HE9091
Principles of Economics
Lecture 2
Elasticity and Consumer
Behaviour
Tan Khay Boon
Email: khayboon@ntu.edu.sg
Topics
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Price Elasticity of Demand
Income Elasticity of Demand
Cross-Price Elasticity of Demand
Price Elasticity of Supply
Total Utility and Marginal Utility
The Rational Spending Rule
Demand and Consumer Surplus
Supply and Producer Surplus
Reference: FBAH or FBL, chapters 4, 5 & 6
Price Elasticity of Demand
• Price elasticity of demand is defined as the
percentage change in quantity demanded from a
1% change in price
– Measure of responsiveness of quantity demanded
to changes in price
• Example:
– Price of beef decreases 1%
– Quantity of beef demanded
increases 2%
– Price elasticity of demand is – 2
P
Q
Calculate Price Elasticity
• Symbol for elasticity is ε
– Lower case Greek letter epsilon
• For small percentage changes in price
ε=
Percentage change in quantity demanded
Percentage change in price
 Price elasticity of demand is always negative
 Ignore the sign and consider the absolute value when
interpreting price elasticity of demand
Elastic Demand
Price Elasticity of Demand
Unit elastic
Elastic
Inelastic
0
1
2
3
• If price elasticity is greater than 1 in absolute
value, demand is elastic
– Percentage change in quantity is greater than
percentage change in price
– Demand is responsive to price
Inelastic Demand
Price Elasticity of Demand
Unit elastic
Elastic
Inelastic
0
1
2
3
• If price elasticity is less than 1 in absolute value,
demand is inelastic
– Percentage change in quantity is less than
percentage change in price
– Quantity demanded is not very responsive to price
Unit Elastic Demand
Price Elasticity of Demand
Unit elastic
Elastic
Inelastic
0
1
2
3
• If price elasticity is 1 in absolute value, demand
is unit elastic
– Price and quantity change by the same percentage
Example: Demand for Pizza
Price
Quantity
ε=
ε=
Old
$1.00
400
New
$0.97
404
% Change
3%
1%
Percentage change in quantity demanded
Percentage change in price
1%
-3%
= -0.33
Demand is inelastic
Determinants of Price Elasticity
of Demand
Substitution
Options
• More options, more
elastic
Budget Share
• Large share, more
elastic
Time
• Long time to adjust,
more elastic
Price Elasticity Notation
ε=
Percentage change in quantity demanded
Percentage change in price
• ΔQ is the change in quantity
– ΔQ / Q is percentage change in quantity
• ΔP is change in price
– ΔP / P is percentage change in price
ε=
ΔQ / Q
ΔP / P
Price Elasticity: Graphical View
ε=
ε=
ε=
ΔP / P
ΔQ
x
Q
P
x
P
ΔQ
ΔP
P
1
Q
slope
A
P
ΔP
Q
x
Price
ε=
ΔQ / Q
ΔP
P–ΔP
ΔQ
D
Q Q+ΔQ
Quantity
Price Elasticity: Graphical View
P=8
Q=3
Slope = 20 / 5 = 4
ε=
P
x
Q
ε=
8
3
1
Price
• At point A
A
P
ΔP
P–ΔP
ΔQ
D
slope
x
1
4
= 0.67
Q Q+ΔQ
Quantity
Price Elasticity and Slope
• When two demand curves cross
– At the common
point demand
is less price elastic
for the steeper
curve
Price
• P / Q is same for both curves
• (1 / slope) is
12
smaller for the
steeper curve
D1
Less Elastic
More Elastic
6
4
D2
4
6
Quantity
12
Price Elasticity on a StraightLine Demand Curve
• Price elasticity is different at each point
ε=
P
Q
x
1
slope
– Slope is the same for the demand curve
– P/Q decreases as price goes down and quantity
goes up
Price Elasticity Pattern
• Price elasticity changes systematically as price goes
down
• At high P and low Q, P / Q is large
• Demand is elastic
• Demand is
inelastic
a
Price
• At the midpoint,
demand is unit elastic
