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. (i) Consumers rank preferences (ii) Preferences are transitive
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. Slope = Marginal Rate of Substitution (MRS)
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
3/28/2017
Constructing an indifference curve a
Pears
Oranges
Point 30 24 20 14 10 8 6 6 7 8 10 13 15 20 a b c d e f g
Pears
fig
Oranges

5. Convex - diminishing marginal rate of substitution
Indifference curves
Convex - diminishing marginal rate of substitution
Indifference map
…preferences

6. An indifference map Units of good Y I5 I4 I3 I2 I1 Units of good X
3/28/2017 I2 I3 I1
An indifference map
Units of good Y
fig
Units of good X

7. Actual choice is based on income & prices Definition
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)

8. A budget line a Units of good Y Units of good X Units of good X 5 10
3/28/2017
A budget line a
Units of
good X 5 10 15
Point on
budget line a
Units of
good Y 30 20 10
Units of good Y
Assumptions
PX = £2
PY = £1
Budget = £30
fig
Units of good X

9. Effect of an increase in income on the budget line
3/28/2017
Effect of an increase in income on the budget line
Units of good Y
Assumptions
PX = £2
PY = £1
Budget = £30
fig
Units of good X

10. Effect on the budget line of a fall in the price of good X
3/28/2017
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
fig
Units of good X

11. Effect on the budget line of a fall in the price of good X
3/28/2017
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
fig
Units of good X

12. Optimal consumption
Where is utility maximised?
Point of tangency
MRSyx = Py\Px

13. Finding the optimum consumption
3/28/2017
Finding the optimum consumption
Units of good Y
Budget line I5 I4 I3 I2 I1 O
fig
Units of good X

14. 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)

15. Deriving a demand curve from a price-consumption curve
3/28/2017
Deriving a demand curve from a price-consumption curve a b
Price-consumption
curve
Expenditure on
all other goods c d Q3 Q4 I4 I3 I2 I1 B1 B2 B3 B4
Units of good X
Demand a P1
Price of good X P2 b P3 c P4 d
fig Q1 Q2
Units of good X

16. 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

17. A conceptual experiment
`What happens to demand if, after the price of a good rises, the consumer’s income is increased so that real income is unchanged?’
Compensating variation
Utility is left unchanged
See Figure 6

18. Income and substitution effects: normal good
3/28/2017 B1
Units of good Y f I1 I2 I3 I4 I5 I6
QX1
Units of Good X

19. General rules Normal goods Inferior goods
income & substitution effects move in the same direction
Inferior goods
income & substitution effects move in opposite directions