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Course: Microeconomics Text: Varian’s Intermediate Microeconomics

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In Chapter 6, we talk about how demand changes when price and income change individually. In this chapter, we want to further analyze how the change in price changes the demand. In particular, we decompose the change in quantity demanded due to price change into substitution effect and income effect. 2

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What happens when a commodity’s price decreases? Substitution effect : the commodity is relatively cheaper, so consumers use more of it, instead of other commodities, which are now relatively more expensive. Income effect : the consumer’s budget of $m can purchase more than before, as if the consumer’s income rose, with consequent income effects on quantities demanded. 3

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x2x2 x1x1 Original choice Consumer’s budget is $m. 4

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x1x1 Lower price for commodity 1 pivots the constraint outwards. Consumer’s budget is $y. x2x2 5

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x1x1 Lower price for commodity 1 pivots the constraint outwards. Consumer’s budget is $m. x2x2 Now only $m’ are needed to buy the original bundle at the new prices, as if the consumer’s income has increased by $m -- $m’. 6

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Slutsky asserted that if, at the new prices, If less income is needed to buy the original bundle then “real income” is increased If more income is needed to buy the original bundle then “real income” is decreased 7

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Changes to quantities demanded due to the change in relative prices, keeping income just enough to buy the original bundle, are the (pure) substitution effect of the price change. Changes to quantities demanded due to the change in ‘real income’ are the income effect of the price change. 8

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Slutsky discovered that changes to demand from a price change are always the sum of a pure substitution effect and an income effect. 9

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x2x2 x1x1 x2’x2’ x1’x1’ 10

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x2x2 x1x1 x2’x2’ x1’x1’ 11

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x2x2 x1x1 x2’x2’ x1’x1’ 12

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x2x2 x1x1 x2’x2’ x 2 ’’ x1’x1’ x 1 ’’ 13

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x2x2 x1x1 x2’x2’ x 2 ’’ x1’x1’ x 1 ’’ 14

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x2x2 x1x1 x2’x2’ x 2 ’’ x1’x1’ x 1 ’’ Lower p 1 makes good 1 relatively cheaper and causes a substitution from good 2 to good 1. (x 1 ’,x 2 ’) (x 1 ’’,x 2 ’’) is the pure substitution effect. 15

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Substitution effect is always negatively related to the price change. Note that the portion of the yellow compensated budget line below x’ 1 is inside the budget set of the original budget, thus these bundles should be less preferred than the original bundle. As a result, the consumer must choose a point at or more than x’ 1 with the compensated budget, and as a result, the substitution effect is positive for a price decrease. 16

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x2x2 x1x1 x2’x2’ x 2 ’’ x1’x1’ x 1 ’’ (x 1 ’’’,x 2 ’’’) 17

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x2x2 x1x1 x2’x2’ x 2 ’’ x1’x1’ x 1 ’’ (x 1 ’’’,x 2 ’’’) The income effect is (x 1 ’’,x 2 ’’) (x 1 ’’’,x 2 ’’’). 18

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x2x2 x1x1 x2’x2’ x 2 ’’ x1’x1’ x 1 ’’ (x 1 ’’’,x 2 ’’’) The change to demand due to lower p 1 is the sum of the income and substitution effects, (x 1 ’,x 2 ’) (x 1 ’’’,x 2 ’’’). 19

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Most goods are normal (i.e. demand increases with income). The substitution and income effects reinforce each other when a normal good’s own price changes. 20

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x2x2 x1x1 x2’x2’ x 2 ’’ x1’x1’ x 1 ’’ (x 1 ’’’,x 2 ’’’) Good 1 is normal because higher income increases demand, so the income and substitution effects reinforce each other. 21

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Since both the substitution and income effects increase demand when own-price falls, a normal good’s ordinary demand curve slopes down. The Law of (Downward-Sloping) Demand therefore always applies to normal goods. 22

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Some goods are inferior (i.e. demand is reduced when income is higher.) The substitution and income effects oppose each other when an inferior good’s own price changes. 23

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x2x2 x1x1 x2’x2’ x1’x1’ 24

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x2x2 x1x1 x2’x2’ x1’x1’ 25

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x2x2 x1x1 x2’x2’ x1’x1’ 26

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x2x2 x1x1 x2’x2’ x 2 ’’ x1’x1’ x 1 ’’ 27

