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### Lecture7

1. 1. Price Change: Income and Substitution Effects
2. 2. THE IMPACT OF A PRICE CHANGEEconomists often separate theimpact of a price change into twocomponents: – the substitution effect; and – the income effect.
3. 3. THE IMPACT OF A PRICE CHANGEThe substitution effect involves thesubstitution of good x1 for good x2 or vice-versa due to a change in relative prices ofthe two goods.The income effect results from an increaseor decrease in the consumer’s real incomeor purchasing power as a result of theprice change.The sum of these two effects is called theprice effect.
4. 4. THE IMPACT OF A PRICE CHANGEThe decomposition of the price effectinto the income and substitutioneffect can be done in several waysThere are two main methods:(i) The Hicksian method; and(ii) The Slutsky method
5. 5. THE HICKSIAN METHODSir John R.Hicks (1904-1989)Awarded the Nobel Laureate inEconomics (with Kenneth J. Arrrow)in 1972 for work on generalequilibrium theory and welfareeconomics.
6. 6. THE HICKSIAN METHODX2 Optimal bundle is Ea, on indifference curve I1. Ea I1 xa X1
7. 7. THE HICKSIAN METHODX2 A fall in the price of X1 The budget line pivots P * out from P Ea I1 xa X1
8. 8. THE HICKSIAN METHOD The new optimum isX2 Eb on I2. The Total Price Effect is xa to xb Eb Ea I2 I1 xa xb X1
9. 9. THE HICKSIAN METHODTo isolate the substitution effect we ask….“what would the consumer’s optimalbundle be if s/he faced the new lower pricefor X1 but experienced no change in realincome?”This amounts to returning the consumerto the original indifference curve (I1)
10. 10. THE HICKSIAN METHOD The new optimum isX2 Eb on I2. The Total Price Effect is xa to xb Eb Ea I2 I1 xa xb X1
11. 11. THE HICKSIAN METHOD Draw a line parallel toX2 the new budget line and tangent to the old indifference curve Eb Ea I2 I1 xa xb X1
12. 12. THE HICKSIAN METHOD The new optimum on I1 isX2 at Ec. The movement from Ea to Ec (the increase in quantity demanded from Xa to Xc) is solely in response to a change in Eb Ea I2 relative prices Ec I1 xa xc xb X1
13. 13. THE HICKSIAN METHODX2 This is the substitution effect. Eb Ea I2 Ec I1 X1Xa Substitution Xc Effect
14. 14. THE HICKSIAN METHODTo isolate the income effect …Look at the remainder of the totalprice effectThis is due to a change in realincome.
15. 15. THE HICKSIAN METHOD The remainder of the totalX2 effect is due to a change in real income. The increase in real income is evidenced by the movement from I1 to I2 Eb Ea I2 Ec I1 X1 Xc Income Effect Xb
16. 16. THE HICKSIAN METHODX2 Eb Ea I2 Ec I1 xa xc xb X1 Sub Income Effect Effect
17. 17. HICKSIAN ANALYSIS and DEMAND CURVES P A fall in priceM 1 = p1 x1 + p2 x 2 from p1 to p1* B AC ∗ M 1 = p1 x1 + p2 x2 P X1 A Marshallian Demand P1 Curve (A & B) B Hicksian Demand P1* C Curve (A & C) X1
18. 18. HICKSIAN ANALYSIS and DEMAND CURVESHicksian (compensated) demandcurves cannot be upward-sloping(i.e. substitution effect cannot bepositive)
19. 19. THE SLUTSKY METHODEugene Slutsky (1880-1948)Russian economist expelled from theUniversity of Kiev for participating instudent revolts.In his 1915 paper, “On the theory ofthe Budget of the Consumer” heintroduced “Slutsky Decomposition”.
20. 20. THE SLUTSKY METHODX2 Optimal bundle is Ea, on indifference curve I1. Ea I1 xa X1
21. 21. THE SLUTSKY METHODX2 A fall in the price of X1 The budget line pivots P * out from P Ea I1 xa X1
22. 22. THE SLUTSKY METHOD The new optimum isX2 Eb on I2. The Total Price Effect is xa to xb Eb Ea I2 I1 xa xb X1
23. 23. THE SLUTSKY METHODSlutsky claimed that if, at the new prices, – 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 decreasedSlutsky isolated the change in demand dueonly to the change in relative prices byasking “What is the change in demandwhen the consumer’s income is adjustedso that, at the new prices, s/he can justafford to buy the original bundle?”
24. 24. THE SLUTSKY METHODTo isolate the substitution effect weadjust the consumer’s moneyincome so that s/he change can justafford the original consumptionbundle.In other words we are holdingpurchasing power constant.
25. 25. THE SLUTSKY METHOD The new optimum isX2 Eb on I2. The Total Price Effect is xa to xb Eb Ea I2 I1 xa xb X1
26. 26. THE SLUTSKY METHOD Draw a line parallelX2 to the new budget line which passes through the point Ea. Eb Ea I2 I1 xa xb X1
27. 27. THE SLUTSKY METHOD The new optimumX2 on I3 is at Ec. The movement from Ea to Ec is the substitution effect Eb Ea I2 Ec I3 xa xc xb X1
28. 28. THE SLUTSKY METHOD The new optimumX2 on I3 is at Ec. The movement from Ea to Ec is the substitution effect Eb Ea I2 Ec I3 xa xc X1 Substitution Effect
29. 29. THE SLUTSKY METHOD The remainder ofX2 the total price effect is the Income Effect. The movement from Ec to Eb. Eb Ea I2 Ec I3 xc xb X1 Income Effect
30. 30. 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 price changes.
