# BEHIND THE DEMAND CURVE II & III

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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

(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

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

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

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

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

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)

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

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

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

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

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

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

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)

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

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

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

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

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