HE9091 Lecture 2 elasticity and consumer

HE9091

Principles of Economics

Lecture 2

Elasticity and Consumer

Behaviour

Tan Khay Boon

Email: [email protected]

Office: HSS-04-25

mailto:[email protected]

Topics

• 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: FBLC, 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

• If price elasticity is greater than 1, demand is

elastic

– Percentage change in quantity is greater than

percentage change in price

– Demand is responsive to price

3


Inelastic

Unit elastic

Elastic

210

Inelastic Demand

• If price elasticity is less than 1, demand is

inelastic

– Percentage change in quantity is less than

percentage change in price

– Quantity demanded is not very responsive to price

3


Inelastic

Unit elastic

Elastic

210

Unit Elastic Demand

• If price elasticity is 1, demand is unit elastic

– Price and quantity change by the same percentage

3


Inelastic

Unit elastic

Elastic

210

Example: Demand for Pizza

Old New % Change

Price $1.00 $0.97 3%

Quantity 400 404 1%



ε =1%

3%= 0.33 Demand is inelastic

Determinants of Price Elasticity

of Demand

• More options, more elastic

Substitution Options

• Large share, more elastic

Budget Share

• Long time to adjust, more elastic

Time

Price Elasticity Notation

• 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 =ΔQ / Q

ΔP / P

ε =ΔQ

Q

P

ΔPx

ε =P

Q

ΔQ

ΔPx

ε =P

Q

1

slopex

P – Δ P

Price

P

D

A

Q Q + Δ Q

Δ Q

Δ P

Quantity

Price Elasticity: Graphical View

• At point A

P = 8

Q = 3

Slope = 20 / 5 = 4

ε =8

3

1

4x = 0.67

P – Δ P

Price

P

D

A

Q Q + Δ Q

Δ Q

Δ P

Quantity

ε =P

Q slope

1x

Price Elasticity and Slope

• When two demand curves cross

• P / Q is same for both curves

• (1 / slope) is

smaller for the

steeper curve

– At the common

point demand

is less price elastic

for the steeper

curve

D1

D2

12

4 6 12

6

4

Quantity

Price

Less Elastic

More Elastic

Price Elasticity on a Straight-

Line Demand Curve

• Price elasticity is different at each point

– Slope is the same for the demand curve

– P/Q decreases as price goes down and quantity

goes up

ε =P

Q

1

slopex

Price Elasticity Pattern

• Price elasticity changes systematically as price goes

down

• At high P and low Q, P / Q is large

• Demand is elastic

• At the midpoint,

demand is unit elastic

• At low P and high Q,

P / Q is small

• Demand is

inelastic

Price

b/2

a/2

a

b

1

1

1

Quantity

Two Special Cases

Perfectly Elastic

Demand

• Infinite price elasticity of

demand

Perfectly Inelastic

Demand

• Zero price elasticity of

demand

Price

Quantity

D

Price

Quantity

D

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 x Q

• Graphing idea: total

expenditure is the area

of a rectangle with height P

and width Q

– Example: P = 2 and

Q = 4

Price

Quantity

D

2

4

Expenditure = 8

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

Quantity (00s of tickets/day)

D

A

Expenditure =

$1,000/day

12

Price (

$/t

icket)

5 6

2


4

D

B

Expenditure =

$1,600/day

12

Price (

$/t

icket)

6

4

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

D

Expenditure =

$1,600/day

12


Price (

$/t

icket)

2 6

8Y

Z

D

Expenditure =

$1,000/day

12


Price (

$/t

icket)

1 6

10

The Effect of a Price Change on

Total ExpenditurePrice $12 $10 $8 $6 $4 $2 $0

Quantity 0 1,000 2,000 3,000 4,000 5,000 6,000

Expenditure $0 $1,000 $1,600 $1,800 $1,600 $1,000 $0

1,800

Price ($/ticket)

Tota

l expenditure

($/d

ay)

2 6 10

1,600

1,000

12


Pri

ce

($

/tic

ke

t)

1 3 4 5 6

10

8

6

4

2

2

Elasticity, Price Change, and

Expenditure

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 corss-

price 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 Cross-

Price Elasticity• Income elasticity of demand:

• Cross-price elasticity of demand:

εI =Percentage change in quantity demanded

Percentage change in Income

εAB =Percentage change in quantity demanded of A

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

Price elasticity of supply =ΔQ / Q

ΔP / P

Price elasticity of supply =P

Q

1

slopex


• If supply curve has a

positive intercept

• Price elasticity of supply

decreases as Q increases

– Graph shows

• Slope = 2

• At A, P = 8 and Q = 2

– Price elasticity of supply

= (8 / 2) (1 / 2) = 2.00

• At B, P = 10 and Q = 3


= (10 / 3) (1 / 2) = 1.672

8A

3

10B

Quantity

Price

4

S


• If supply curve has a zero

intercept

• Price elasticity of supply is

1.00

– Graph shows

• Slope = 1 / 3

• At A, P = 4 and Q = 12


= (4 / 12) (3) = 1.00

• At B, P = 5 and Q = 15


= (5 / 15) (3) = 1.00 15

5B

ΔP

Δ Q

S

12

4A

Quantity

Price

Perfectly Inelastic Supply

• Zero price elasticity of

supply

• No response to

change in price

• Example: land in

Tokyo

• Supply is completely

fixed

• Any one-of-a-kind

item has perfectly

inelastic supply

• Work of art (Mona

Lisa)

