Chapter 2: Fundamentals of Welfare Economics -In order to evaluate government policies, we need a...

Chapter 2: Fundamentals Chapter 2: Fundamentals of Welfare Economicsof Welfare Economics-In order to evaluate government -In order to evaluate government

policies, we need a general frameworkpolicies, we need a general framework

-We can’t evaluate each policy on a -We can’t evaluate each policy on a case-by-case basiscase-by-case basis-ie: Lower interest rates lowers -ie: Lower interest rates lowers unemployment, then raising minimum wage unemployment, then raising minimum wage increases unemployment (counter-increases unemployment (counter-productive)productive)

-Welfare Economics – the branch of economic -Welfare Economics – the branch of economic theory concerned with the social desirability theory concerned with the social desirability of alternate economic states and policiesof alternate economic states and policies

Chapter 2: Fundamentals Chapter 2: Fundamentals of Welfare Economicsof Welfare Economics

Welfare EconomicsWelfare Economics First Fundamental Theorem of First Fundamental Theorem of

Welfare EconomicsWelfare Economics Second Fundamental Theorem of Second Fundamental Theorem of

Welfare EconomicsWelfare Economics

33

Starting Point: Starting Point: Pure Exchange Pure Exchange

EconomyEconomy We start with a simple model:We start with a simple model:

– 2 people2 people– 2 goods, each of fixed quantity2 goods, each of fixed quantity– Determine good allocationDetermine good allocation

The important results of this The important results of this simple, 2-person model hold in simple, 2-person model hold in more real-world cases of many more real-world cases of many people and many commoditiespeople and many commodities

44

Pure Exchange Pure Exchange Economy ExampleEconomy Example

Two people: Maka and SusanTwo people: Maka and Susan Two goods: Food (f) & Video Games (V)Two goods: Food (f) & Video Games (V) We put Maka on the origin, with the y-We put Maka on the origin, with the y-

axis representing food and the x axis axis representing food and the x axis representing video gamesrepresenting video games

If we connect a “flipped” graph of If we connect a “flipped” graph of Susan’s goods, we get an EDGEWORTH Susan’s goods, we get an EDGEWORTH BOX, where y is all the food available BOX, where y is all the food available and x is all the video games: and x is all the video games:

55

Maka’s Goods GraphMaka’s Goods Graph

Video Games

Foo

d

u

O xMaka

Ou is Maka’s food, and Ox Is Maka’s Video Games

66

Edgeworth BoxEdgeworth Box

Video Games

Foo

d

u

O xMaka

O’w is Susan’s food, and O’y is Susan’s Video Games

w

ry O’

Susan

s

Total food in the market is Or(=O’s) and total Video Games is Os (=O’r)

Each point in the Edgeworth Box represents one possible good allocation

77

Edgeworth and utilityEdgeworth and utility

We can then add INDIFFERENCE curves We can then add INDIFFERENCE curves to Maka’s graph (each curve indicating to Maka’s graph (each curve indicating all combinations of goods with the same all combinations of goods with the same utility) utility) – Curves farther from O have a greater utilityCurves farther from O have a greater utility– (For a review of indifference curves, refer to (For a review of indifference curves, refer to

Intermediate Microeconomics)Intermediate Microeconomics) We can then superimpose Susan’s utility We can then superimpose Susan’s utility

curvescurves– Curves farther from O’ have a greater utilityCurves farther from O’ have a greater utility

88

Maka’s Utility CurvesMaka’s Utility Curves

Video Games

Foo

d

OMaka

Maka’s utility is greatest at M3

M1

M2

M3

99

Edgeworth Box and Edgeworth Box and UtilityUtility

Video Games

Foo

d

OMaka

Susan has the highest utility at S3

r O’

Susan

s

At point A, Maka has utility of M3 and Susan has Utility of S2

M1

M2

M3

S1

S2

S3

A

1010

Edgeworth Box and Edgeworth Box and UtilityUtility

Video Games

Foo

d

OMaka

If consumption is at A, Maka has utility M1 while Susan has utility S3

r O’

Susan

s

By moving to point B and then point C, Maka’s utility increases while Susan’s remains constant

M1M2

M3

S3A B

C

1111

Pareto EfficiencyPareto Efficiency

Video Games

Foo

d

OMaka

Point C, where the indifference curves barely touch is called PARETO EFFICIENT, as one person can’t be made better off without harming the other.

