1. Chapter 5 – The Theory of Demand
Thus far we have studied supply and demand and 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

2. Chapter 5 – The 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

3. Chapter 5 – The Theory of Demand
5.7 Compensating & Equivalent Variation
5.8 Market Demand
5.9 Labor and Leisure
5.10 Consumer Price Index (CPI)

4. • Demand and Optimal Choice
Y (units)
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 •
PX = 4
X (units)
XA=2
XB=10

5. • • Demand and Optimal Choice
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 • •
PX = 2
PX = 4
X (units)
XA=2
XB=10 20

6. • • • 5.1 The Price Consumption Curve
Y (units)
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 •
Price consumption curve • •
PX = 1
PX = 2
PX = 4
X (units)
XA=2
XB=10
XC=16 20

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

8. 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

9. 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.
x/Py = y/Px
y = xPx/Py
2) Pxx + Py(Px/Py)x = I
Pxx + Pxx = I
3) x= I/2Px

10. 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

11. Demand Example Step 1: Pxx+y=12 Step 2: y=Pxx Step 3: Pxx+Pxx=12

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

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

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

15. 5.3 The Income Consumption Curve
Y (units)
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 • • •
X (units) 20

16. The Income Consumption & Demand Curves
Y (units)
I=92
I=68 U3
Income consumption curve
I=40 U2 U1
X (units) PX $2
I=92
I=40
I=68
X (units)

17. 5.4 The Engel Curve
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.

18. Normal and Inferior Goods
• 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.

19. Engel Curve Graph I ($) “X is a normal good” Engel Curve 92 68 40
X (units)

20. Normal and Inferior.
• 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

21. A good can be normal over some ranges and inferior over others
Y (units)
Example:
I=400
A good can be normal over some ranges and inferior over others
I=300 U3
I=200 U2 U1
X (units)
I ($)
Example: Backward Bending Engel Curve
400
300
Engel Curve
200
X (units)

22. 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

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

24. The substitution effect always is negative
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.
The 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…

25. Example: Normal Good: Income and Substitution Effects
Y (units)
Example: Normal Good: Income and Substitution Effects
BL2
Let Px decrease
BL1 A • C • • B U2
BLd U1
Substitution
Income
X (units)
XA XB XC

26. Example: Inferior Good: Income and Substitution Effects
Y (units)
Example: Inferior Good: Income and Substitution Effects
BL2
“X is an inferior good” • C
BL1 A • U2
BLd • B U1
Income
Substitution
XA XC XB
X (units)

27. 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 (BL2)
2) The budget line must be tangent to the old indifference curve (U1)

28. • • • BLd Budget line slopes Slope of B1 = -Px1/Py
Y (units)
Budget line slopes
Slope of B1 = -Px1/Py
Slope of B2 = -Px2/Py
Slope of Bd = -Px2/Py
BL2
BL1 A • C • • B
BLd U2 U1
Substitution
Income
X (units)
XA XB XC

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

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

31. Substitution and Income Effect Example:
Suppose U(x,y) = 2x1/2 + y.
MUx = 1/x1/2 MUy = 1.
Py = $1 and I = $10.
Suppose that Px = $ What is the (initial) optimal consumption basket?
Tangency Condition:
MUx/MUy = Px/Py
1/x1/2 = Px

32. Solving for x:
x = 1/(Px2)
x = 1/(0.5)2
x = 4
Substituting, xA = 4 into the budget constraint:
Pxx + Pyy = 10
0.5(4) + (1)y = 10
yA = 8
UA = 2xA1/2 +yA
UA=2(41/2)+8
UA=12

33. 2) Suppose that px = $0.20. What is the (final) optimal consumption basket?
Using the demand derived in (a),
x = 1/(Px2)
xc = 1/(0.2)2
xc = 25
Pxx + Pyy = 10
0.2(25) + (1)y = 10
yC =5
UC=2xC1/2+yC
UC=2(251/2)+5
UC=15

34. Decomposition basket (New Prices, Old Utility)
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/x1/2 = .2
xb=25
U = 2x1/2 + y
12 = 2(25)1/2 + y
yB = 2
Substitution Effect: xB-xA = = 21
Income Effect: xC-xB = = 0

35. 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 Giffen Goods)

36. Example: Giffen Good: Income and Substitution Effects
Y (units)
Example: Giffen Good: Income and Substitution Effects
BL2
“X is a Giffen good” C •
BL1 A U2 • • B
Income U1
Substitution
X (units) XC XA XB

