Chapter 5 Theory of Demand Thus

Chapter 5 – Theory of Demand • Thus far we have studied supply and demand their equilibrium • In this chapter we will see how the demand curve arises out of consumer theory • Shifts in demand will be dissected and consumer choices will be investigated further 1

Chapter 5 – Theory of Demand • In this chapter we will study: 5. 1 Price Consumption Curve 5. 2 Deriving the Demand Curve 5. 3 Income Consumption Curve 5. 4 Engel Curve 5. 5 Substitution and Income Effects 5. 6 Consumer Surplus 2

Chapter 5 – Theory of Demand 5. 7 Compensating & Equivalent Variation 5. 8 Market Demand 5. 9 Labor and Leisure 5. 10 Consumer Price Index (CPI) 3

Y (units) Demand Optimal Choice At a given income and faced with prices Px and Py, an individual will maximize their utility given the Tangency condition, resulting in a consumption of Good x as seen below: 10 • 0 XA=2 PX = 4 XB=10 X (units) 4

Y (units) When the price of x decreases, a consumer will maximize given the new budget line and a new amount of x will be consumed. 10 • 0 Demand Optimal Choice XA=2 • PX = 4 XB=10 PX = 2 20 X (units) 5

Y (units) 5. 1 The Price Consumption Curve The price consumption curve for good x plots all the utility maximization points as the price of x changes. This reveals an individual’s demand curve for good x. 10 • 0 XA=2 Price consumption curve • PX = 4 XB=10 • PX = 1 PX = 2 XC=16 20 X (units) 6

Example: Individual Demand Curve for X PX The points found on the price consumption curve produce the typically downward-sloping demand curve we are familiar with. PX = 4 • • PX = 2 • PX = 1 XA=2 XB=10 XC=16 U increasing X 7

5. 2 Deriving the Demand Curve Algebraically, we can derive an individual’s demand using the following equations: Pxx + Pyy = I (budget constraint) MUx/Px = MUy/Py (tangency point) 1) Solve (2) for y 2) Substitute y from (2) into (1) 3) Solve for x 8

General Example: Suppose that U(x, y) = xy. MUx = y and MUy = x. The prices of x and y are Px and Py, respectively and income = I. 1) x/Py = y/Px y = x. Px/Py 2) Pxx + Py(Px/Py)x = I P xx + P xx = I 3) x= I/2 Px 9

Specific Demand Example Let U=xy, therefore MUx=y and MUy=x Let income=12, Py=1. Graph demand as Px increases from $1 to $2 to $3. Step 1: Pxx+Pyy=I Pxx+y=12 Step 2: MUx/MUy=Px/Py y/x=Px y=Pxx 10

Demand Example Step 1: Pxx+y=12 Step 2: y=Pxx Step 3: Pxx+Pxx=12 x=6/Px X(1)=6 X(2)=3 X(3)=2 11

PX Demand Example Maximizing at each point, we arrive at the following demand curve: PX = 3 PX = 2 PX = 1 • 2 • 3 • 6 U increasing X 12

Y (units) Demand, Choice and Income At a given income, a consumer maximizes using tangency as seen below: 10 • I = 10 0 XA=2 XB=10 X (units) 13

Y (units) 10 • Demand, Choice, and Income When income increases the budget line shifts out, resulting in a new equilibrium • I=12 I = 10 0 XA=2 XB=3 20 X (units) 14

Y (units) 5. 3 The Income Consumption Curve The income consumption curve for good x plots all the utility maximization points as income changes. This is shown by shifting the demand curve for x. 10 Income consumption curve • • • 0 20 X (units) 15

Y (units) The Income Consumption & Demand Curves I=92 I=68 I=40 0 PX U 3 U 2 U 1 10 I=68 X (units) 18 24 I=40 Income consumption curve $2 10 18 24 I=92 X (units) 16

The income consumption curve for good x also can be written as the quantity consumed of good x for any income level. This is the individual’s Engel Curve for good x. When the income consumption curve is positively sloped, the slope of the Engel curve is positive. 17

