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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

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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

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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

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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

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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

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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

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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

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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

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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)

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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)

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

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

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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)

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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

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

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

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

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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

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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)

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

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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

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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

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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

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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

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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

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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

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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

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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

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

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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

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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

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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

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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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