• At low P and high Q,
P / Q is small
 1
 1
 1
a/2
b/2
Quantity
b
Two Special Cases
Perfectly Elastic
Demand
Perfectly Inelastic
Demand
• Infinite price elasticity of
demand
• Zero price elasticity of
demand
Price
Price
D
D
Quantity
Quantity
Elasticity and Total Expenditure`
• When price increases, total expenditure can
increase, decrease or remain the same
– The change in expenditure depends on elasticity
• Terminology: total expenditure = total
revenue
– Calculate as P Q
• Graphing idea: total
expenditure is the area
of a rectangle with height P
and width Q
– Example: P = 2 and
Q=4
x
Price
Expenditure = 8
2
D
4
Quantity
Price Elasticity and Total
Expenditure
• Movie ticket price increases from $2 to $4
– A and B are both below the midpoint of the curve
• Inelastic portion of the demand curve
– Total revenue increases when price increases
D
12
Expenditure =
$1,000/day
Price ($/ticket)
Price ($/ticket)
12
A
2
5
6
Quantity (00s of tickets/day)
D
Expenditure =
$1,600/day
B
4
4
6
Quantity (00s of tickets/day)
Price Elasticity and Total
Expenditure
• Movie ticket price increases from $8 to $10
– Prices are both above the midpoint of the curve
• Elastic portion of the demand curve
– Total revenue decreases
8
Y Expenditure =
$1,600/day
D
2
6
Quantity (00s of tickets/day)
Price ($/ticket)
Price ($/ticket)
12
12
10
Z
Expenditure =
$1,000/day
D
1
6
Quantity (00s of tickets/day)
The Effect of a Price Change on
Total Expenditure
Price
$12
$10
$8
$6
$4
$2
$0
Quantity
0
100
200
300
400
500
600
Expenditure
$0
Total expenditure ($/day)
$1,000 $1,600 $1,800 $1,600 $1,000
12
Price ($/ticket)
10
8
6
4
2
1
3
4
5
6
2
Quantity (00s of tickets/day)
$0
1,800
1,600
1,000
2
6
Price ($/ticket)
10
Elasticity, Price Change, and
Expenditure
The Midpoint Formula for
Elasticity of Demand
• Elasticity is different at each point on the demand
curve
• Compare 2 points and get 2 answers
– Depends on which point is the starting point
• Start at A and elasticity is 2
• Start at B and elasticity is 1
– A more stable solution is
needed
• Use the midpoint formula
P
4
3
ΔP
ΔQ
4
6
Q
The Midpoint Formula for
Elasticity of Demand
• Midpoint formula
– Use average quantity in the numerator
– Use average price in the denominator
ε=
ε=
ΔQ / [(QA + QB)/2]
Δ P / [(PA + PB)/2]
Δ Q / (QA + QB)
Δ P / (PA + PB)
• Elasticity using midpoint
formula is 1.40
P
4
3
ΔP
ΔQ
4
6
Q
Cross-Price Elasticity of Demand
• Substitutes and complements affect demand
• Cross-price elasticity of demand is defined
as the percentage change in quantity
demanded of good A from a 1 percent change
in the price of good B
• Sign of cross-price elasticity shows
relationship between the goods
– Complements have negative cross-price elasticity
– Substitutes have positive cross-price elasticity
– Do not ignore the sign when interpreting crossprice elasticity of demand
Income Elasticity of Demand
• Income elasticity of demand is defined as
the percentage change in quantity demanded
from a 1 percent change in income
• Income elasticity of demand can be positive or
negative
– Positive income elasticity is a normal good
– Negative income elasticity is an inferior good
– Do not ignore the sign when interpreting income
elasticity of demand
Calculate Income and CrossPrice Elasticity
• Income elasticity of demand:
Percentage change in quantity demanded
εI =
Percentage change in Income
• Cross-price elasticity of demand:
Percentage change in quantity demanded of A
εAB =
Percentage change in Price of B
