Price Change: Income and Substitution Effects
THE IMPACT OF A PRICE CHANGE Economists often searate the imact of a rice change into two comonents: the substitution i effect; and the income effect.
THE IMPACT OF A PRICE CHANGE The substitution effect involves the substitution of good for good 2 or viceversa due to a change in relative rices of the two goods. The income effect results from an increase or decrease in the consumer s real income or urchasing ower as a result of the rice change. The sum of these two effects is called the The sum of these two effects is called the rice effect.
THE IMPACT OF A PRICE CHANGE The decomosition of the rice effect into the income and substitution effect can be done in several ways There are two main methods: (i) The Hicksian method; and (ii) The Slutsky method
THE HICKSIAN METHOD Sir John R.Hicks (904-989) 989) Awarded the Nobel Laureate in Economics (with Kenneth J. Arrrow) in 972 for work on general equilibrium theory and welfare economics.
THE HICKSIAN METHOD X 2 Otimal bundle is E a, on indifference curve I. E a I X a
THE HICKSIAN METHOD Af lli th i fx X 2 A fall in the rice of X P* The budget line ivots out from P E a I a X
THE HICKSIAN METHOD X 2 The new otimum is E b on I 2. The Total Price Effect is a to b E a E b I 2 I a b X
THE HICKSIAN METHOD To isolate the substitution effect we ask. what would the consumer ss otimal bundle be if s/he faced the new lower rice for X but eerienced no change in real income? This amounts to returning the consumer to the original indifference curve (I )
THE HICKSIAN METHOD X 2 The new otimum is E b on I 2. The Total Price Effect is a to b E a E b I 2 I a b X
THE HICKSIAN METHOD X 2 Draw a line arallel to the new budget line and tangent to the old indifference curve E a E b I 2 I a b X
THE HICKSIAN METHOD X 2 E a The new otimum on I is at Ec. The movement from Ea to Ec (the increase in quantity demanded from Xa to Xc) is solely in resonse to a change in E b I 2 relative rices E c I a c b X
THE HICKSIAN METHOD X 2 This is the substitution effect. E aec E b I 2 I X a Substitution Effect X c X
THE HICKSIAN METHOD To isolate the income effect Look at the remainder of the total rice effect This is due to a change in real income.
THE HICKSIAN METHOD X 2 E aec E b The remainder of the total effect is due to a change in real income. The increase in real income is evidenced by the movement from I to I 2 I 2 I X c Income Effect X b X
THE HICKSIAN METHOD X 2 E aec E b I 2 I a c b Sub Income Effect Effect X
M HICKSIAN ANALYSIS and DEMAND CURVES 2 2 P AC B A fall in rice from * to M 2 2 P P A X Marshallian Demand Curve (A & B) P * C B Hicksian Demand Curve (A & C) X
HICKSIAN ANALYSIS and DEMAND CURVES Hicksian (comensated) demand curves cannot be uward-sloing (i.e. substitution effect cannot be ositive)
THE SLUTSKY METHOD Eugene Slutsky (880-948) Russian economist eelled from the University of Kiev for articiating in student revolts. In his 95 aer, On the theory of the Budget of the Consumer he introduced Slutsky Decomosition.
THE SLUTSKY METHOD X 2 Otimal bundle is E a, on indifference curve I. E a I X a
THE SLUTSKY METHOD Af lli th i fx X 2 A fall in the rice of X P* The budget line ivots out from P E a I a X
THE SLUTSKY METHOD X 2 The new otimum is E b on I 2. The Total Price Effect is a to b E a E b I 2 a I b X
THE SLUTSKY METHOD Slutsky claimed that if, at the new rices, less income is needed to buy the original bundle then real income has increased more income is needed to buy the original bundle then real income has decreased Slutsky isolated the change in demand due only to the change in relative rices by asking What is the change in demand when the consumer s income is adjusted so that, t at the new rices, s/he can just afford to buy the original bundle?
THE SLUTSKY METHOD To isolate the substitution effect we adjust the consumer s s money income so that s/he change can just afford the original consumtion bundle. In other words we are holding urchasing ower constant.