r O’

Susan

s

M1M2

M3

S3C

1212


When an allocation is NOT pareto When an allocation is NOT pareto efficient, it is wasteful (at least one efficient, it is wasteful (at least one person could be made better off)person could be made better off)– Pareto efficiency evaluates the desirability of an Pareto efficiency evaluates the desirability of an

allocationallocation A PARETO IMPROVEMENT makes one person A PARETO IMPROVEMENT makes one person

better off without making anyone else worth better off without making anyone else worth off (like the move from A to C)off (like the move from A to C)

However, there may be more than one pareto However, there may be more than one pareto improvement:improvement:

1313


Video Games

Foo

d

OMaka

If we start at point A:-C is a pareto improvement that makes Maka better off-D is a pareto improvement that makes Susan better off-E is a pareto improvement that makes both better off

r O’

Susan

s

M1M2

M3

S3C

S5

S4

A

D

E

1414

The Contract CurveThe Contract Curve Assuming any possible starting point, we can Assuming any possible starting point, we can

find all possible pareto efficient points and find all possible pareto efficient points and join them to create a CONTRACT CURVEjoin them to create a CONTRACT CURVE

All along the contract curve, opposing All along the contract curve, opposing indifferent curves are TANGENT to each indifferent curves are TANGENT to each otherother

Since the slope of the indifference curve is Since the slope of the indifference curve is the willingness to trade, or MARGINAL RATE the willingness to trade, or MARGINAL RATE OF SUBSTITUTION (x for y) (MRSOF SUBSTITUTION (x for y) (MRSxyxy), along ), along this contract curve:this contract curve: Susan

VfMakaVf MRSMRS

Pareto Efficiency Condition

1515

The Contract CurveThe Contract Curve

Video Games

Foo

d

OMaka

r O’

Susan

s

1616

Starting Point:Starting Point:Economy with Economy with

productionproduction A production economy can be analyzed A production economy can be analyzed using the PRODUCTION POSSIBILITIES using the PRODUCTION POSSIBILITIES CURVE/FRONTIERCURVE/FRONTIER– The PPC shows all combinations of 2 goods The PPC shows all combinations of 2 goods

that can be produced using available inputsthat can be produced using available inputs– The slope of the PPC shows how much of The slope of the PPC shows how much of

one good must be sacrificed to produce one good must be sacrificed to produce more of the other good, or MARGINAL RATE more of the other good, or MARGINAL RATE OF TRANSFORMATION (x for y) (MRTSOF TRANSFORMATION (x for y) (MRTSxyxy))

Note that although the slope is negative, the negative is assumed and Note that although the slope is negative, the negative is assumed and rarely shown in simple calculationsrarely shown in simple calculations

1717

Production Possibilities Production Possibilities CurveCurve

Rob

ots

Pizzas

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8

9

10

Here the MRTSpr is equal to (7-5)/(2-1)=-2, or two robots must be given up for an extra pizza.

The marginal cost of the 3rd pizza, or MCp=2 robots

The marginal cost of the 6th and 7th robots, or MCr=1 pizza

Therefore, MRTSxy=MCx/MCy

Therefore, MRTSpr=2/1=2

1818

Efficiency and Efficiency and ProductionProduction

If production is possible in an economy, If production is possible in an economy, the Pareto efficiency condition becomes:the Pareto efficiency condition becomes:

PersonBxy

PersonAxyxy MRSMRSMRT

Assume that MRT>MRS. A person could Assume that MRT>MRS. A person could transform x into y at the rate of MRS and transform x into y at the rate of MRS and have x left over, thus increasing his have x left over, thus increasing his utilityutility

Assume that MRT<MRS. A person could Assume that MRT<MRS. A person could transform y in x at the rate of MRS and transform y in x at the rate of MRS and have y left over, thus increasing utilityhave y left over, thus increasing utility

Pareto Efficiency cannot occur at Pareto Efficiency cannot occur at inequalityinequality

1919

Efficiency & Production Efficiency & Production ExampleExample

Assume MRTAssume MRTprpr=3/4 and MRS=3/4 and MRSprpr=2/4.=2/4.– Therefore Maka could get 3 more robots by transforming 4 pizzasTherefore Maka could get 3 more robots by transforming 4 pizzas– BUT Maka only needs to get 2 robots for 4 pizzas to maintain utilityBUT Maka only needs to get 2 robots for 4 pizzas to maintain utility– Therefore his utility increases from the extra robot, Pareto efficiency isn’t achievedTherefore his utility increases from the extra robot, Pareto efficiency isn’t achieved