Price Elasticity of Supply
• Price elasticity of supply
– Percentage change in quantity supplied from a
1 percent change in price
ΔQ / Q
Price elasticity of supply =
Price elasticity of supply =
P
Q
ΔP / P
x
1
slope
Price Elasticity of Supply
• If supply curve has a
positive intercept
– Price elasticity of supply
= (8 / 2) (1 / 2) = 2.00
B
10
8
A
Price
• Price elasticity of supply
decreases as Q increases
– Graph shows
• Slope = 2
• At A, P = 8 and Q = 2
S
4
• At B, P = 10 and Q = 3
– Price elasticity of supply
= (10 / 3) (1 / 2) = 1.67
2
Quantity
3
Price Elasticity of Supply
• If supply curve has a zero
intercept
B
5
4
Price
• Price elasticity of supply is
1.00
– Graph shows
• Slope = 1 / 3
• At A, P = 4 and Q = 12
S
ΔP
A
ΔQ
– Price elasticity of supply
= (4 / 12) (3) = 1.00
• At B, P = 5 and Q = 15
– Price elasticity of supply
= (5 / 15) (3) = 1.00
12
Quantity
15
Perfectly Inelastic and Elastic
Supply
• Zero price elasticity of
supply
 Infinite price elasticity
of supply
• No response to change in
price
 Sell all you can at a fixed
price
Price
Price
S
S
Quantity
Quantity
Determinants of Price Elasticity
of Supply
Input Flexibility
• Uses adaptable inputs, more
elastic
• Resources move where
Mobility of Inputs
needed, more elastic
• Alternative inputs easy to find,
Produce
Substitute Inputs
more elastic
Time
• Long run, more elastic
Needs versus Wants
• Some goods are required for subsistence
– These are needs
• Beyond subsistence, behavior is driven by wants
– Rice or noodle
– Hamburger or chicken sandwich
• Wants depend on price
• Unlimited wants with limited resources means
consumers have to prioritize wants when making
choices.
Wants and Utility
• Utility: the satisfaction people derive from
consumption
– Well-being, happiness
– Measured indirectly
• Subjective
• Observable
– Cannot be compared between people
• Individual goal is to maximize utility
– Allocate resources accordingly
Sarah's Utility from Ice Cream
Utils/hour
Cones /
Hour
Total Utility
0
1
2
0
50
90
3
4
5
120 140 150 140
150
140
120
90
50
1
2
6
3
4
Cones/hour
5
6
Sarah's Marginal Utility from Ice
Cream
Cones /
Hour
Total Utility
Marginal Utility
0
1
2
3
4
5
6
0
50
90
120
140
150
140
50
40
30
20
10
• Marginal utility: the additional utility from
consuming one more
Change in utility
Marginal utility =
Change in consumption
-10
Diminishing Marginal Utility
Law of Diminishing Marginal Utility
Tendency for additional utility gained
from consuming an additional unit of a good
to decrease as consumption increases
beyond some point
Diminishing Marginal Utility
• Marginal utility can increase at low levels of
consumption
– First unit stimulates your desire for more
• First unit of food/drinks
• Eventually marginal utility declines
– Continue consuming
• Apply Cost-Benefit Principle
– Consume an additional unit as long as the marginal
utility (benefit) is greater than the marginal cost
• Law of Diminishing
Marginal Utility applies
– As you buy more of a single
good, its marginal utility
decreases
– When you buy less of that
good, its marginal utility
increases
Marginal Utility
• Assume a fixed budget
• Decide how much of each
good to buy
Marginal Utility
Spending on Two Goods
Budget Allocation
• Maximize utility when the marginal utility per
dollar spent is the same for all goods
• No Money Left On the Table Principle
– Current spending has marginal utility of a dollar spent
on one good higher than the marginal utility of a
dollar spent on the other good
