (i.e.
  normal good) or negative (i.e. inferior good)
• A rise in the price of a normal good induces a
  negative substitution effect and a negative
  income effect, both of which act to reduce the
  demand for good x
• A rise in the price of an inferior good, however,
  induces a negative substitution effect but a
  positive income effect, thus the overall effect
  is ambiguous

75
VIII. Inferior and Giffen Goods

• If, when the price of an inferior good rises, the
  positive income effect dominates the negative
  substitution effect, we have the case of a Giffen
  Good
• That is, a good for which demand rises (falls)
  when price rises (falls)
• Giffen goods are very inferior good

76
Figure 15 Income and Substitution Effects Good
x Normal / Non-Giffen
y
A
I0
C
E1
E0
I1
E2
x
0
A C
B
77
Figure 15 Income and Substitution Effects Good
x Inferior / Non-Giffen
y
I1
A
I0
E1
C
E0
E2
x
0
A C
B
78
Figure 15 Income and Substitution Effects Good
x Inferior / Giffen
y
I1
A
E1
C
E0
E2
I0
x
0
A C
B
79
VIV. Measuring Real Income

• When we decomposed the change in demand resulting
  from a change in price into an income and
  substitution effect, we did so by varying money
  income
• Specifically, when the price of good x fell, we
  varied the consumers money income to hold his
  real income constant, where real income was
  defined as the consumers ability to enjoy a
  particular level of utility

80
VIV. Measuring Real Income

• Varying money income is this way is known as a
  Hicks Compensating Variation in money income
  (HCV)
• HCV allows consumer to enjoy original level of
  utility at the new relative price ratio
• We compensate the consumer for the change in
  price
• Sounds odd in respect of a price fall.

81
Figure 16.1 Hicks Compensating
Variation (Price Fall)
y



A
C
B

I1
I0
x
0

82
Figure 16.2 Hicks Compensating
Variation (Price Rise)
y


B
C
A

I1
I0
x
0

83
VIV. Measuring Real Income

• An alternative definition of real income is the
  ability to consumer not a particular level of
  utility, but a particular bundle of goods
• i.e. we vary the consumers money income
  following a change in price to permit him to
  consumer his original bundle of goods at the new
  relative price ratio
• The is know as the Slutsky Compensating
  Variation (SCV) in money income.

84
Figure 16.3 Slutsky Compensating
Variation (Price Fall)
y


A
C
I0
B

I2
I1
x
0

85
Figure 16.4 Slutsky Compensating
Variation (Price Rise)
y
B


C
I2
A

I1
I0
x
0

86
VIV. Measuring Real Income

• Both Hicks and Slutsky compensating variations
  adjust the consumers new level of income (i.e.
  the level following the price change) such that
  he is able to enjoy either his original level of
  utility (Hicks) or his original consumption
  bundle (Slutsky)
• An alternative approach is to adjust the
  consumers original level of income in such a way
  that he is able to enjoy the level of utility
  (Hicks) or the consumption bundle (Slutsky) that
  he would have been able to enjoy were he to face
  the change in prices

87
VIV. Measuring Real Income

• That is, we vary the consumers money income at
  the original relative price ratio to enable him
  to enjoy the level of real income (i.e. utility
  or consumption bundle) that he would have been
  able to enjoy from the price change
• i.e. we provide the consumer with an Equivalent
  Variation in money income
• A variation in money income that will adjust the
  consumers real income in a manner analogous to
  the price change

88
Figure 16.5 Hicks Equivalent Variation (Price
Fall)
y
B


A
C

I1
I0
x
0

89
Figure 16.6 Hicks Equivalent Variation (Price
Rise)
y


C
A
B

I1
I0
x
0

90
Figure 16.7 Slutsky Equivalent
Variation (Price Fall)
y
B


A
I2
C

I1
I0
x
0

91
Figure 16.8 Slutsky Equivalent
Variation (Price Rise)
y


C
A
I0
B

I2
I1
x
0

92
VIV. Measuring Real Income

• To summarise, we have eight cases
• Hicks / Slutsky
• Compensating Variation / Equivalent Variation
• Price Rise / Price Fall