We can therefore reinterpret Pareto efficiency as:We can therefore reinterpret Pareto efficiency as:

PersonBxy

PersonAxy

y

x MRSMRSMC

MC

2020

First Fundamental First Fundamental Theorem Of Welfare Theorem Of Welfare

EconomicsEconomicsIFIF

1)1) All consumers and producers act as All consumers and producers act as perfect competitors (no one has market perfect competitors (no one has market power)power)

andand2) 2) A market exists for each and every A market exists for each and every

commoditycommodityThenThen

Resource allocation is Pareto Resource allocation is Pareto EfficientEfficient

2121

First Fundamental Theorem First Fundamental Theorem of Welfare Economics of Welfare Economics

OriginsOrigins From microeconomic consumer theory, From microeconomic consumer theory, we know that:we know that:

y

xPersonAxy P

PMRS

Since this holds true for all people:Since this holds true for all people:PersonBxy

PersonAxy MRSMRS

Which is the first requirement for Pareto Which is the first requirement for Pareto efficiency, before production is efficiency, before production is consideredconsidered

2222


OriginsOrigins From basic economic theory, a perfect competitive From basic economic theory, a perfect competitive firm produces where P=MC, therefore:firm produces where P=MC, therefore:

y

x

y

x

P

P

MC

MC

But we know that MRT is the ratio of But we know that MRT is the ratio of MC’s, therefore:MC’s, therefore:

y

xxy P

PMRT

2323


OriginsOrigins Again from microeconomic consumer Again from microeconomic consumer theory, this changes to:theory, this changes to:

But we know that MRT is the ratio of But we know that MRT is the ratio of MC’s, therefore:MC’s, therefore:

y

xxy P

PMRT

2424

The Law of DemandThe Law of Demand There is an inverse relationship There is an inverse relationship

between the quantity of anything that between the quantity of anything that people will want to purchase and the people will want to purchase and the price they must pay to obtain it:price they must pay to obtain it:

ceteris paribus (all else held equal)ceteris paribus (all else held equal)

This causes demand curves to be This causes demand curves to be downward slopingdownward sloping

When prices increase, people buy When prices increase, people buy lessless

When prices decrease, people buy When prices decrease, people buy moremore

2525

Price/Unit

$

Qn/yr

A B C D E

5.00 4.00 3.00 2.00 1.00

10 20 30 40 50

The Individual’s Demand Schedule

Number of Songs per Year

Pric

e of

Son

gs (

$)

1

2

3

4

5

10 20 30 40 500

A

B

C

D

E

Change in PriceMovement alongthe Demand

2626

Note:Note:We always graph P on vertical axis and Q on horizontal axis, but we write demand as Q as a function of P… If P is written as function of Q, it is called the inverse demand:

Normal Form: Qd=100-2PInverse form: P =50 - Qd/2

Markets defined by commodity, geography, time.

2727

Movement Along Movement Along Demand/Demand/ Changes in Quantity DemandedChanges in Quantity Demanded

A A change in a good’s own pricechange in a good’s own price

– results in a results in a change in quantity change in quantity demandeddemanded

– the same thing as a the same thing as a movement movement alongalong the same demand curve. the same demand curve.

2828

Shifts/Changes in Shifts/Changes in Demand*Demand*

AA change inchange in one or more of theone or more of the non-price determinantsnon-price determinants of of demand (income, tastes, etc)demand (income, tastes, etc)– results in aresults in a change inchange in demanddemand * *

– also called aalso called a shift in demand*shift in demand*

*The whole demand schedule

2929

A Shift in the Demand A Shift in the Demand CurveCurve

Quantity of Songs Demanded

Pric

e of

Son

gs (

$)

1

2

3

4

5

20 30 40 50 600 8070

D1D3

Decrease in Demand

Suppose universitiesoutlaw the use of MP3 Players

D2

Increase in Demand

Suppose the federalgovernment givesevery student a SanDisk MP3 player

3030

““Everything Else” : Everything Else” : The “Determinants”/ The “Determinants”/ “Shifters” “Shifters” of “Demand”of “Demand” Factors other than Factors other than Price which affect Price which affect “Demand” : “Demand” :

1) Income, wealth1) Income, wealth 2) Tastes and 2) Tastes and

preferencespreferences 3) The price of 3) The price of

related goodsrelated goods– ComplementsComplements– SubstitutesSubstitutes

4) Expectations4) Expectations– Future pricesFuture prices– IncomeIncome– Product availabilityProduct availability

5) Population (market 5) Population (market size)size)

What movement would these What movement would these factors cause?factors cause?

