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.Effects
2、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$y can purchase more than before,as if
3、 the consumers income rose,with consequent income effects on quantities demanded.Effects of a Price Changex1Lower price for commodity 1pivots the constraint outwards.Consumers budget is$y.x2yp2Effects of a Price Changex1Lower price for commodity 1pivots the constraint outwards.Consumers budget is$y.
4、x2yp2yp2Now only$y are needed to buy the original bundle at the new prices,as if the consumers income has increased by$y-$y.The Idea behind the Slutsky EquationDivide the total changes to demand from a price change into pure substitution effect;1)2)an income effect.Pure Substitution Effectu“What is
5、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 Onlyx2x1x2x2x1x
6、1Lower p1 makes good 1 relativelycheaper and causes a substitutionfrom good 2 to good 1.(x1,x2)(x1,x2)is the pure substitution effect.Pure Substitution Effect Is Always Negative!x2x1x2x2x1x1(x1,x2)must always be on theright-hand-side of (x1,x2)by WRSP!And Now The Income Effectx2x1x2x2x1x1(x1,x2)And
7、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:1)A nice way to divide
8、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 changes.Slutskys Effects for Norma
9、l Goodsx2x1x2x2x1x1(x1,x2)Good 1 is normal becausehigher income increasesdemand x2x1x2x2x1x1(x1,x2)Good 1 is normal becausehigher income increasesdemand,so the income and substitution effects reinforce each other.Slutskys Effects for Normal GoodsuSince both the substitution and income effects increa
10、se 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.demand is reduced by higher inco
11、me).uThe substitution and income effects oppose each other when an income-inferior goods own price changes.Slutskys Effects for Income-Inferior Goodsx2x1x2x1Slutskys Effects for Income-Inferior Goodsx2x1x2x2x1x1Slutskys Effects for Income-Inferior Goodsx2x1x2x2x1x1The pure substitution effect is as
12、fora normal good.But,.Slutskys Effects for Income-Inferior Goodsx2x1x2x2x1x1(x1,x2)The pure substitution effect is as for a normal good.But,the income effect is in the opposite direction.Slutskys Effects for Income-Inferior Goodsx2x1x2x2x1x1(x1,x2)The pure substitution effect is as for a normal good
13、.But,the income effect is in the opposite direction.Good 1 is income-inferior because an increase to income causes demand to fall.Slutskys Effects for Income-Inferior Goodsx2x1x2x2x1x1(x1,x2)The overall changes to demand arethe sums of the substitution and income effects.Giffen GoodsuIn rare cases o
14、f 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 a price change into a pure substitution effect
15、 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”choiceIt is the choice at the new price but with compensated incomeOnce this is found,we can calculate the pure substitution effect and income effect