• If the income consumption curve shows that the consumer purchases more of good x as her income rises, good x is a normal good. • Equivalently, if the slope of the Engel curve is positive, the good is a normal good. • If the income consumption curve shows that the consumer purchases less of good x as her income rises, good x is an inferior good. • Equivalently, if the slope of the Engel curve is negative, the good is an inferior good. 18

I ($) “X is a normal good” Engel Curve 92 68 40 0 10 18 24 X (units) 19

• Some goods are normal or inferior over different income levels Example: Kraft Dinner a) at extreme low incomes, Kraft dinner consumption goes up as income increases (because starving is bad) -Kraft Dinner is a normal good at extreme low incomes b) as income rises, people substitute away from Kraft Dinner to “real foods” -Kraft dinner is an inferior good at most incomes 20

Y (units) I=400 I=300 I=200 U 1 0 A good can be normal over some ranges and inferior over others U 3 U 2 13 16 18 X (units) I ($) 400 300 Engel Curve Example: Backward Bending Engel Curve 200 13 16 18 X (units) 21

5. 5 Substitution and Income Effects When the price of a good decreases, two effects occur: 1) The good is cheaper compared to other goods; consumers will substitute the cheaper good for more expensive goods 2) Consumers experience an increase in purchasing power similar to an increase in income 22

· Definition: As the price of x falls, all else constant, purchasing power rises. This is called the income effect of a change in price. ð The income effect may be negative (normal good) or positive (inferior good). 23

As the price of x falls, all else constant, good x becomes cheaper relative to good y. This change in relative prices alone causes the consumer to adjust his/ her consumption basket. This effect is called the substitution effect. ðThe substitution effect always is negative Usually, a move along a demand curve will be composed of both effects. ·Graphically, these effects can be distinguished as follows… 24

Y (units) Example: Normal Good: Income and Substitution Effects BL 2 Let Px decrease BL 1 A • C • B • U 1 Substitution U 2 BLd Income 0 XA XB XC X (units) 25

Y (units) Example: Inferior Good: Income and Substitution Effects BL 2 “X is an inferior good” C A • • BL 1 U 2 • BLd B Income U 1 Substitution 0 XA XC XB X (units) 26

Finding the DECOMPOSITION Budget Line The decomposition budget line (BLd) that satisfies 2 conditions: 1) The budget line represents a change in the price ratio; it must be parallel to the new budget line (BL 2) 2) The budget line must be tangent to the old indifference curve (U 1) 27

Y (units) Budget line slopes Slope of B 1 = -Px 1/Py BL 2 BL 1 Slope of B 2 = -Px 2/Py Slope of Bd = -Px 2/Py A • C • B • U 1 Substitution U 2 BLd Income 0 XA XB XC X (units) 28

Steps to Finding Substitution and Income Effects: 1) Using initial prices (and tangency), find a) start point (xa, ya) b) start utility (Ua) 2) Using final prices (and tancency), find a) end point (xc, yc) b) end utility (Uc) 29

Steps to Finding Substitution and Income Effects: 3) Using final prices and start utility for a) decomposition point (xb, yb) 4) Solve: a) Substitution Effect: x. B-x. A b) Income Effect: x. C-x. B 30

Substitution and Income Effect Example: Suppose U(x, y) = 2 x 1/2 + y. MUx = 1/x 1/2 MUy = 1. Py = $1 and I = $10. 1. Suppose that Px = $0. 50. What is the (initial) optimal consumption basket? Tangency Condition: MUx/MUy = Px/Py 1/x 1/2 = Px 31

Solving for x: x = 1/(Px 2) x = 1/(0. 5)2 x=4 Substituting, x. A = 4 into the budget constraint: Pxx + Pyy = 10 0. 5(4) + (1)y = 10 y. A = 8 UA = 2 x. A 1/2 +y. A UA=2(41/2)+8 UA=12 32