3131

Review of Demand Review of Demand TerminologyTerminology DemandDemand: a schedule of quantities : a schedule of quantities

that will be bought/unit of time, at that will be bought/unit of time, at various prices, ceteris paribus.various prices, ceteris paribus.

Quantity DemandedQuantity Demanded:: a specific a specific amount that will be demanded /unit of amount that will be demanded /unit of time at a specific price, ceteris time at a specific price, ceteris paribus. paribus.

There is a difference between There is a difference between between a between a change in the Quantity change in the Quantity DemandedDemanded and a and a shift in Demand.shift in Demand.

3232

Shift vrs. MovementShift vrs. Movement

Pric

e of

Cig

aret

tes,

per

pac

k

Number of Cigarettes smoked per day

10 20

$2

$4

A tax raises the price of cigarettes, resulting in amovement along the demand curve

A policy to discouragesmoking (no smoking inpublic buildings) shiftsthe demand curve left

Pric

e of

Cig

aret

tes,

per

pac

k

Number of Cigarettes smoked per day

10 20

$2

DD’ D

3333

Normal vrs. Inferior GoodsNormal vrs. Inferior GoodsFor normal goods, Demand decreasesWith income

Pric

e of

Chi

cken

Chicken eaten in a month10 20

$2

DD’

Pric

e of

Kra

ft D

inne

r

Kraft Dinner eaten in a month

10 20

$2

D

For inferior goods, Demand increasesWhen income decrease

D’

30

3434

Supply: ProfitSupply: Profit

The The CostCost side of the profitside of the profit equation depends on theequation depends on the Costs Costs of Productionof Production which depend onwhich depend on

the kinds of inputs (factors the kinds of inputs (factors of production) usedof production) used

the amount of each input the amount of each input usedused

prices of inputs usedprices of inputs usedtechnologytechnology

3535

Supply: DefinitionSupply: Definition A schedule that shows how much A schedule that shows how much

of a product a firm will supply at of a product a firm will supply at alternative prices for a given time alternative prices for a given time period “ceteris paribus”.period “ceteris paribus”.

3636

The Law of SupplyThe Law of Supply• The price of a product or service and The price of a product or service and

the quantity supplied are directly the quantity supplied are directly related: “ceteris paribus”related: “ceteris paribus”

• Causes an upward sloping supply curveCauses an upward sloping supply curve

• The higher the price of a good, the more The higher the price of a good, the more sellers will make availablesellers will make available

• The lower the price of a good, the fewer The lower the price of a good, the fewer sellers will make availablesellers will make available

• All else being equalAll else being equal

3737

The Individual Producer’s Supply The Individual Producer’s Supply ScheduleSchedule

Qnty of Songs Supplied Price / (thousands / Song year)

F $5 550

G 4 400

H 3 350

I 2 250

J 1 200Quantity of Songs Supplied

(thousands of constant-quality units per year)

Pric

e of

Son

g ($

)1

2

3

4

5

100 2003004005000

J

I

H

G

F

600

Change in PriceMovement alongThe Supply

3838

Movement Along Movement Along Supply/Supply/

Changes in Quantity SuppliedChanges in Quantity Supplied

– A change in a good’s own price A change in a good’s own price leads to aleads to a change in quantity change in quantity suppliedsupplied..

that is, athat is, a movement alongmovement along the supply the supply curve.curve.

3939

Shifts/Changes in Shifts/Changes in SupplySupply

A change in one or more of the A change in one or more of the non-price determinants of supply non-price determinants of supply leads to aleads to a– change in supplychange in supply which iswhich is the the

same thing assame thing as a a

– shift shift of the supply curve.of the supply curve.