93
Figure 16.1 Hicks Compensating
Variation (Price Fall)
y



A
C
B

I1
I0
x
0

94
Figure 16.2 Hicks Compensating
Variation (Price Rise)
y


B
C
A

I1
I0
x
0

95
Figure 16.3 Slutsky Compensating
Variation (Price Fall)
y


A
C
I0
B

I2
I1
x
0

96
Figure 16.4 Slutsky Compensating
Variation (Price Rise)
y
B


C
I2
A

I1
I0
x
0

97
Figure 16.5 Hicks Equivalent Variation (Price
Fall)
y
B


A
C

I1
I0
x
0

98
Figure 16.6 Hicks Equivalent Variation (Price
Rise)
y


C
A
B

I1
I0
x
0

99
Figure 16.7 Slutsky Equivalent
Variation (Price Fall)
y
B


A
I2
C

I1
I0
x
0

100
Figure 16.8 Slutsky Equivalent
Variation (Price Rise)
y


C
A
I0
B

I2
I1
x
0

101
X. Applications

• Two key areas
• (i) Labour Supply
• (ii) Intertemporal Choice.

102
X.1 Labour Supply

• Consider individuals role as a supplier of
  factor services
• Individuals sell their labour to firms in return
  for a wage.
• Individual makes a choice between income and
  leisure given the dual constraints of time and
  the wage

103
Figure 17 Budget Constraint
Y
Ymax
w

Y0
L
0
T
104
Figure 18 Preferences
Y
I2

I1

I0
L
0
105
Figure 21 Labour Market Equilibrium
Y
Ymax
Y1 Y0 w(T L1) Ymax Y0 wT
E0
Y1
I1
w
A
Y0
L
0
L1
T
106
Figure 22 Increase in Unearned Income
Y
E2
Y2
I2
E1
Y1
B
I1
A
Y0
L
0
L1 L2
T
107


Figure 23 Increase in Wage Rate
Y
E2
I2
E1
I1

L
0
T
L2 L1
108


Figure 23 Increase in Wage Rate
Y
E2
E3
I2
E1
I1

L
0
T
L3 L2 L1
109
X.1 Labour Supply

• Note that the income and substitution effects
  work against one another
• Because leisure is a normal good, the income
  effect from the increase in wage increases the
  demand for leisure
• But the wage rate is the opportunity cost, or
  price, of leisure. Thus, an increase in the wage
  rate / price of leisure induces a substitution
  away from leisure

110

Figure 23 Increase in Wage Rate

Y
E1-E2 Total Effect (L1-L2) E1-E3 Substitution
Effect (L1-L3) E3-E2 Income Effect (L3-L2)
E2
E3
I2
E1
I1

L
0
T
L3 L2 L1
111
Figure 24 Labour Supply Curve
w
Ls
E2

w2
E1
w1

(T-L)
0

(T-L1) (T-L2) T
112
X.1 Labour Supply

• If the income effect dominates the substitution
  effect, then we have a situation in which an
  increase in the wage (i.e. the price of leisure)
  leads to an increase in the demand for leisure
• That is
• Leisure is Giffen
• but Normal!

113
Figure 25 Increase in Wage Rate
Y
E1-E2 Total Effect (L1-L2) E1-E3 Substitution
Effect (L1-L3) E3-E2 Income Effect (L3-L2)
I2
I1
E3
E2
E1

L
0
L3 L1
L2 T
114
Figure 26 Labour Supply Curve
w
Ls
E2

w2
E1
w1

(T-L)
0

(T-L2) (T-L1) T
115
X.1 Labour Supply

• Empirically, we tend to see labour supply curves
  bending backwards at high wage rates
• i.e.