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x2x2 x1x1 x2’x2’ x 2 ’’ x1’x1’ x 1 ’’ The pure substitution effect is as for a normal good. But, …. 28

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x2x2 x1x1 x2’x2’ x 2 ’’ x1’x1’ x 1 ’’ (x 1 ’’’,x 2 ’’’) The pure substitution effect is as for a normal good. But, the income effect is in the opposite direction. 29

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x2x2 x1x1 x2’x2’ x 2 ’’ x1’x1’ x 1 ’’ (x 1 ’’’,x 2 ’’’) The overall changes to demand are the sums of the substitution and income effects. 30

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In rare cases of extreme income-inferiority, the income effect may be larger than the substitution effect, causing quantity demanded to fall as own-price rises. Such goods are Giffen goods. 31

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x2x2 x1x1 x2’x2’ x1’x1’ A decrease in p 1 causes quantity demanded of good 1 to fall. 32

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x2x2 x1x1 x2’x2’ x1’x1’ x 1 ’’’ x 2 ’’’ A decrease in p 1 causes quantity demanded of good 1 to fall. 33

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x2x2 x1x1 x2’x2’ x 2 ’’ x1’x1’ x 1 ’’ x 1 ’’’ x 2 ’’’ Substitution effect Income effect A decrease in p 1 causes quantity demanded of good 1 to fall. 34

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Giffen good can only result when the income effect of an inferior good is so strong that it dominates the substitution effect. This may be possible for poor households where the low-quality necessity has taken up a large portion of expenditure. This case is very rare, even if exists, so we have confidence that the Law of Demand almost always holds. 35

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If we denote m’ as the income required to obtain the original bundle at the new prices, so that m’=p’ 1 x 1 + p 2 x 2 and m=p 1 x 1 + p 2 x 2. Thus the change in real income is m’– m = (p’ 1 – p 1 ) x 1 Or 36

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The substitution effect is The Income effect is Total Effect 37

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In terms of derivative (or rate of change): Which is known as the Slutsky Equation. (This is just a rough presentation. The tools need for formal derivations is not covered in this class.) 38

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Slutsky’s method of decomposition is not the only reasonable way. Hicks proposed another way of holding “real income” constant. Instead of compensating him to be able to buy back the original bundle, Hicks method compensates the consumer to buy back a bundle that gives him the same utility as before. 42

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Hicks Substitution Effect is also negative, because of the convex preference. (It can also be shown by revealed preference.) The nominal income required to maintain the utility constant is less than the one required to buy back the same bundle. It implies a larger income effect for a price decrease, but a smaller income effect for a price increase. 44

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If government wants to impose tax to support public expenditure, or to ‘punish’ consumption of a good, say, due to pollution, various means can be used. Here, given the revenue are the same in equilibrium, how do the effects of income tax and quantity tax on good 1 differ? (Note: Income and tax rates are regarded as given for consumers. The tax rate is adjusted so that at equilibrium the tax revenue is the same.) 45

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Income tax corresponds to an inward shift of budget line. Quantity tax corresponds to an inward rotation of the budget line. When the revenues are held the same for comparison, the budget line for the income tax must pass through the optimal point for quantity tax. (Note: The tax revenue is tx 1 *, where x 1 * is the optimal quantity under quantity tax.) 47

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With the same tax revenue, the utility level attained is higher with income tax than with the quantity tax. But quantity tax has a stronger effect in reducing the consumption of good 1 than income tax. 48

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Consider a similar case. Now a tax is imposed to reduce consumption of certain good, but at the same time, an equivalent amount is rebated (given back) to the consumer. Again, consumer has to take the rebate and tax rate constant for his decision. 49

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Note that the new consumption bundle must be on the original budget line, because in equilibrium, the tax amount and rebate are the same. The consumer has become worse off after this quantity tax and rebate program. 51

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In this chapter, a decomposition of price effect on quality demand is introduced. Substitution effect: effect of change of price holding ‘real income’ constant. Income effect: effect of change in real income. For normal goods, both effects are negative w.r.t. a price rise. For inferior goods, sub. effect is negative, but income effect is positive w.r.t. a price rise. Giffen goods can only be inferior goods with very strong income effect. 52

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