4040

S1S2

a

c

A Shift in the Supply CurveA Shift in the Supply Curve

Quantity of Songs Supplied(millions of constant-quality units per year)

Pric

e of

Son

gs (

$)

1

2

3

4

5

20 40 60 80 1000 140120

When supply decreases the quantity suppliedwill be less at each price: ie: Singers form a union and successfully negotiate higher wages

b

d

S2

When supply increasesthe quantity suppliedwill be greater at each price: ie: producer finds that she can use some cheaper singers from Newfoundland

b

d

4141

Factors other than Price that Factors other than Price that affect Supplyaffect Supply – 1) 1) Cost of inputs Cost of inputs (price in factor markets)(price in factor markets)

– 2) Technology and Productivity2) Technology and Productivity– 3) Taxes and Subsidies3) Taxes and Subsidies– 4) Price Expectations 4) Price Expectations (in the product (in the product

market)market)

– 5) Number of firms in the industry5) Number of firms in the industry

““Everything Else” : The Everything Else” : The “Determinants”/“Shifters” of “Determinants”/“Shifters” of SupplySupply

How will these shift How will these shift supply?supply?

4242

Market Equilibrium Price & QuantityMarket Equilibrium Price & Quantity

MarketMarket: where prices tend toward : where prices tend toward equality through the continuous equality through the continuous interaction of buyers and sellers: interaction of buyers and sellers: the market forces of demand and the market forces of demand and supplysupply

Single Equilibrium Price

4343

Putting Demand and Supply Putting Demand and Supply Together: Finding Market Together: Finding Market EquilibriumEquilibrium

(1) (2) (3) (4) (5)Difference

Price per Quantity Supplied Quantity Demanded (2) - (3)Constant-Quality (Songs (Songs (Songs

Song per year) per year) per year) Condition

$5 100 million 20 million 80 million

4 80 million 40 million 40 million

3 60 million 60 million 0

2 40 million 80 million -40 million

1 20 million 100 million -80 million

Excess quantitysupplied (surplus)

Excess quantitysupplied (surplus)

Excess quantitydemanded (shortage)

Excess quantitydemanded (shortage)

4444

S

D

Market Equilibrium: Market Equilibrium: DefinitionDefinition

Quantity of Songs(millions of constant-quality units per year)

Pric

e pe

f S

ong

($)

1

2

3

4

5

20 40 60 80 1000

Excess quantity supplied at price $5

Excess quantity demanded at price $1

A B

Market clearing, orequilibrium, price

E QD= QS

The condition in a market when quantity supplied equals quantity demanded at a particular price; a point from where there tends to be no movement

4545

The Law of Supply & The Law of Supply & DemandDemand

The price of any good will adjust until The price of any good will adjust until the price is such that the quantity the price is such that the quantity demanded is equal to the quantity demanded is equal to the quantity suppliedsupplied

A high price will result in excess supply, A high price will result in excess supply, pushing price down, and a low price will pushing price down, and a low price will result in excess demand, pushing price result in excess demand, pushing price up up

the market clears resulting in a single the market clears resulting in a single market clearing or equilibrium pricemarket clearing or equilibrium price..

4646

Qd = 500 – 4p QS = -100 + 2p

p = price of cranberries (dollars per barrel) Q = demand or supply in millions of barrels per year

4747

a. The equilibrium price of cranberries is calculated by equating demand to supply:

Qd = QS … or…

500 – 4p = -100 + 2p …solving,

500+100=2p+4pp* = $100

b. plug equilibrium price into either demand or

supply to get equilibrium quantity:

Qd = 500-4dQd = 500-4(100)

Qd = 100

4848

Example: The Market For Cranberries

Price

Quantity

Market Supply: P = 50 + QS/2

50

Price

Quantity

Market Demand: P = 125 - Qd/4


P*=100

125

4949

Price

Quantity

Market Demand: P = 125 - Qd/4


Q* = 100

P*=100

125

•


50

5050

Comparative Statics: Shifts in Comparative Statics: Shifts in Demand &/or SupplyDemand &/or Supply

– 1.) Decide whether Demand &/or Supply is 1.) Decide whether Demand &/or Supply is affected.affected.

– 2.) Decide in which direction the affected 2.) Decide in which direction the affected Demand &/or Supply will move.Demand &/or Supply will move.

– 3.) Use a Demand and Supply diagram to 3.) Use a Demand and Supply diagram to determine the new equilibrium.determine the new equilibrium.