THE SLUTSKY METHOD X 2 The new otimum is E b on I 2. The Total Price Effect is a to b E a E b I 2 a I b X
THE SLUTSKY METHOD X 2 Draw a line arallel to the new budget line which asses through the oint Ea. E a E b I 2 a I b X
X 2 THE SLUTSKY METHOD The new otimum on I 3 is at Ec. The movement from Ea to Ec is the substitution effect E a E b I 2 E c I 3 a c b X
X 2 THE SLUTSKY METHOD The new otimum on I 3 is at Ec. The movement from Ea to Ec is the substitution effect E a E b I 2 E c I 3 a c X Substitution Effect
X 2 THE SLUTSKY METHOD The remainder of the total t rice effect is the Income Effect. The movement from Ec to Eb. E a E b I 2 E c I 3 c b Income Effect X
THE SLUTSKY METHOD for NORMAL GOODS Most goods are normal (i.e. demand increases with income). The substitution and income effects reinforce each other when a normal good s own rice changes.
X 2 THE SLUTSKY METHOD for NORMAL GOODS The income and substitution effects reinforce each other. E a E b I 2 E c I 3 a c b X
THE SLUTSKY METHOD for NORMAL GOODS Since both the substitution and income effects increase demand when own-rice falls, a normal good s ordinary demand curve sloes downwards. The Law of Downward-Sloing Demand therefore always alies to normal goods.
THE SLUTSKY EQUATION Let M 2 2 be the original budget constraint and let M 2 2 2 reresent the budget constraint after the Slutsky comensating variation in income has been carried out.
THE SLUTSKY S EQUATION X 2 Demand for is M 2 < M d, M, 2, 2 M 2 2 E a E a M a 2 2 2 X
THE SLUTSKY EQUATION M 2 -M M M M 2 2 2 2 2 2 2 2 2 2 - M - M M M M M 2 2 2 2 2 2 - M M M M M M 2 2 - M M M - as M i th h i M= gives the change in money income needed to consume the original consume the original bundle of goods (at E A )
THE SLUTSKY S EQUATION The demand curve holding M constant is given by d,, M, M d 2 2, () which is the change in demand for due to the change in its own rice, holding M and the rice of 2 constant
THE SLUTSKY EQUATION The income effect is given by m d d, M,,, 2 2 M 2 (2) The change in demand due to the Slutsky substitution effect is given by s d d, M,,, 2 2 2 M (3)
Given THE SLUTSKY EQUATION d,, M, M d 2 2, () m d d,, M, M 2 2, 2 (2) s d d,, M, M 2 2 2, (3) Claim s m (4) Show this by substituting equations (), (2) and (3) into equation (4)
THE SLUTSKY EQUATION s m Divide across by s m Recall M ( ) M so
THE SLUTSKY EQUATION Substituting ( ) M s m Gives s m M THE SLUTSKY EQUATION
THE SLUTSKY METHOD: INFERIOR GOODS Some goods are (sometimes) inferior (i.e. demand is reduced by higher income). The substitution i and income effects oose each other when an inferior good s own rice changes.
THE SLUTSKY METHOD: INFERIOR X 2 E a GOODS E b I 2 The substitution effect is as er usual. But, the income effect is in the oosite direction. a b E c c I 3 a to c a to c c to b X
GIFFEN GOODS In rare cases of etreme inferiority, the income effect may be larger in size than the substitution effect, causing quantity demanded to rise as own rice falls. Such goods are Giffen goods. Giffen goods are very inferior goods.
X 2 a to c THE SLUTSKY METHOD for b INFERIOR GOODS In rare cases of etreme incomeinferiority, the income effect may be larger in size than the I 2 substitution effect, causing quantity E a demanded ded to fall as own-rice falls. E b I 2 effect may be larger a c E c I 3 c to b X
SLUTSKY S EFFECT FOR GIFFEN GOODS Slutsky s decomosition of the effect of a rice change into a ure substitution effect and an income effect thus elains why the Law of Downward-Sloing Demand is violated for very inferior goods.
DECOMPOSITION of TOTAL PRICE EFFECT: PERFECT COMPLEMENTS X 2 A fall in the rice of X I I2 I 2 No substitution effect Original Budget Constraint A=C B New Budget Constraint X
DECOMPOSITION of TOTAL PRICE EFFECT PERFECT SUBSTITUTES?