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1、Chapter EightSlutsky EquationWhat Are We Doing in this Chapter?u We take a further look at the comparative statics of demand function with respect to prices;uWe divide the changes in demand due to price changes into two effects: Substitution effect; Income effect? Why? Deeper economic intuition.Effe
2、cts of a Price ChangeuWhat happens when a commoditys price decreases? Substitution effect: the commodity is relatively cheaper, so consumers substitute it for now relatively more expensive other commodities.Effects of a Price ChangeIncome effect: the consumers budget of $y can purchase more than bef
3、ore, as if the consumers income rose, with consequent income effects on quantities demanded.Effects of a Price Changex1Lower price for commodity 1 pivots the constraint outwards.Consumers budget is $y.x2Effects of a Price Changex1Lower price for commodity 1 pivots the constraint outwards.Consumers b
4、udget is $y.x2Now only $y are needed to buy theoriginal bundle at the new prices, as if the consumers income hasincreased by $y - $y.The Idea behind the Slutsky EquationDivide the total changes to demand from a price change into pure substitution effect; 2) an income effect.Pure Substitution Effectu
5、“What is the change in demand when the consumers income is adjusted so that, at the new prices, she can only just buy the original bundle?”uI.e., changes in demand without changes in real incomePure Substitution Effect Onlyx2x1x2x1Pure Substitution Effect Onlyx2x1x2x2x1x1Pure Substitution Effect Onl
6、yx2x1x2x2x1x1Lower p1 makes good 1 relatively cheaper and causes a substitution from good 2 to good 1. (x1,x2) (x1,x2) is thepure substitution effect.Pure Substitution Effect Is Always Negative!x2x1x2x2x1x1(x1,x2) must always be on the right-hand-side of (x1,x2) by WRSP!And Now The Income Effectx2x1
7、x2x2x1x1(x1,x2)And Now The Income Effectx2x1x2x2x1x1(x1,x2)The income effect is (x1,x2) (x1,x2).The Overall Change in Demandx2x1x2x2x1x1(x1,x2)The change to demand due to lower p1 is the sum of the income and substitution effects,(x1,x2) (x1,x2).Question: What is the Contribution of Slutsky?Answer:
8、1) A nice way to divide the total changes in demand; 2) Show that the pure substitution effect is always negative.Slutskys Effects for Normal GoodsuMost goods are normal (i.e. demand increases with income).uThe substitution and income effects reinforce each other when a normal goods own price change
9、s.Slutskys Effects for Normal Goodsx2x1x2x2x1x1(x1,x2)Good 1 is normal because higher income increases demand x2x1x2x2x1x1(x1,x2)Good 1 is normal because higher income increases demand, so the incomeand substitutioneffects reinforceeach other. Slutskys Effects for Normal GoodsuSince both the substit
10、ution and income effects increase demand when own-price falls, a normal goods ordinary demand curve slopes down.uThe Law of Downward-Sloping Demand therefore always applies to normal goods.Slutskys Effects for Normal GoodsSlutskys Effects for Income-Inferior GoodsuSome goods are income-inferior (i.e
11、. demand is reduced by higher income).uThe substitution and income effects oppose each other when an income-inferior goods own price changes.Slutskys Effects for Income-Inferior Goods x2x1x2x1Slutskys Effects for Income-Inferior Goods x2x1x2x2x1x1Slutskys Effects for Income-Inferior Goods x2x1x2x2x1
12、x1The pure substitution effect is as for a normal good. But, .Slutskys Effects for Income-Inferior Goods x2x1x2x2x1x1(x1,x2)The pure substitution effect is as for a normal good. But, the income effect isin the opposite direction. Slutskys Effects for Income-Inferior Goods x2x1x2x2x1x1(x1,x2)The pure
13、 substitution effect is as for a normal good. But, the income effect isin the opposite direction. Good 1 isincome-inferiorbecause anincrease to incomecauses demand tofall. Slutskys Effects for Income-Inferior Goods x2x1x2x2x1x1(x1,x2)The overall changes to demand are the sums of the substitution and
14、income effects.Giffen GoodsuIn rare cases of extreme income- inferiority, the income effect may be larger in size than the substitution effect, causing quantity demanded to fall as own-price rises.uSuch goods are Giffen goods.Slutskys Effects for Giffen GoodsuSlutskys decomposition of the effect of
15、a price change into a pure substitution effect and an income effect thus explains why the Law of Downward-Sloping Demand is violated for extremely income- inferior goods.Summary: The Key to This ChapteruTo be able to find the “auxiliary” choice It is the choice at the new price but with compensated income Once this is found, we can calculate the pure substitution effect and income effect