2) Suppose that px = $0. 20. What is the (final) optimal consumption basket? Using the demand derived in (a), x = 1/(Px 2) xc = 1/(0. 2)2 xc = 25 Pxx + Pyy = 10 0. 2(25) + (1)y = 10 y. C =5 UC=2 x. C 1/2+y. C UC=2(251/2)+5 UC=15 33

3) What are the substitution and income effects that result from the decline in Px? Decomposition basket (New Prices, Old Utility) Tangency: MUx/MUy = Px/Py 1/x 1/2 =. 2 xb=25 U = 2 x 1/2 + y 12 = 2(25)1/2 + y y. B = 2 Substitution Effect: x. B-x. A = 25 - 4 = 21 Income Effect: x. C-x. B = 25 - 25 = 0 34

Giffen Goods If a good is so inferior that the net effect of a price decrease of good x, all else constant, is a decrease in consumption of good x, good x is a Giffen good. ·For Giffen goods, demand does not slope down. ·When might an income effect be large enough to offset the substitution effect? The good would have to represent a very large proportion of the budget. (Some economists debate the existence of 35 Giffen Goods)

Y (units) BL 2 Example: Giffen Good: Income and Substitution Effects “X is a Giffen good” C • BL 1 A U 2 • Income • B U 1 Substitution 0 XC XA XB X (units) 36

· The individual’s demand curve can be seen as the individual’s willingness to pay curve. · On the other hand, the individual must only actually pay the market price for (all) the units consumed. · For example, you may be willing to pay $40 for a haircut, but upon arriving at the stylist, discover that the price is only $30 · The difference between willingness to pay and the amount you pay is the Consumer Surplus 37

Definition: The net economic benefit to the consumer due to a purchase (i. e. the willingness to pay of the consumer net of the actual expenditure on the good) is called consumer surplus. The area under an ordinary demand curve and above the market price provides a measure of consumer surplus. Note that a consumer will receive more surplus from the first good than from the last good. 38

Consumer Surplus Price Consumer Surplus: The difference between what a consumer is willing to pay and what they pay for each item Consumer Surplus Equilibrium Or market Price P* D Q* Quantity 39

Efficiency of the Equilibrium Quantity Price $16 Consumer Surplus = area of triangle =1/2 bh =1/2(16 -8)(10) =40 This calculation Only works for A linear demand curve $8 D 10 Quantity 40

Consumer Surplus Example 1 Craig’s demand for model cars is given by the demand curve P=20 -Q. If model cars cost $10 each, how much consumer surplus does Craig have? P=20 -Q 10=Q, Craig buys 10 model cars Consumer Surplus =1/2 bh =1/2(10)(20 -10) =50 41

· In practice, a consumer’s demand curve is difficult to estimate · Consumer Surplus can be estimated using the optimal choice diagram (budget lines and indifference curves) · Since utility is difficult to measure, consumer surplus is measured through the money needed when a price change occurs: 42

COMPENSATING VARIATION: The minimum amount of money a consumer must be compensated after a price increase to maintain the original utility. -The consumer’s ORIGINAL Utility is important. EQUIVALENT VARIATION: The change in money to give a equivalent utility to a price change. -The consumer’s FINAL Utility is important. 43

Y (units) N • A Compensating Variation -A change in the price of x shifts BL 1 to BL 2 -Consumption moves from point A to point C -A BL at new prices that would maintain original utility is parallel to BL 2 C -NM represents the U 2 money required to return B a consumer to their original utility, consuming U 1 at B • M • BL 1 O BL 2 X (units) 44

Equivalent Variation Y (units) Q N • D • A -A change in the price of x shifts BL 1 to BL 2 -Consumption moves from point A to point C -A BL at old prices that would make the equivalent move to the new utility is C -NQ represents the parallel to BL 1 U 2 money equivalent to a price change, resulting in consumption at D • U 1 BL 1 O BL 2 X (units) 45