– Take a dollar away from the good with low marginal
utility and spend it on the good with high marginal
utility
• Marginal utilities per dollar begin to equalize
Sarah's Ice Cream
• Budget = $400, Chocolate = $2 per pint, Vanilla = $1 per pint
• Buy 200 pints of vanilla and 100 pints of chocolate
Vanilla
Ice Cream
12
200
Pints/yr
MU (utils/ pint)
Marginal utility is 12 for vanilla, 16 for chocolate
MU per $ for vanilla = 12/1 = 12
MU per $ for chocolate = 16/2 = 8
Buy more vanilla and buy less chocolate
MU (utils/ pint)
•
•
•
•
Chocolate
Ice Cream
16
100
Pints/yr
Sarah's Next Step
Increase vanilla by 100 and reduce chocolate by 50
Marginal utility of vanilla is 8, MU per $ = 8/1 = 8
Marginal utility of chocolate is 24, MU per $ = 24/2 = 12
Buy more chocolate and buy less vanilla
Vanilla
Ice Cream
MU (utils/ pint)
MU (utils/ pint)
•
•
•
•
12
8
200
Pints/yr
300
24
Chocolate
Ice Cream
16
50
100
Pints/yr
Sarah's Equilibrium
• Optimal combination: highest total utility
• 250 pints vanilla; 75 pints chocolate
• Marginal utility / price is the same for all goods
Vanilla
Ice Cream
10
250
Pints/yr
MU (utils/ pint)
MU (utils/ pint)
• Marginal utility of vanilla = 10, MU per $ = 10/1 = 10
• Marginal utility of , chocolate 20, MU per $ = 20/2 = 10
Chocolate
Ice Cream
20
75
Pints/yr
Sarah's Choices
Scenario
1
Vanilla
Chocolate
Scenario
2
Vanilla
Chocolate
Scenario
3
Vanilla
Chocolate
Price
Quantity
$1
$2
200
100
Price
Quantity
$1
$2
300
50
Price
Quantity
$1
$2
250
75
Marginal
Utility
12
16
Marginal
Utility
8
24
Marginal
Utility
10
20
MU / $
12
8
MU / $
8
12
MU / $
10
10
Rational Spending Rule
The Rational Spending Rule
Spending should be allocated across goods so that
the marginal utility per dollar
is the same for each good
Rational Spending Rule
• Rational Spending Rule can be written
algebraically
• Notation
–
–
–
–
MUC is the marginal utility from chocolate
MUV is the marginal utility from vanilla
PC is the price of chocolate
PV is the price of vanilla
• Rational Spending Rule
MUC / PC = MUV / PV
• The marginal utility per dollar spent on chocolate
equals the marginal utility per dollar spent on
vanilla
Substitution Effect
• When the price of a good goes up, substitutes for
that good are relatively more attractive
– At the higher price less is demanded because some
buyers switch to the substitute good
– If the price of vanilla ice cream goes up, some buyers
will buy less vanilla and more chocolate
Income Effect
• Changes in price affect the buyers' purchasing
power
– Acts like a change in income
• Suppose vanilla ice cream goes from $1 per pint
to $2
– If Sarah spends all her income $400 on vanilla, the
amount she can buy goes down by half.
– Real income in terms of vanilla decreases
– At the original prices, she could buy 100 pints of
vanilla and 150 pints of chocolate
• At new price for vanilla, she buys 100 vanilla and only
100 chocolate
Rational Spending and Price
Changes
• Suppose price of vanilla increases from $1 to $2
• At the original equilibrium
MUC / PC = MUV / PV
• With the increase in PV, MUV / PV < MUC / PC
– If Sarah buys more chocolate, MUC will go down
– If Sarah buys less vanilla, MUV will go up
– To get to a new optimal spending point,
• Buy more chocolate
• Buy less vanilla
• Stop when the marginal utility per dollar is the same
Chocolate Ice Cream Price
Goes Down
• Originally: $400 budget, $1 per pint for vanilla,
and $2 per pint for chocolate
– What if chocolate is now $1 per pint?
