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# Microeconomics: Income and Substitution Effects

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Consumer Behavior: Income and Substitution Effects
The Consumer’s Reaction to a Change in Income
Engel Curve or Engel’s Law
The Consumer’s Reaction to a Change in Price
The Consumer’s Demand Function
Cobb-Douglas Utility Function
The Slutsky Substitution Effect
The Hicks substitution effect

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### Microeconomics: Income and Substitution Effects

1. 1. Consumer Behavior (II): Income and Substitution Effects Dr. Manuel Salas-Velasco University of Granada, Spain 1
2. 2. Consumer Behavior (II) Introduction Dr. Manuel Salas-Velasco 2
3. 3. The Budget Constraint Quantity of X QuantityofY XP M vertical intercept horizontal intercept YP M Slope Y X P P  The equation for the budget line: X P P P M Y Y X Y  Relative price ratio Budget set The budget set consists of all bundles that are affordable at the given prices and income Dr. Manuel Salas-Velasco 3
4. 4. The Consumer’s Utility Maximizing Choice Quantity of X QuantityofY E • The consumer’s utility is maximized at the point (E) where an indifference curve is tangent to the budget line • The condition for utility maximization Y Y X X P MU P MU  X* Y* (X*, Y*) is the utility-maximizing bundle • The optimum quantities (X*, Y*) obtained by solving the Lagrangean problem tell us how much of each good an individual consumer will demand, assuming that he/she behaves rationally and optimizes his/her utility within his/her budget. Dr. Manuel Salas-Velasco 4
5. 5. Consumer Behavior (II) The Consumer’s Reaction to a Change in Income Dr. Manuel Salas-Velasco 5
6. 6. Shifts in the Budget Line 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 0 2 4 6 8 10 12 0 1 2 3 4 5 Quantity of ice-cream (week), X Quantityoflemonade(week),Y M’ = 20; PX = 2; PY = 1 M = 10; PX = 2; PY = 1 X P P P M Y Y X Y  XY 210  XY 2-20 Prices are held constant and income increases (e.g. the consumer’s income doubles) YP M XP M XP M  YP M  M’ > M Dr. Manuel Salas-Velasco 6
7. 7. Response to Income Changes 1U 2U 3U Y X Income-Consumption Curve E1 E2 E3 X, Y, normal goods Prices are held constant Income increases: M1 < M2 < M3 • Increases in money income cause a parallel outward shift of the budget line • The utility-maximizing point moves from E1 to E2 to E3 YX PP , XP M1 XP M2 XP M3 YP M2 YP M3 YP M1 • By joining all the utility-maximizing points, an income-consumption line is traced out * 1X * 2X * 3Y * 3X * 1Y * 2Y Dr. Manuel Salas-Velasco 7
8. 8. How Consumption Changes as Income Changes M Y Engel Curve for good Y, with good Y as normal M1 M2 M3 * 1Y * 2Y * 3Y  MPPYY YX ,, Dr. Manuel Salas-Velasco 8
9. 9. Engel Curve or Engel’s Law  A general reference to the function which shows the relationship between various quantities of a good a consumer is willing to purchase at varying income levels (ceteris paribus) Ernst Engel (1821-1896)  A German statistician who studied the spending patterns of groups of people of different incomes  People spent a smaller and smaller proportion of their incomes on food as those incomes increased Dr. Manuel Salas-Velasco 9
10. 10. Consumer Behavior (II) The Consumer’s Reaction to a Change in Price Dr. Manuel Salas-Velasco 10
11. 11. Shifts in the Budget Line 0 2 4 6 8 10 12 0 1 2 3 4 5 6 7 8 9 10 0 2 4 6 8 10 12 0 1 2 3 4 5 Quantity of ice-cream (week), X Quantityoflemonade(week),Y X P P P M Y Y X Y  M = 10; PX = 2; PY = 1 XY 210  M = 10; P’X = 1; PY = 1Decrease in the price of X (50%) XY -10 YP M XP M XP M  Dr. Manuel Salas-Velasco 11
12. 12. Response to Changes in a Good’s Price MPY , 1 XP 2 XP Y X Price-Consumption Curve E1 E2 E3 Decrease in the price of X: Price of Y and income are held constant: 3 XP> > YP M 1 XP M 2 XP M 3 XP M 1U 2U 3U * 1X * 2X * 3X * 1Y * 2Y * 3Y Dr. Manuel Salas-Velasco 12
13. 13. How Consumption Changes as Price Ratio Changes Quantity, X Price of X Demand Curve for X * 1X * 2X * 3X 1 XP 2 XP 3 XP Dr. Manuel Salas-Velasco 13