Y (units) Q • N Compensating and Equivalent Variation D • A M • • BL 1 O B U 2 C U 1 -Here a price DECREASE occurs -MN is the max amount a consumer would PAY for this price decrease -NQ is the amount a consumer would be PAID instead of a price decrease BL 2 X (units) 46

CV and EV Steps 1) Calculate ORIGINAL and NEW consumption points that maximize utility. (Use tangency condition. ) 2) Calculate ORIGINAL and NEW utility. 3 a) Compensating Variation: With ORIGINAL UTILITY and NEW PRICES, minimize expenditure ECV CV=I-ECV 3 b) Equivalent Variation: With FINAL UTILITY and ORIGINAL PRICES, minimize expenditure EEV 47 EV=EEV-I

Consumer Surplus Example 2 Hosea’s utility demand for mini xylophones and yogurt (x and y) is represented by U=x 2+y 2 MUx=2 x MUy=2 y. Hosea has $20. Mini xylophones originally cost $2 while yogurt cost $1. Due to an outbreak of mad xylophone disease, price of healthy mini xylophones decreased to $1 each. Calculate compensating and equivalent variation. 48

Consumer Surplus Example 2 Originally (at point A): MUx/Px=MUy/Py 2 x/2=2 y/1 2 X=4 Y X=2 Y Px. X+Py. Y=I 2 X+Y=20 5 Y=20 Y=4 X=2 Y X=8 After price change (at point C): MUx/Px=MUy/Py 2 x/1=2 y/1 X=Y Px. X+Py. Y=I X+Y=20 X=10 X=Y Y=10 49

Consumer Surplus Example 2 Originally (at point A): After price change (at point C): Y=4 X=10 X=8 Y=10 U(A) =42+82 =16+64 =80 U(B) =102+102 =100+100 =200 Decrease in price causes an increase in utility. Here we have maximized utility given a budget constraint. 50

Y (units) N • A Compensating Variation Compensating variation: at the new prices (budget line parallel to the new budget line), minimize expenditure to achieve the original utility (U 1). • M • BL 1 O C B U 2 U 1 BL 2 X (units) 51

Consumer Surplus Example 2 Compensating variation: at the new prices (budget line parallel to the new budget line), minimize expenditure to achieve the original utility. MUx/Px=MUy/Py 2 x/1=2 y/1 X=Y U=x 2+y 2 80=x 2+x 2 40=x 2 401/2=x 401/2=y 52

Consumer Surplus Example 2 Compensating variation: at the new prices (budget line parallel to the new budget line), minimize expenditure to achieve the original utility. 401/2=x 401/2=y Px. X+Py. Y=I X+Y=I 2(401/2)=I 12. 65=ECV 53

Consumer Surplus Example 2 Compensating variation: the maximum amount a consumer will pay to receive a price discount CV=Original I-ECV CV=20 -12. 65 CV=7. 35 Hosea would pay a maximum of $7. 35 to be able to buy mini xylophones at a reduced price of $1. 54

Equivalent Variation Y (units) Q N • D • A Given the old prices, minimize expenditure to achieve the new utility • B U 2 U 1 BL 1 O BL 2 X (units) 55

Consumer Surplus Example 2 Equivalent variation: at the old prices (budget line parallel to the old budget line), minimize expenditure to achieve the new utility. MUx/Px=MUy/Py 2 x/2=2 y/1 X=2 Y U=x 2+y 2 200=4 y 2+y 2 40=y 2 401/2=y 2(401/2)=x 56

Consumer Surplus Example 2 Equivalent variation: at the old prices (budget line parallel to the old budget line), minimize expenditure to achieve the new utility. 401/2=y 2(401/2)=x Px. X+Py. Y=I 2 X+Y=I 2(2(401/2))+401/2=I 31. 62=EEV 57

Consumer Surplus Example 2 Equivalent variation: the minimum amount a consumer would have to be paid to be as well off as a price decrease EV=EEV-Original I EV=31. 62 -20 EV=11. 62 Hosea would need to be paid $11. 62 to be as well off as a decrease in the price of xylophones. 58