37. 5.6 Consumer Surplus
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

38. Example: Consumer's Surplus
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.

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

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

41. 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=20-Q
10=Q, Craig buys 10 model cars
Consumer Surplus =1/2bh
=1/2(10)(20-10)
=50

42. 5.7 Compensating and Equivalent Variation
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:

43. Compensating and Equivalent Variation
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.

44. Compensating Variation
Y (units)
-A change in the price of x shifts BL1 to BL2
-Consumption moves from point A to point C
-A BL at new prices that would maintain original utility is parallel to BL2 N • A • C
-NM represents the money required to return a consumer to their original utility, consuming at B M U2 B • U1
BL2
BL1 O
X (units)

45. • • • Equivalent Variation
Y (units) Q
-A change in the price of x shifts BL1 to BL2
-Consumption moves from point A to point C
-A BL at old prices that would make the equivalent move to the new utility is parallel to BL1 D • N • A • C
-NQ represents the money equivalent to a price change, resulting in consumption at D U2 U1
BL2
BL1
X (units) O

46. Compensating and Equivalent Variation
Y (units)
Compensating and Equivalent Variation Q
-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 D • N • A B • M U2 • C U1
BL2
BL1 O
X (units)

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

48. Consumer Surplus Example 2
Hosea’s utility demand for mini xylophones and yogurt (x and y) is represented by U=x2+y2
MUx=2x MUy=2y.
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.

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

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

51. Compensating Variation
Y (units)
Compensating variation: at the new prices (budget line parallel to the new budget line), minimize expenditure to achieve the original utility (U1). N • A • C M U2 B • U1
BL2
BL1 O
X (units)

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.
MUx/Px=MUy/Py
2x/1=2y/1
X=Y
U=x2+y2
80=x2+x2
40=x2
401/2=x
401/2=y

53. 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
PxX+PyY=I
X+Y=I
2(401/2)=I
12.65=ECV

54. Consumer Surplus Example 2
Compensating variation: the maximum amount a consumer will pay to receive a price discount
CV=Original I-ECV
CV=
CV=7.35
Hosea would pay a maximum of $7.35 to be able to buy mini xylophones at a reduced price of $1.

55. • • • Equivalent Variation
Y (units) Q
Given the old prices, minimize expenditure to achieve the new utility D • N • A • B U2 U1
BL2
BL1
X (units) O

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.
MUx/Px=MUy/Py
2x/2=2y/1
X=2Y
U=x2+y2
200=4y2+y2
40=y2
401/2=y
2(401/2)=x

57. 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
PxX+PyY=I
2X+Y=I
2(2(401/2))+401/2=I
31.62=EEV

58. 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=
EV=11.62
Hosea would need to be paid $11.62 to be as well off as a decrease in the price of xylophones.

59. Compensating and Equivalent Variation
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.

60. COMPENSATING VARIATION:
Compensating and Equivalent Variation
COMPENSATING VARIATION:
Original Utility and new prices
EQUIVALENT VARIATION:
Final Utility and old prices

61. 5.8 Market Demand
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

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

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

64. Market Demand
Algebraically the demand curves are as follows:

65. 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. B • $4 A • • • DM $2 DC DK O 6 9 2 3
Sushi

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

67. Externalities
Generally we assume that one consumer’s demand does not depend on the demand of others
In some cases, a person’s demand has an EXTERNAL effect on another’s demand – an externality exists
You are less likely to purchase a guard dog if your neighbour has one
You are more likely to eat sushi if all your friends do

68. Externalities
If one consumer's demand for a good changes with the number of other consumers who buy the good, there are externalities.
If one person's demand with the number of other consumers, then the externality is positive.
If one person's demand with the number of other consumers, then the externality is negative.
Examples: Telephone (physical network)
Software (virtual network)
increases
decreases

69. Example: iPads
Apple’s IPad has been growing in popularity and is an example of a bandwagon effect.
People often buy an iPad because their friends have it
-They are purchased to “BE COOL”
-They are purchased because more people are using iTunes for games and aps than other alternatives
If iPad prices decrease, an individual’s demand will increase due to the new price and due to the number of friends who buy iPads due to the new price

70. • • • Bandwagon Effect (increased quantity demanded when more
Example: IPads and The Bandwagon Effect PX
Bandwagon Effect (increased
quantity demanded when more
consumers purchase)
DNew
DOriginal • A 20 • B • C 10
Pure
Price
Effect
Market Demand
Bandwagon Effect 60
X (units)