• With the decrease in PC,
MUV / PV < MUC / PC
– If Sarah buys more chocolate, MUC will go down
– If Sarah buys less vanilla, MUV will go up
– To get to a new optimal spending point,
• Buy more chocolate
• Buy less vanilla
• Stop when marginal utility per dollar is the same
Market and Social Welfare
• Market is the aggregation of individual consumer
demand and producer supply
• Consumers and producers are able to acquire
welfare from consumption and production of
products in the market
• Welfare of the society (Economic surplus) is
obtained by the sum of the consumers and
producers welfare
• Economic surplus = Consumer surplus +
producer surplus
Individual and Market Demand
Curves
• The market demand is the horizontal sum of
individual demand curves
– At each possible price, add up the number of units
demanded by individuals to get the market demand
Smith
Jones
Market
Consumer Surplus
• Consumer surplus is the difference between
the buyer's reservation price and the market
price
• With multiple buyers
– Find the consumer surplus for each buyer
– Add up the individual surplus for each buyer
Consumer Surplus on a Graph
• When a product is sold in
whole units, the demand
curve is a stair-step
function
– If the market supplied only
one unit, the maximum price
would be $11
• For the second unit, the
price is $10, and so on
• The last buyer gets no
consumer surplus
Price
12
11
10
9
8
7
6
Vanilla Ice Cream
5
4
3
2
1
D
2
4
6
8
Units/day
10
12
Consumer Surplus on a Graph
• Market price is $6 for all
sales
• Total consumer surplus
• The first sale generates $5
of consumer surplus
– Reservation price of $11
minus the price of $6
• Selling the second unit has
$4 of consumer surplus,
and so on
• Total consumer surplus
is the area under the
demand curve and
above market price
Price
Vanilla Ice Cream
12
11
10
9
8
7
6
5
4
3
2
1
D
2
4
6
8
Units/day
10
12
Consumer Surplus for Milk
• Consider the market
demand and supply of
milk
Price ($/liter)
– The equilibrium price is $2
per liter
– The equilibrium quantity is
4,000 liters per day
• Last customer pays his
reservation price and gets
no consumer surplus
S
3.00
2.00
D
1.00
1
2
3
4
5
6
Quantity (000s of liters/day)
Consumer Surplus for Milk
• Horizontal intercept of
demand
• Market price
• Market quantity
– Remember: area of a right
triangle is ½ base times
height
• The area is
½ (4,000 liter)($1) = $2,000
Consumer
Surplus
3.00
Price ($/liter)
• Price is $2 and quantity
is 4,000 liters per day
• Consumer surplus is the
area of the triangle
between:
S
2.00
D
1.00
1
2
3
4
5
6
Quantity (000s of liter/day)
Reservation Number of
Price (¢)
Cans (000s)
1
1.5
2
3
6
6
10
13
15
16
Deposit (cents/can)
Individual supplier: Harry's
Supply Curve
6
3
2
1
6
10 13 16
Recycled cans
(100s of cans/day)
Individual and Market Supply
Curves
• Two suppliers: Harry and Barry
Deposit (cents/can)
Harry’s Supply Curve
1.5
Barry’s Supply Curve
Market Supply Curve
6
6
6
3
3
3
2
2
1.5
1
2
1
10 13 16
15
Recycled cans
(00s of cans/day)
6
1.5
10 13 16
15
Recycled cans
(00s of cans/day)
6
1
0
12 20 26
Recycled cans
(00s of cans/day)
32
30
Producer Surplus
• Producer surplus is the difference between the
market price and the seller's reservation price
• Reservation price = Marginal cost which is the
supply curve
• Producer surplus is the area above the supply
curve and below the market price