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
1
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
2
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)
3
Y (units)
Demand and 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 and 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 = xPx/Py
2) Pxx + Py(Px/Py)x = I
Pxx + Pxx = I
3) x= I/2Px
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
The Income Consumption & Demand Curves
Y (units)
I=92
I=68
I=40
0
U3
Income consumption curve
U2
U1
10
18 24
I=40
I=68
X (units)
PX
$2
10
I=92
18 24
X (units)
16
The income consumption curve for good x also
can be written as the quantity consumed of good
x for any income level. This is the individual’s
Engel Curve for good x.
When the income consumption curve is
positively sloped, the slope of the Engel
curve is positive.
17
• If the income consumption curve shows that the
consumer purchases more of good x as her income
rises, good x is a normal good.
• Equivalently, if the slope of the Engel curve is
positive, the good is a normal good.
• If the income consumption curve shows that the
consumer purchases less of good x as her income
rises, good x is an inferior good.
• Equivalently, if the slope of the Engel curve is
negative, the good is an inferior good.
18
I ($)
“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
U1
0
A good can be normal over some
ranges and inferior over others
U3
U2
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.
 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.
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…
24
Y (units)
Example:
Normal Good: Income and
Substitution Effects
BL2
Let Px decrease
BL1
A
•
C
•
•
B
U1
Substitution
U2
BLd
Income
0
XA
XB
XC
X (units)
25
Y (units)
Example: Inferior Good: Income and Substitution
Effects
BL2
“X is an inferior good”
•
C
A
•
BL1
U2
•
BLd
B
Income
U1
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 (BL2)
2) The budget line must be tangent to the
old indifference curve (U1)
27
Y (units)
Budget line slopes
Slope of B1 = -Px1/Py
BL2
BL1
Slope of B2 = -Px2/Py
Slope of Bd = -Px2/Py
A
•
C
•
•
B
U1
Substitution
U2
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: xB-xA
b) Income Effect: xC-xB
30
Substitution and Income Effect Example:
Suppose U(x,y) = 2x1/2 + y.
MUx = 1/x1/2 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/x1/2 = Px
31
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
32
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
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/x1/2 = .2
xb=25
U = 2x1/2 + y
12 = 2(25)1/2 + y
yB = 2
Substitution Effect: xB-xA = 25 - 4 = 21
Income Effect: xC-xB = 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)
Example: Giffen Good: Income and
Substitution Effects
BL2
“X is a Giffen good”
C
•
BL1
A
U2
•
Income
•
B
U1
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*
Quantity39
Efficiency of the Equilibrium Quantity
Price
$16
Consumer
Surplus
Consumer Surplus = area of triangle
=1/2bh
=1/2(16-8)(10)
=40
This calculation
Only works for
A linear demand
curve
$8
D
10
Quantity40
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
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 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
•
M
•
BL1
O
C
B
U2
U1
-NM represents the money
required to return a consumer
to their original utility,
consuming at B
BL2
X (units)
44
Equivalent Variation
Y (units)
Q
N
•
D
•A
-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
•
C
U2
-NQ represents the money
equivalent to a price change,
resulting in consumption at D
U1
BL1
O
BL2
X (units)
45
Y (units)
Q
•
N
Compensating and Equivalent Variation
D
•A
M
•
•
BL1
O
B
U2
C
-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
U1
BL2
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.
3a) Compensating Variation:
With ORIGINAL UTILITY and NEW PRICES,
minimize expenditure ECV
CV=I-ECV
3a) Compensating Variation:
With FINAL UTILITY and ORIGINAL PRICES,
minimize expenditure EEV
EV=EEV-I
47
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.
48
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=2Y
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
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 (U1).
•
M
•
BL1
O
C
B
U2
U1
BL2
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
2x/1=2y/1
X=Y
U=x2+y2
80=x2+x2
40=x2
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
PxX+PyY=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
U2
U1
BL1
O
BL2
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
2x/2=2y/1
X=2Y
U=x2+y2
200=4y2+y2
40=y2
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
PxX+PyY=I
2X+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
61
demand
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
63
Sushi
Algebraically the demand curves are as follows:
10  2 P when P  5
QC ( P)  {
0 when P  5
9  3P when P  3
Qk ( P)  {
0 when P  3
These combine to give us :
19  5 P when P  3
Qm ( P )  {10 - 2P when 3  P  5
0 when P  5
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
•
•
•
•
DC
DK
O
2 3
DM
6
9
65
Sushi
P
10
P
P
Q = 10 - p
Q = 10 - p
Q = 30 - 6p
Q = 20 - 5p
4
Consumer 1
Q
Consumer 2
Q
Aggregate demand
Note that at a price of $4,
10-p=30-6P=6
66
Q
 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
67
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 increases with the number of
other consumers, then the externality is positive.
If one person's demand decreases with the number of
other consumers, then the externality is negative.
Examples: Telephone (physical network)
Software (virtual network)
68
•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
69
PX Example: IPads and The Bandwagon Effect
DNew
DOriginal
20
10
Bandwagon Effect (increased
quantity demanded when more
consumers purchase)
•
A
•
B
Pure
Price
Effect
30 38
•
C
Market Demand
Bandwagon Effect
60
X (units)
70
•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
71
PX
Example: The Snob Effect
Market Demand
1200
Snob Effect (decreased
quantity demanded when more
consumers purchase)
•
A
•
•
C
900
B
D10 Cars
D50 Cars
Pure Price Effect
Snob Effect
10
13
18
X (units) 72
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
73
externality.
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
74
= 300
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.)
75
 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?
76
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.
77
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.
max U  U ( y, l )
l
s.t. 24  L  l
s.t. y  Lw
78
Y (units)
600
w=25
480
w=20
360
w=15
240
120
w=10
w=5
Labour and Leisure
As wage is increasing, a consumer’s
maximization may cause him/her to increase
or decrease leisure:
••
•
•
•
O
Leisure (l)
79
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”)
80
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.
81
Daily Income in units of composite good, Y
Example: A Backward Bending Supply of
600
Labor
W=25
480
U5
360
• •A
U3
240
•C
Wage increases from $15 to
$25, causing an increase in
leisure time
W=15 B
Income
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Substitution
12 13 14 15
Substitution Effect (LB-LA)
•24
Leisure (hours)
Income Effect (LC-LB)
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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:
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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.
40
B
•
•
30
0
60
A
80
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.
Food
84
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
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assumed no substitution occurs
CPI
Clothing
40
B
• •
C
•A
30
0
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.
60
80
Food
86
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
87
dollars of increased spending each year
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
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Chapter 5 Key Concepts
Compensating & Equivalent Variation
Market Demand
Externalities
Labor and Leisure
Backwards Bending Labor Supply
Consumer Price Index (CPI)
89