• Hope Diamond

Price

Quantity

S

Perfectly Elastic Supply

Infinite price elasticity of

supply

Sell all you can at a fixed

price

Inputs purchased at a

constant price

No volume discounts

Constant proportions of

production

Lemonade example

Cost of production is 14¢ at

all levels of Q

Marginal cost

P = 14¢

Price

Quantity

S

Determinants of Price Elasticity

of Supply

• Uses adaptable inputs, more elastic

Input Flexibility

• Resources move where needed, more elastic

Mobility of Inputs

• Alternative inputs easy to find, more elastic

Produce Substitute Inputs

• Long run, more elasticTime

• 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

The Midpoint Formula for

Elasticity of Demand

P

Q

ΔP

Δ Q

4

3

4 6

The Midpoint Formula for

Elasticity of Demand

• Midpoint formula

– Use average quantity in the numerator

– Use average price in the denominator

• Elasticity using midpoint

formula is 1.40

ΔQ / [(QA + QB)/2]

Δ P / [(PA + PB)/2]ε =

Δ Q / (QA + QB)

Δ P / (PA + PB)ε =

P

Q

ΔP

Δ Q

4

3

4 6

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 CreamCones /

Hour0 1 2 3 4 5 6

Total Utility 0 50 90 120 140 150 140

Cones/hour

Utils

/hou

r

1 3 4 5 62

150140

120

90

50

Sarah's Marginal Utility from Ice

Cream

• Marginal utility: the additional utility from

consuming one more

Cones /

Hour0 1 2 3 4 5 6

Total Utility 0 50 90 120 140 150 140

Marginal Utility 50 40 30 20 10 -10

Marginal utility = Change in utility

Change in consumption

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

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

Spending on Two Goods

• Assume a fixed budget

• Decide how much of each

good to buy

• 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

Ma

rgin

al U

tilit

y

Ma

rgin

al U

tility

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

• $400 budget

• Chocolate is $2 per pint

• Vanilla is $1 per pint

• Buy 200 pints of vanilla

and 100 pints of

chocolate

• Marginal utility is 12 for

vanilla, 16 for chocolate

Pints/yr

Vanilla

Ice Cream

12

200

MU

(u

tils

/ pin

t)

Chocolate

Ice Cream

Pints/yr

16

100

MU

(u

tils

/ pin

t)

Sarah's Next Step

• Increase vanilla by 100

• Reduce chocolate by 50

• Marginal utility of vanilla is 8

• Marginal utility of chocolate

is 24

Chocolate

Ice Cream

Pints/yr

16

100M

U (u

tils

/ pin

t)50

24

Pints/yr

Vanilla

Ice Cream

200

MU

(u

tils

/ pin

t)

300

8

12

Sarah's Equilibrium

• Optimal combination:

highest total utility

• 250 pints vanilla; 75 pints

chocolate

• Marginal utility / price is

the same for all goods

• Marginal utility of vanilla

10, chocolate 20

MU

(u

tils

/ pin

t)

Pints/yr

Vanilla

Ice Cream

250

10

MU

(u

tils

/ pin

t)

Chocolate

Ice Cream

Pints/yr

20

75

Sarah's ChoicesScenario

1Price Quantity

Marginal

Utility MU / $

Vanilla $1 200 12 12

Chocolate $2 100 16 8

Scenario

2Price Quantity

Marginal

Utility MU / $

Vanilla $1 300 8 8


Scenario

3Price Quantity

Marginal

Utility MU / $

Vanilla $1 250 10 10


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• 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 on vanilla, the amount

she can buy goes down by half

– 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 surplusD

Units/day

Marg

inal utilit

y

(utils

/ pin

t)1

2

3

4

5

6

7

8

9

10

11

12

2 4 6 8 10 12

Vanilla Ice Cream

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

D

Units/day

Marg

inal utilit

y

(utils

/ pin

t)1

2

3

4

5

6

7

8

9

10

11

12

2 4 6 8 10 12

Vanilla Ice Cream

Consumer Surplus for Milk

• Consider the market

demand and supply of

milk

– 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

Quantity (000s of liters/day)

Price (

$/liter)

1

1.00

2.00

3.00

2 3 4 5 6

S

D

Consumer Surplus for Milk

• Price is $2 and quantity

is 4,000 liters per day

• Consumer surplus is the

area of the triangle

between:

• 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

Quantity (000s of liter/day)

Price (

$/liter)

1

1.00

2.00

3.00

2 3 4 5 6

S

D

Consumer

Surplus

Individual supplier: Harry's

Supply CurveReservation

Price (¢)

Number of

Cans (000s)

1 6

1.5 10

2 13

3 15

6 16

Recycled cans

(100s of cans/day)D

eposit (

cents

/can)

6 10 13 16

6

3

2

1

Individual and Market Supply

Curves• Two suppliers: Harry and Barry

Recycled cans

(00s of cans/day)

Deposit (

cents

/can)

Harry’s Supply Curve

Recycled cans

(00s of cans/day)

Barry’s Supply Curve

Recycled cans

(00s of cans/day)

016

6

16

6

32

6

6

1

6

1

12

1

10

1.5 1.5

10 20

1.5

13

3

2

15

13

3

2

15

26

3

2

30

Market Supply Curve

Producer Surplus• Producer surplus is the difference between the

market price and the seller's reservation price

• Reservation price = Marginal cost which is on the

supply curve

• Producer surplus is the area above the supply

curve and below the market price

HE9091 Lecture 2 elasticity and consumer

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