§Note that in the previous example CV did not equal EV ($7. 35 is not equal to $11. 62). §This occurs because the price change has a non-zero income effect. §Although CV and EV try to approximate Consumer surplus, generally neither will However, §If the income effect is zero, CV=CS=EV -ie: Quasi-Linear Utility functions. 59

COMPENSATING VARIATION: Original Utility and new prices EQUIVALENT VARIATION: Final Utility and old prices 60

·In the economy, each market has many individuals demanding a good ·Each individual maximizes their own utility when deciding on the amount they will buy ·Each individual has a maximum price they will pay and a maximum amount of the item they would want ·Ie: I’d pay $5 per episode of House, up to 20 episodes…how much would you pay? ·The sum of individual demand creates market demand 61

·Consider the following individuals’ demand for Sushi: Price $1 Craig’s 8 Demand Kristy’s 6 Demand Total 14 Demand $2 $3 $4 6 4 2 3 0 0 9 4 2 62

Price Market Demand Here the individual demand curves (DK and DC) combine to form market demand (DM). $4 • • $2 O 2 • 3 6 DK • 9 DC DM Sushi 63

·Algebraically the demand curves are as follows: 64

Price Market Demand In section A of market demand, Qm=Qc+QK. (it is important to add the normal form: Q=f(P), not the inverse form: P=f(Q). ) In section B of market demand, Qm=QC. $4 • • $2 • • DK O 2 3 6 9 DM DC Sushi 65

P 10 P P Q = 10 - p 4 Consumer 1 Q = 30 - 6 p Q = 20 - 5 p Q Consumer 2 Q Aggregate demand Note that at a price of $4, 10 -p=30 -6 P=6 66 Q

· Basic economic theory states that as an individual’s wage increases they will work more; the benefit from an additional hour of work outweighs the benefit from an additional hour of watching TV (House of course) · In practice however, high wage earners tend to work less than minimum wage earners · Is this the end of economics as we know it? 67

Assume: “Labor” includes all work hours when the consumer is earning income. (L hours per day at wage rate w per hour. Let w = $5) “Leisure” includes all nonwork activities (so hours of leisure, l = 24 – L) U= U(y, l) Utility depends on consumption of a composite good (y) and hours of leisure. 68

The composite good, y, has price py = $1 • Daily income = w. L ·The budget line gives all the combinations of y and l that the consumer can afford. If l = 24, y = 0 If l = 0, y = 120 Slope of budget line is -$5. 69

Y (units) 600 w=25 480 w=20 360 Labour and Leisure As wage is increasing, a consumer’s maximization may cause him/her to increase or decrease leisure: w=15 240 120 O w=10 w=5 • • • Leisure (l) 70

ðThe substitution effect leads to less leisure and more labor as w increases. ðAs w increases, the consumer feels as though he has more income because less work is needed to buy a unit of y. This creates an income effect. ðIf leisure is a normal good, the income effect on leisure is positive ðTherefore, the income effect on labor is negative (labor is a “bad”) 71

This information can be used to construct the consumer’s labor supply function, L(w). ðIf the substitution effect of a wage increase outweighs the income effect, the labor supply slopes upwards ðIf the income effect of a wage increase outweighs the substitution effect, the labor supply curve bends backwards. 72

Daily Income in units of composite good, Y Example: A Backward Bending Supply of 600 Labor W=25 480 U 5 360 U 3 • • A • C Wage increases from $15 to $25, causing an increase in leisure time 240 W=15 B 120 Income Substitution 12 13 14 15 Substitution Effect (LB-LA) • 24 Leisure (hours) Income Effect (LC-LB) 73

Chapter 5 Key Concepts ØDeriving Demand ØPrice Consumption Curve ØDemand Curve ØIncome Consumption Curve ØEngel Curve ØSubstitution and Income Effects ØDecomposition Budget Line ØConsumer Surplus 74

Chapter 5 Key Concepts ØCompensating & Equivalent Variation ØMarket Demand ØLabor and Leisure ØBackwards Bending Labor Supply 75