71. Example: Hybrid Cars
When the first few Hybrid Cars came to Edmonton, everyone wanted them
Even though studies showed they (originally) cost more over their lifetime than a normal car and may actually pollute the environment more, people wanted them as a status symbol
As prices decreased and more cars become available, demand became more realistic
This is an example of the SNOB EFFECT: demand decreases as others buy the good

72. • • • Snob Effect (decreased quantity demanded when morePX
Example: The Snob Effect
Snob Effect (decreased
quantity demanded when more
consumers purchase)
Market Demand • A
1200 • C • B
900
D10 Cars
Pure Price Effect
D50 Cars
Snob Effect
X (units)

73. Externalities Example 1
The newest craze to hit the market is cell phone implants – not only do you never lose your phone, but you can now talk to all your friends IN YOUR MIND!
The one catch is that IMPhones can only call other IMPhones. Estimated demand for IMPhones is Q=5,000-10P and current prices are $100 each. After prices drop to $80, demand is seen to be 4500 units. Calculate and explain the externality.

74. Externalities Example 1
Original Demand: Q=5,000-10P
Q=5,000-10(100)
Q=4,000
New Demand along original curve:
Q=5,000-10P
Q=5,000=10(80)
Q=4,200
Externality = Actual Demand-Estimated Demand
= 4,500-4,200
= 300

75. Externalities Example 1
There is a POSITIVE EXTERNALITY or bandwagon effect of 300 units; the demand curve shifts due to others buying the new IMPhone.
(IMPhones become more valuable as more people install them.)

76. 5.9 Labour and Leisure
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?

77. 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.

78. The composite good, y, has price py = $1
Daily income = wL
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.

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

80. The substitution effect leads to less leisure and more labor as w increases.
As 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.
If leisure is a normal good, the income effect on leisure is positive
Therefore, the income effect on labor is negative (labor is a “bad”)

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

82. Example: A Backward Bending Supply of Labor
Daily Income in units of composite good, Y
600
Example: A Backward Bending Supply of Labor
W=25
480
Wage increases from $15 to $25, causing an increase in leisure time U5
360 • C U3 • • A
W=15
240 B
Income
120
Substitution • 24
Leisure (hours)
Substitution Effect (LB-LA) Income Effect (LC-LB)

83. 5.10 The Consumer Price Index
The Consumer Price Index (CPI) is an important measure of inflation and prices
CPI is an aggregate measure of the cost on an average “basket” of goods each year
CPI is used for price increases and wage increases from year to year
The Canadian Government used the CPI for taxes and payments
Calculation of the CPI can lead to a substitution bias:

84. CPI
Clothing
Given initial prices of Pf=$3 and Pc=$8, an average consumer will consume 80 food and 30 clothing for a total cost of $480.
At new prices of Pf=$6 and Pc=$9, an average consumer will consume 60 food and 40 clothing for a total cost of $720. 40 • B A 30 • 60 80
Food

85. The CPI Problem
The “Ideal” CPI would be the ratio of the new expenses to the old expenses: $720/$480=1.5
In reality, it is difficult and costly to track consumption as so many goods are consumed: toilet paper may change by -2% one year while cheese increases by 5%
For practical reasons, a set consumer basket is used from year to year; only prices chance
This causes a “substitution bias”: most consumers will substitute away from expensive goods, yet the CPI assumed no substitution occurs

86. CPI
Clothing
Practically, the CPI assumes every year consumption occurs at A. In year 2, a consumer assumed to purchase A at a cost of $750 would much rather purchase basket C. • C 40 • B 30 • A 60 80
Food

87. The CPI Problem
The “Practical” CPI would be the ratio of the new estimated cost of living to the old cost of living: $750/$480=1.5625
In reality, the cost of living increased by 50%, yet the CPI estimated an increase in the cost of living of 56.25%.
Every year the CPI shows growth of less than 10%.
Economists estimate this growth may be 0.5%-1.5% too high, which in the US accounts for billions of dollars of increased spending each year

88. Chapter 5 Key Concepts Deriving Demand Price Consumption Curve
Demand Curve
Income Consumption Curve
Engel Curve
Substitution and Income Effects
Decomposition Budget Line
Consumer Surplus

89. Chapter 5 Key Concepts Compensating & Equivalent Variation
Market Demand
Externalities
Labor and Leisure
Backwards Bending Labor Supply
Consumer Price Index (CPI)