14. 14. The Consumer’s Demand Function Y Y X X P MU P MU  X U MUX    Y U MUY    • We are interested in finding the individual demand curve for the good X; an expression for quantity demanded as a function of all prices and income • The condition for utility maximization is: U = U (X, Y) 1 YMUX 1 XMUY YX P X P Y 11    1)1(  Y X P P XY • Let’s suppose that the utility function is: U = X Y + X + Y Dr. Manuel Salas-Velasco 14
15. 15. The Consumer’s Demand Function 1)1(  Y X P P XY PX X + PY Y = M M P P XPXP Y X YX        1)1( X = X (PX, PY, M) Consumer’s demand function (generalized demand function) MPPXXP YXX  )1( MPPXPXP YXXX  YXX PPMXP 2 X YX P PPM X 2   Dr. Manuel Salas-Velasco 15
16. 16. The Own-Price Demand X YX P PPM X 2   ),,( MPPXX YX ),,( MPPXX YX M = \$100; PY = \$10 Consumer’s demand function The own-price demand curve (ordinary demand function for X): X = f (PX), ceteris paribus X X P P X 2 10100   X X P P X 2 110   Suppose we use the following parametric values: • However, economists by convention always graph the demand function with price on the vertical axis and quantity demanded on the horizontal axis The inverse demand function PX X X PX   5.0 55 Dr. Manuel Salas-Velasco 16
17. 17. The Engel Curve X YX P PPM X 2   ),,( MPPXX YX ),,( MPPXX YX PX = \$5; PY = \$10 Consumer’s demand function The Engel curve for X 52 105    M X 10 5  M X 2 1 10  M X X M elasticityIncome M X    If Income Elasticity is positive, then X is a normal good (quantity demanded increases as income increases, ceteris paribus) Suppose we use the following parametric values:  positive M X 10 1    positive   elasticityIncome X is a normal good Dr. Manuel Salas-Velasco 17
18. 18. The Cross-Price Demand Curve X YX P PPM X 2   ),,( MPPXX YX ),,( MPPXX YX PX = \$5; M = \$100 Consumer’s demand function Suppose we use the following parametric values: 52 5100    YP X 10 95 YP X   10 5.9 YP X  Cross-price demand curve for X • We hold the own price of good X and money income constant; we focus on the relationship between the quantity demanded of good X and the price of good Y X P P elasticityprice-Cross Y Y   X If CPE is positive, then X,Y are substitutes If CPE is negative, then X,Y are complements )( 10 1 positive P X Y    positive   elasticityprice-Cross X is a substitute for Y Dr. Manuel Salas-Velasco 18
19. 19. Cobb-Douglas Utility Function Y Y X X P MU P MU  X U MUX    Y U MUY    • The condition for utility maximization is: U = U (X, Y) 2 1 2 1 2 1   XYMUX 2 1 2 1 2 1   YXMUY YX P YX P XY 2 1 2 1 2 1 2 1 2 1 2 1   PX X + PY Y = M M P P XPXP Y X YX  XP M X 2 MXPX 2 Consumer’s demand function for X • The utility function is: 2 1 2 1 YXU  2 1 2 1 2 1 2 1 2 1 2 1    XY YX P P X Y Y X P P X Y  Y X P P XY  PX = 4; M = 800; PY = 1 100 8 800 X X* = 100 units Dr. Manuel Salas-Velasco 19
20. 20. Consumer Behavior (II) Income and Substitution Effects Dr. Manuel Salas-Velasco 20
21. 21. The Income Effect and the Substitution Effect of a Price Change Quantity, X Price of X Own-Price Demand Curve for X (Inverse Ordinary Demand Function for X) * 1X * 2X * 3X 1 XP 2 XP 3 XP • When price of good X falls, the optimal consumption level (or quantity demanded) of good X increases • What are the underlying reasons for a response in the quantity demanded of good X due to a change in its own price? • Substitution effect: the impact that a change in the price of a good has on the quantity demanded of that good, which is due to the resulting change in relative prices (PX/PY) • Income effect: the impact that a change in the price of a good has on the quantity demanded of that good due strictly to the resulting change in real income (or purchasing power) Total effect Dr. Manuel Salas-Velasco 21
22. 22. Income and Substitution Effects YP M 1 XP M 2 XP M Y X Price of Y and monetary income are held constant: MPY , Decrease in the price of X: 1 XP > 2 XP * 1X * 2X * 1Y* 2Y 1U 2U E1 E2 YP PX 1 YP PX 2 TE SE total effect (TE) = substitution effect (SE) + income effect (IE) IE Dr. Manuel Salas-Velasco 22
23. 23. The Substitution Effect: Two Definitions in the Literature Eugene Slutsky 1880-1948 Sir John R. Hicks 1904-89 The Slutsky substitution effect The Hicks substitution effect The effect on consumer choice of changing the price ratio, leaving his/her initial utility unchanged The effect on consumer choice of changing the price ratio, leaving the consumer just able to afford his/her initial bundle Dr. Manuel Salas-Velasco 23