31. 31. THE SLUTSKY METHOD for NORMAL GOODS The income andX2 substitution effects reinforce each other. Eb Ea I2 Ec I3 xa xc xb X1
32. 32. THE SLUTSKY METHOD for NORMAL GOODS Since both the substitution and income effects increase demand when own-price falls, a normal good’s ordinary demand curve slopes downwards. The “Law” of Downward-Sloping Demand therefore always applies to normal goods.
33. 33. THE SLUTSKY EQUATIONLet M 1 = p1 x1 + p2 x 2be the original budget constraintand let ∗ M 2 = p1 x1 + p2 x 2represent the budget constraint after theSlutsky compensating variation in incomehas been carried out.
34. 34. THE SLUTSKY EQUATION Demand for x1 isX2 M2 < M1 x1 = x ( p1 , p2 , M ) d M 1 = p1 x1 + p2 x2 Ea xa X1 ∗M 2 = p1 x1 + p2 x2
35. 35. THE SLUTSKY EQUATIONM2 - M1∆M = M 2 − M 1 = ( ∗ p1 x1 ) + p2 x 2 - ( p1 x1 + p2 x 2 ) ∗∆M = M 2 − M 1 = p1 x1 + p2 x 2 - p1 x1 − p2 x 2 ∗∆M = M 2 − M 1 = p1 x1 - p1 x1 ∗∆M = M 2 − M 1 = x1 p1 - p1( )∆M = x1∆p1 as ( ∗ p1 ) - p1 = ∆p1gives the change in moneyincome needed toconsume the original ∆M=x1∆p1bundle of goods (at EA)
36. 36. THE SLUTSKY EQUATIONThe demand curve holding Mconstant is given by ∆x1 = x d ( ∗ p1 , ) p2 , M 1 − x d ( p1 , p2 , M 1 ) (1)which is the change in demand for x1 due tothe change in its own price, holding M andthe price of x2 constant
37. 37. THE SLUTSKY EQUATIONThe income effect is given by ∗ ( ) ∗ ( ∆x m = x d p1 , p2 , M 1 − x d p1 , p2 , M 2 ) (2)The change in demand due to the Slutskysubstitution effect is given by ( ) ∆x s = x d p1 , p2 , M 2 − x d ( p1 , p2 , M 1 ) ∗ (3)
38. 38. THE SLUTSKY EQUATIONGiven ∆x1 = x d ( p ,M )− x ( p , p ,M ) ∗ p1 , 2 1 d 1 2 1 (1) ∆x m = x (p , p ,M )− x (p , p ,M ) d ∗ 1 2 1 d ∗ 1 2 2 (2) ∆x s = x (p , p ,M )− x ( p , p ,M ) d ∗ 1 2 2 d 1 2 1 (3)Claim ∆x1 = ∆x s + ∆x m (4)Show this by substituting equations (1), (2)and (3) into equation (4)
39. 39. THE SLUTSKY EQUATION ∆x1 = ∆x s + ∆x mDivide across by ∆p1 ∆x1 ∆x s ∆xm = + ∆p1 ∆p1 ∆p1Recall ∆M = x1∆p1 so ∆p1 = (−) ∆M x1
40. 40. THE SLUTSKY EQUATIONSubstituting ∆p1 = (−)∆M x1 ∆x1 ∆xs ∆xm = + ∆p1 ∆p1 ∆p1 Gives ∆x1 ∆x s ∆x m THE = − x1 SLUTSKY ∆p1 ∆p1 ∆M EQUATION
41. 41. THE SLUTSKY METHOD: INFERIOR GOODS Some goods are (sometimes) inferior (i.e. demand is reduced by higher income). The substitution and income effects “oppose” each other when an inferior good’s own price changes.
42. 42. THE SLUTSKY METHOD: INFERIOR GOODS The substitution X2 effect is as per usual. But, the income effect is in the opposite Eb direction. I2 Ea Ec I3 xa xb xc X1xa to xc xc to xb
43. 43. GIFFEN GOODSIn rare cases of extreme inferiority,the income effect may be larger insize than the substitution effect,causing quantity demanded to riseas own price falls.Such goods are Giffen goods.Giffen goods are very inferior goods.
44. 44. THE SLUTSKY METHOD for INFERIOR GOODS In rare cases of X2 extreme income- inferiority, the income effect may be larger Eb in size than the I2 substitution effect, causing quantity Ea demanded to fall as Ec own-price falls. I3 xb xa xcxa to xc X1 xc to xb
45. 45. SLUTSKY’S EFFECT FOR GIFFEN GOODSSlutsky’s decomposition of the effectof a price change into a puresubstitution effect and an incomeeffect thus explains why the “Law”of Downward-Sloping Demand isviolated for very inferior goods.
46. 46. DECOMPOSITION of TOTAL PRICE EFFECT: PERFECT COMPLEMENTS X2 A fall in the price of X1 I1 I2 No substitution effect B New BudgetOriginal ConstraintBudget A=CConstraint X1
47. 47. DECOMPOSITION of TOTAL PRICE EFFECT PERFECT SUBSTITUTES ?