# BEHIND THE DEMAND CURVE II & III Indifference Analysis 1. Assumptions 2. Indifference curves & the budget constraint 3. Derivation of the demand curve.

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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

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

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

fig Pears 30 24 20 14 10 8 6 Oranges 6 7 8 10 13 15 20 Point abcdefgabcdefg Combinations of pears and oranges that Clive likes the same amount as 10 pears and 13 oranges Constructing an indifference curve

fig Pears Oranges Pears 30 24 20 14 10 8 6 Oranges 6 7 8 10 13 15 20 Point abcdefgabcdefg Constructing an indifference curve

fig a Pears Oranges Pears 30 24 20 14 10 8 6 Oranges 6 7 8 10 13 15 20 Point abcdefgabcdefg Constructing an indifference curve

fig a b Pears Oranges Pears 30 24 20 14 10 8 6 Oranges 6 7 8 10 13 15 20 Point abcdefgabcdefg Constructing an indifference curve

fig a b c d e f g Pears Oranges Pears 30 24 20 14 10 8 6 Oranges 6 7 8 10 13 15 20 Point abcdefgabcdefg Constructing an indifference curve

fig 6 26 7 Units of good Y Units of good X a b Y = 4 X = 1 MRS = 4 MRS = Y/ X Deriving the marginal rate of substitution (MRS)

fig a b Units of good Y Units of good X 26 67 d Y = 4 X = 1 Y = 1 X = 1 MRS = 1 MRS = 4 13 14 9 c MRS = Y/ X Deriving the marginal rate of substitution (MRS)

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

fig Units of good Y Units of good X I1I1 I2I2 I3I3 I4I4 I5I5 An indifference map

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)

fig Units of good X 0 5 10 15 Units of good Y 30 20 10 0 Assumptions P X = £2 P Y = £1 Budget = £30 A budget line

fig Units of good Y Units of good X a Units of good X 0 5 10 15 Units of good Y 30 20 10 0 Assumptions P X = £2 P Y = £1 Budget = £30 Point on budget line a A budget line

fig Units of good Y Units of good X a b Units of good X 0 5 10 15 Units of good Y 30 20 10 0 Point on budget line a b Assumptions P X = £2 P Y = £1 Budget = £30 A budget line

fig Units of good Y Units of good X a b c Units of good X 0 5 10 15 Units of good Y 30 20 10 0 Point on budget line a b c Assumptions P X = £2 P Y = £1 Budget = £30 A budget line

fig Units of good Y Units of good X a b c d Units of good X 0 5 10 15 Units of good Y 30 20 10 0 Point on budget line a b c d Assumptions P X = £2 P Y = £1 Budget = £30 A budget line

fig Units of good Y Units of good X Assumptions P X = £2 P Y = £1 Budget = £30 Effect of an increase in income on the budget line

fig Units of good Y Units of good X Assumptions P X = £2 P Y = £1 Budget = £40 Budget = £40 Budget = £30 16 7 m n Effect of an increase in income on the budget line

fig Effect on the budget line of a fall in the price of good X Units of good Y Units of good X Assumptions P X = £2 P Y = £1 Budget = £30

fig Effect on the budget line of a fall in the price of good X Units of good Y Units of good X Assumptions P X = £2 P Y = £1 Budget = £30

fig Effect on the budget line of a fall in the price of good X Units of good Y Units of good X Assumptions P X = £1 P Y = £1 Budget = £30

fig Effect on the budget line of a fall in the price of good X Units of good Y Units of good X Assumptions P X = £1 P Y = £1 Budget = £30 B1B1 B2B2 a b c

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

fig Finding the optimum consumption Units of good Y Units of good X O

fig Finding the optimum consumption I1I1 I2I2 I3I3 I4I4 I5I5 Units of good Y Units of good X O

fig I1I1 I2I2 I3I3 I4I4 I5I5 Units of good Y O Units of good X Budget line Finding the optimum consumption

fig I1I1 I2I2 I3I3 I4I4 I5I5 Units of good Y O Units of good X Finding the optimum consumption r v s u Y1Y1 X1X1 t

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)

fig Deriving a demand curve from a price-consumption curve B1B1 I1I1 Expenditure on all other goods Units of good X a

fig I2I2 Deriving a demand curve from a price-consumption curve B1B1 B2B2 I1I1 Expenditure on all other goods Units of good X a b Fall in the price of X

fig I2I2 Deriving a demand curve from a price-consumption curve B1B1 B2B2 I1I1 Expenditure on all other goods Units of good X a b Further falls in the price of X

fig Deriving a demand curve from a price-consumption curve B1B1 B2B2 B3B3 I3I3 I2I2 I1I1 I4I4 B4B4 Expenditure on all other goods Units of good X a b c d Further falls in the price of X

fig Deriving a demand curve from a price-consumption curve B1B1 B2B2 B3B3 I3I3 I2I2 I1I1 I4I4 B4B4 Expenditure on all other goods Units of good X Price - consumption curve a b c d

fig Deriving a demand curve from a price-consumption curve B1B1 B2B2 B3B3 I3I3 I2I2 I1I1 I4I4 B4B4 Expenditure on all other goods Units of good X a Price - consumption curve b c d Price of good X Units of good X P1P1 Q1Q1 a

fig Deriving a demand curve from a price-consumption curve B1B1 B2B2 B3B3 I3I3 I2I2 I1I1 I4I4 B4B4 Expenditure on all other goods Units of good X a Price - consumption curve b c d Price of good X Units of good X a Demand P1P1 P2P2 P3P3 P4P4 Q1Q1 Q2Q2 Q3Q3 Q4Q4 b c d

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 consumers income is increased so that real income is unchanged? Compensating variation Utility is left unchanged See Figure 6

Units of good Y I1I1 I2I2 I3I3 I4I4 I5I5 I6I6 B1B1 f QX1QX1 Income and substitution effects: normal good Units of Good X

Units of good Y I1I1 I2I2 I3I3 I4I4 I5I5 I6I6 B2B2 h B1B1 QX1QX1 f Rise in the price of good X Income and substitution effects: normal good Units of Good X QX3QX3

Units of good Y B2B2 Substitution effect B1B1 QX1QX1 h f I1I1 I2I2 I3I3 I4I4 I5I5 I6I6 QX2QX2 B 1a Substitution effect of the price rise g Income and substitution effects: normal good Units of Good X QX3QX3

Units of good Y I1I1 I2I2 I3I3 I4I4 I5I5 I6I6 Substitution effect Income effect QX1QX1 h f g B2B2 B1B1 QX2QX2 QX3QX3 B 1a Income effect of the price rise Income and substitution effects: normal good

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

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