24. 24. The Slutsky Substitution Effect YP M 1 XP M 2 XP M Y X Price of Y and monetary income are held constant: MPY , Decrease in the price of X: 1 XP > 2 XP * 1X * 2X * 1Y* 2Y 1U 2U E1 E2 YP PX 1 YP PX 2 YP PX 2 E3 3U * 3X * 3Y • We do this by shifting the line AB to a parallel line CD that just passes through E1 (keeping purchasing power constant) • To remove the income effect, imagine reducing the consumer’s money income until the initial bundle is just attainable A B C D • Although is still affordable, it is not the optimal purchase at the budget line CD  * 1 * 1 ,YX • The optimal bundle of goods is: SE IE YP M  2 XP M  TE X is a normal goodDr. Manuel Salas-Velasco 24
25. 25. The Slutsky Substitution Effect YP M 1 XP M 2 XP M Y X * 1X * 2X * 1Y* 2Y 1U 2U E1 E2 YP PX 1 YP PX 2 YP PX 2 2 XP M  E3 3U * 3X * 3Y YP M  A B C D MPYPX YX  * 1 1* 1E1: MPYPX YX  * 1 2* 1 MM  MMM  Change (reduction) in money income necessary to make the initial bundle affordable at the new prices M’= amount of money income that will just make the original consumption bundle affordable: MMM  E3: MPYPX YX  * 3 2* 3 SE IE TE )( 12* 1 XX PPXM  X is a normal goodDr. Manuel Salas-Velasco 25
26. 26. Example XP M X 10 10  )(14 310 120 10* 1 weekquartsX    )(16 210 120 10* 2 weekquartsX    • The individual demand function for milk is: • Consumer’s income is \$120 per week and PX is \$3 per quart: • Let’s suppose that the price of milk falls to \$2 per quart: • The total change (total effect): 2* 1 * 2  XX MMM  14)32(14)( 12* 1  XX PPXM 106\$14120  MMM Level of income necessary to keep purchasing power constant )(3.15 210 106 10* 3 weekquartsX    • The substitution effect is: 3.1143.15* 1 * 3  XX • The income effect is: 0.7 (16 – 15.3) Dr. Manuel Salas-Velasco 26
27. 27. The Hicks substitution effect YP M 1 XP M 2 XP M Y X MPY , 1 XP > 2 XP * 1X * 2X * 1Y* 2Y 1U 2U E1 E2 YP PX 1 YP PX 2 YP PX 2 2 XP M  E3 * 3X * 3Y YP M  • To remove the income effect, imagine reducing the consumer’s money income until the initial indifference curve is just attainable • We do this by shifting the line AB to a parallel line CD that just touches the indifference curve U1 (the utility level is held constant at its initial level) A B C D SE IE TE • The intermediate point E3 divides the quantity change into a substitution effect (SE) and an income effect (IE) X is a normal goodDr. Manuel Salas-Velasco 27
28. 28. Income and Substitution Effects: Inferior Good 1U 2U E1 E2 E3 * 1X * 2X * 3X Y X MPY , 1 XP > 2 XP A B C D substitution effect income effect total effect • The consumer is initially at E1 on budget line AF F • With a decrease in the price of good X, the consumer moves to E2; the quantity of X demanded increases (total effect) • The total effect can be broken down into: o A substitution effect (associated with a move from E1 to E3) o An income effect (associated with a move from E3 to E2) X is an inferior good • The substitution effect exceeds the income effect, so the decrease in the price of good X leads to an increase in the quantity demanded Dr. Manuel Salas-Velasco 28
29. 29. Income and Substitution Effects: The Giffen Good 1U 2U E1 E2 E3 * 1X* 2X * 3X Y X MPY , 1 XP > 2 XP A B C D substitution effect income effect total effect • The consumer is initially at E1 on budget line AF F • With a decrease in the price of good X, the consumer moves to E2; the quantity of X demanded decrease (total effect) • The total effect can be broken down into: o A substitution effect (associated with a move from E1 to E3) o An income effect (associated with a move from E3 to E2) X is a Giffen good• The income effect exceeds the substitution effect, so the decrease in the price of good X leads to a decrease in the quantity demanded Dr. Manuel Salas-Velasco 29
30. 30. Income and Substitution Effects of a reduction in price of good X holding income and the price of good Y constant Good X is: Substitution effect Income effect Total effect Normal Increase Increase Increase Inferior (not Giffen) Increase Decrease Increase Giffen (also inferior) Increase Decrease Decrease Dr. Manuel Salas-Velasco 30