INTMIC9.jpg Chapter 8 Slutsky Equation Effects of a Price Change uWhat happens when a commodity’s price decreases? –Substitution effect: the commodity is relatively cheaper, so consumers substitute it for now relatively more expensive other commodities. Effects of a Price Change –Income effect: the consumer’s budget of $y can purchase more than before, as if the consumer’s income rose, with consequent income effects on quantities demanded. Effects of a Price Change x2 x1 Original choice Consumer’s budget is $y. Effects of a Price Change x1 Lower price for commodity 1 pivots the constraint outwards. Consumer’s budget is $y. x2 Effects of a Price Change x1 Lower price for commodity 1 pivots the constraint outwards. Consumer’s budget is $y. x2 Now only $y’ are needed to buy the original bundle at the new prices, as if the consumer’s income has increased by $y - $y’. Effects of a Price Change uChanges to quantities demanded due to this ‘extra’ income are the income effect of the price change. Effects of a Price Change uSlutsky discovered that changes to demand from a price change are always the sum of a pure substitution effect and an income effect. Real Income Changes uSlutsky asserted that if, at the new prices, –less income is needed to buy the original bundle then “real income” is increased –more income is needed to buy the original bundle then “real income” is decreased Real Income Changes x1 x2 Original budget constraint and choice Real Income Changes x1 x2 Original budget constraint and choice New budget constraint Real Income Changes x1 x2 Original budget constraint and choice New budget constraint; real income has risen Real Income Changes x1 x2 Original budget constraint and choice Real Income Changes x1 x2 Original budget constraint and choice New budget constraint Real Income Changes x1 x2 Original budget constraint and choice New budget constraint; real income has fallen Pure Substitution Effect uSlutsky isolated the change in demand due only to the change in relative prices by asking “What is the change in demand when the consumer’s income is adjusted so that, at the new prices, she can only just buy the original bundle?” Pure Substitution Effect Only x2 x1 x2’ x1’ Pure Substitution Effect Only x2 x1 x2’ x1’ Pure Substitution Effect Only x2 x1 x2’ x1’ Pure Substitution Effect Only x2 x1 x2’ x2’’ x1’ x1’’ Pure Substitution Effect Only x2 x1 x2’ x2’’ x1’ x1’’ Pure Substitution Effect Only x2 x1 x2’ x2’’ x1’ x1’’ Lower p1 makes good 1 relatively cheaper and causes a substitution from good 2 to good 1. Pure Substitution Effect Only x2 x1 x2’ x2’’ x1’ x1’’ Lower p1 makes good 1 relatively cheaper and causes a substitution from good 2 to good 1. (x1’,x2’) ® (x1’’,x2’’) is the pure substitution effect. And Now The Income Effect x2 x1 x2’ x2’’ x1’ x1’’ (x1’’’,x2’’’) And Now The Income Effect x2 x1 x2’ x2’’ x1’ x1’’ (x1’’’,x2’’’) The income effect is (x1’’,x2’’) ® (x1’’’,x2’’’). The Overall Change in Demand x2 x1 x2’ x2’’ x1’ x1’’ (x1’’’,x2’’’) The change to demand due to lower p1 is the sum of the income and substitution effects, (x1’,x2’) ® (x1’’’,x2’’’). Slutsky’s Effects for Normal Goods uMost goods are normal (i.e. demand increases with income). uThe substitution and income effects reinforce each other when a normal good’s own price changes. Slutsky’s Effects for Normal Goods x2 x1 x2’ x2’’ x1’ x1’’ (x1’’’,x2’’’) Good 1 is normal because higher income increases demand x2 x1 x2’ x2’’ x1’ x1’’ (x1’’’,x2’’’) Good 1 is normal because higher income increases demand, so the income and substitution effects reinforce each other. Slutsky’s Effects for Normal Goods Slutsky’s Effects for Normal Goods uSince both the substitution and income effects increase demand when own-price falls, a normal good’s ordinary demand curve slopes down. uThe Law of Downward-Sloping Demand therefore always applies to normal goods. Slutsky’s Effects for Income-Inferior Goods uSome goods are income-inferior (i.e. demand is reduced by higher income). uThe substitution and income effects oppose each other when an income-inferior good’s own price changes. Slutsky’s Effects for Income-Inferior Goods x2 x1 x2’ x1’ Slutsky’s Effects for Income-Inferior Goods x2 x1 x2’ x1’ Slutsky’s Effects for Income-Inferior Goods x2 x1 x2’ x1’ Slutsky’s Effects for Income-Inferior Goods x2 x1 x2’ x2’’ x1’ x1’’ Slutsky’s Effects for Income-Inferior Goods x2 x1 x2’ x2’’ x1’ x1’’ The pure substitution effect is as for a normal good. But, …. Slutsky’s Effects for Income-Inferior Goods x2 x1 x2’ x2’’ x1’ x1’’ (x1’’’,x2’’’) The pure substitution effect is as for a normal good. But, the income effect is in the opposite direction. Slutsky’s Effects for Income-Inferior Goods x2 x1 x2’ x2’’ x1’ x1’’ (x1’’’,x2’’’) The pure substitution effect is as for a normal good. But, the income effect is in the opposite direction. Good 1 is income-inferior because an increase to income causes demand to fall. Slutsky’s Effects for Income-Inferior Goods x2 x1 x2’ x2’’ x1’ x1’’ (x1’’’,x2’’’) The overall changes to demand are the sums of the substitution and income effects. Giffen Goods uIn 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. Slutsky’s Effects for Giffen Goods x2 x1 x2’ x1’ A decrease in p1 causes quantity demanded of good 1 to fall. Slutsky’s Effects for Giffen Goods x2 x1 x2’ x1’ x1’’’ x2’’’ A decrease in p1 causes quantity demanded of good 1 to fall. Slutsky’s Effects for Giffen Goods x2 x1 x2’ x2’’ x1’ x1’’ x1’’’ x2’’’ Substitution effect Income effect A decrease in p1 causes quantity demanded of good 1 to fall. Slutsky’s Effects for Giffen Goods uSlutsky’s decomposition of the effect of 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.