BEHIND THE DEMAND CURVE II

1
BEHIND THE DEMAND CURVE II III

• Indifference Analysis
• 1. Assumptions
• 2. Indifference curves the budget constraint
• 3. Derivation of the demand curve
• 4. Income substitution effects

2
Assumptions

• (i) Consumers rank preferences
• (ii) Preferences are transitive
• A to B, B to C then A to C
• (iii) Non-satiation
• Ordinal approach - ranking
• Assumptions ? Indifference curve

3
Indifference curve

• Definition
• joins together all the different combinations of
  two goods which yield the same utility...
• Construction
• Slope Marginal Rate of Substitution (MRS)
• MRS?Y\ ?X or MUy \ MUx
• Give up Y for X - same utility

4
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
5
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
Pears
Oranges
6
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
7
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
8
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
9
Deriving the marginal rate of substitution (MRS)
MRS 4
DY 4
MRS ?Y/?X
Units of good Y
Units of good X
10
Deriving the marginal rate of substitution (MRS)
a
MRS 4
DY 4
b
26
MRS ?Y/?X
DX 1
Units of good Y
MRS 1
d
DY 1
6
7
Units of good X
11
Indifference curves

• Convex - diminishing marginal rate of
  substitution
• Indifference map
• preferences

12
An indifference map
Units of good Y
Units of good X
13
Budget constraint

• Actual choice is based on income prices
• Budget constraint
• Definition
• Shows all combinations of the two goods the
  consumer is able to buy, given prices and income
• Exhaust income
• Prices and income fixed
• What if a price changes? (figure 3)
• What if income changes? (figure 4)

14
A budget line
Units of good X 0 5 10 15
Units of good Y 30 20 10 0
Assumptions PX 2 PY 1 Budget 30
15
A budget line
a
Units of good X 0 5 10 15
Units of good Y 30 20 10 0
Units of good Y
Assumptions PX 2 PY 1 Budget 30
Units of good X
16
A budget line
a
Point on budget line a b
Units of good X 0 5 10 15
Units of good Y 30 20 10 0
b
Units of good Y
Assumptions PX 2 PY 1 Budget 30
Units of good X
17
A budget line
a
Point on budget line a b c
Units of good X 0 5 10 15
Units of good Y 30 20 10 0
b
Units of good Y
c
Assumptions PX 2 PY 1 Budget 30
Units of good X
18
A budget line
a
Point on budget line a b c d
Units of good X 0 5 10 15
Units of good Y 30 20 10 0
b
Units of good Y
c
Assumptions PX 2 PY 1 Budget 30
d
Units of good X
19
Effect of an increase in income on the budget line
Units of good Y
Units of good X
20
Effect of an increase in income on the budget line
Units of good Y
Budget 40
Budget 30
Units of good X
21
Effect on the budget line of a fall in the price
of good X
Assumptions PX 2 PY 1 Budget 30
Units of good Y
Units of good X
22
Effect on the budget line of a fall in the price
of good X
Assumptions PX 2 PY 1 Budget 30
Units of good Y
Units of good X
23
Effect on the budget line of a fall in the price
of good X
Assumptions PX 1 PY 1 Budget 30
Units of good Y
Units of good X
24
Effect on the budget line of a fall in the price
of good X
a
Assumptions PX 1 PY 1 Budget 30
Units of good Y
B2
B1
c
b
Units of good X
25
Optimal consumption

• Where is utility maximised?
• Point of tangency
• MRSyx Py\Px

26
Finding the optimum consumption
Units of good Y
O
Units of good X
27
Finding the optimum consumption
Units of good Y
I5
I4
I3
I2
I1
O
Units of good X
28
Finding the optimum consumption
Units of good Y
I5
I4
I3
I2
I1
O
Units of good X
29
Finding the optimum consumption
Units of good Y
I5
I4
I3
I2
I1
O
Units of good X
30
Derivation of the demand schedule

• Step 1 Price falls - B pivots right
• Step 2 Optimal point of consumption changes
• join optima price consumption curve
• Step 3 Map optima into price-quantity space
• Step 4 Demand curve (figure 5)

31
Deriving a demand curve from a price-consumption
curve
Expenditure on all other goods
B1
Units of good X
32
Deriving a demand curve from a price-consumption
curve
Fall in the price of X
a
Expenditure on all other goods
I1
B1
Units of good X
33
Deriving a demand curve from a price-consumption
curve
a
Expenditure on all other goods
I1
B1
Units of good X
34
Deriving a demand curve from a price-consumption
curve
a
b
Expenditure on all other goods
c
d
I4
I3
I2
I1
B4
B3
B1
B2
Units of good X
35
Deriving a demand curve from a price-consumption
curve
a
b
Expenditure on all other goods
c
d
I4
I3
I2
I1
B4
B3
B1
B2
Units of good X
36
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
Price of good X
Q1
Units of good X
37
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
Q2
Units of good X
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Income substitution effects

• A price change
• (i) Income effect
• i.e. the change in demand due to a change in
  real income..
• (ii) Substitution effect
• i.e. the change in demand due to a change in
  relative prices
• Identifying the two effects

39
A conceptual experiment

• What happens to demand if, after the price of a
  good rises, the consumers income is increased so
  that real income is unchanged?
• Compensating variation
• Utility is left unchanged
• See Figure 6

40
Income and substitution effects normal good
Units of good Y
I1
I2
I3
I4
I5
I6
QX1
Units of Good X
41
Income and substitution effects normal good
Rise in the price of good X
Units of good Y
f
I1
I2
I3
I4
I5
B1
I6
QX3
QX1
Units of Good X
42
Income and substitution effects normal good
h
Units of good Y
f
I1
I2
I3
I4
I5
B2
B1
I6
QX3
QX1
QX2
Units of Good X
43
Income and substitution effects normal good
g
h
Units of good Y
f
I1
I2
I3
I4
I5
B2
B1a
B1
I6
QX3
QX1
QX2
Units of Good X
Substitution effect
44
General rules

• Normal goods
• income substitution effects move in the same
  direction
• Inferior goods
• income substitution effects move in opposite
  directions