116
Figure 27 Labour Supply Curve
w
Ls

H (T-L)
0


117
X.1 Labour Supply

• Rather than at low wage rates
• i.e.

118
Figure 28 Labour Supply Curve
w
Ls

H (T-L)
0


119
X.1 Labour Supply

• Moreover, backward bending labour supply curves
  are usually observed for males but nor females
• i.e.

120
Figure 29 Labour Supply Curve
w


H (T-L)
0


121
X.1 Labour Supply

• Implications of backward bending labour supply
  curve
• Multiple equilibria
• Unstable equilibria
• What happens to w if it is perturbed slightly
  above / below its equilibirum level, w? Do
  forces of excess demand / excess supply force w
  back to w

122
Figure 29 Labour Supply Curve
w
Ld
Ls
Unstable Equilibrium
E1
Stable Equilibrium
E2

H (T-L)
0


123
X.2 Intertemporal Choice

• Assume individual lives for two periods with a
  lifetime income endowment of y (y1, y2)
• Consumption over time is c (c1, c2)
• Now, x saved today (i.e. period 1) will yield
  (1r)x tomorrow (i.e. period 2)
• The future value of x today is thus (1r)x

124
X.2 Intertemporal Choice

• Conversely, the present value of x received
  tomorrow (i.e. period 2) is
• Intuitively, if we receive x tomorrow, can
  borrow z today, where

125
X.2 Intertemporal Choice

• Thus, given an income endowment of
• Then the maximum period 1 income is
• And the maximum period 2 income is

126
Figure 30 Intertemporal Budget Constraint
y2




y1
0

127
X.2 Intertemporal Choice

• Assume individual consumes in both periods
• If the value of consumption in period 1 is ,
  then can save in period 1 for period
  2 consumption in excess of period 2 income,

128
Figure 30 Intertemporal Budget Constraint
c2, y2




c1, y1
0

129
Figure 30 Intertemporal Budget Constraint
c2, y2




c1, y1
0

130
Figure 30 Intertemporal Budget Constraint
c2, y2




c1, y1
0

131
X.2 Intertemporal Choice

• Note the effects of changes in income endowment
  or interest rate
• Change in income endowment shifts the
  inter-temporal budget constraint parallel
• Changes in interest rate pivot the budget
  constraint around the initial income endowment

132
Figure 30 Intertemporal Budget Constraint
c2, y2




y1
0

133
Figure 30 Intertemporal Budget Constraint
c2, y2




y1
0

134
Figure 30 Intertemporal Budget Constraint
c2, y2




c1, y1
0

135
Figure 30 Intertemporal Budget
Constraint Increase in Rate of Interest
c2, y2




c1, y1
0

136
X.2 Intertemporal Choice

• Consider a borrower
• That is
• (c1 - y1) gt 0
• How does he react to changes in interest rate?

137
Figure 30 Intertemporal Budget Constraint Period
1 Borrowing
c2, y2




c1, y1
0

138
Figure 30 Intertemporal Budget
Constraint Borrower (Fall in Interest Rate)
c2, y2




c1, y1
0

139
X.2 Intertemporal Choice

• Thus, if interest rate falls
• (i) Borrower remains a borrower
• (ii) Is better-off
• (iii) Increases borrowing is c1 a normal good

140

• Figure 30 Intertemporal Budget Constraint
• Borrower (Fall in Interest Rate)
• Substitution Effect E0-E2
• Income Effect E2-E1

c2, y2




c1, y1
0

141
X.2 Intertemporal Choice

• If interest rate rises
• (i) Borrower is definitely worse off

142
Figure 30 Intertemporal Budget
Constraint Borrower Increase in Interest Rate
c2, y2




c1, y1
0

143
X.2 Intertemporal Choice

• Conversely, for savers (c1 - y1) lt0
• Rise in interest rates (i) Remain savers (ii)
  Better off (iii) Increase saving if c2 is a
  normal good
• Fall in interest rate (i) Definitely worse off