– 4.) Calculate the new equilibrium (if 4.) Calculate the new equilibrium (if possible)possible)

•Suppose something in the demand &/or the supply “ceteris paribus” assumptions changes.

•How is the MARKET affected?

5151

Comparative Statics: Gas Comparative Statics: Gas PricesPrices

Summer 2009: Gas prices at Summer 2009: Gas prices at equilibrium at $1.07 per literequilibrium at $1.07 per liter

Winter arrives and certain drivers Winter arrives and certain drivers limit or end their driving for the limit or end their driving for the season (shift in demand)season (shift in demand)–The new market equilibrium is The new market equilibrium is $0.87 per liter$0.87 per liter

Cold Weather causes a decrease in Cold Weather causes a decrease in gas pricesgas prices

5252

S

D1

P1

Q1

E1

Ford Escape Market Consider the Consider the

market for Ford market for Ford Escapes.Escapes.

1.1. For each event For each event identify whether identify whether demand or demand or supply is supply is affected.affected.

2.2.Determine the Determine the direction of direction of change.change.

3.3.Draw a diagram Draw a diagram to illustrate how to illustrate how equilibrium is equilibrium is changed.changed.

5353

Steelworkers Strike Raises Steelworkers Strike Raises Steel PricesSteel Prices

D

S1

Q1

P1

E1

FordEscape Market

S2

Q2

P2

E2

5454

New Automated Machinery New Automated Machinery IntroducedIntroduced

S1

D

P1

Q1

E1

Ford Escape Market

S2

P2

Q2

E2

5555

Price of Station Wagons RisesPrice of Station Wagons Rises

S

D1

P2

Q2

E2

Ford Escape Market

D2

P1

Q1

E1

5656

D1

Stock Market Crash Lowers Stock Market Crash Lowers WealthWealth

S

P1

Q1

E1

Ford Escape Market

D2

P2

Q2

E2

5757

Simultaneous ShiftsSimultaneous Shifts

– 2 events2 events 1.1. supply supply 2.2. demand demand

only only supply supply P, P, Q.Q. only only demand demand P, P, Q.Q.

Example of a double shift.

5858

D1

Shifts in Demand and in Shifts in Demand and in SupplySupply

S1

P1

Q1

E1

D2

S2

P2

Q2

E2

5959

D1


S1

P1

Q1

E1

D2

S2

P2

Q2

E2

6060


second possibilitysecond possibility– 2 events2 events

1.1. supply supply 2.2. demand demand

only only supply supply P, P, Q.Q. only only demand demand P, P, QQ

Example of a double shift.

6161


S1

D1

P1

E1

Q1

S2

D2

P2

E2

Q2

6262

D1


S1

Q1

P1

E1

D2

S2

Q2

P2

E2

6363

Qd = 500 – 4p QS = -100 + 2p

p = price of cranberries (dollars per barrel) Q = demand or supply in millions of barrels per year

Assume that a plague reduced cranberry supply and fear of inflection likewise reduced cranberry demand so that:

Qd = 400 – 4p QS = -200 + 2p

6464

a. The new equilibrium price of cranberries is calculated by equating demand to supply:

Qd = QS … or…

400 – 4p = -200 + 2p …solving,

400+200=2p+4pp* = $100

b. plug equilibrium price into either demand or

supply to get equilibrium quantity:

Qd = 400-4dQd = 400-4(100)

Qd = 0

6565

Price

Quantity

Old Market Demand: P = 125 - Qd/4

Old Market Supply: P = 50 + QS/2

QOLD

POLD=PNew

125

•


50

New Market Supply: P = 100 + QS/2

New Market Demand: P = 100 - Qd/4

QNew

6666

Elasticity: Percentage ChangeElasticity: Percentage ChangeConsider the following:Consider the following:

– An increase of 50 cents or an increase An increase of 50 cents or an increase of 50% in the price of a hamburgerof 50% in the price of a hamburger

– An increase of $100 or an increase of An increase of $100 or an increase of 1% in the price of a new car1% in the price of a new car

Percentage changes are easier to Percentage changes are easier to grasp than the amount of changegrasp than the amount of change

– Therefore economists often use Therefore economists often use elasticities to examine percentage elasticities to examine percentage change or responsivenesschange or responsiveness

6767

Price Elasticity of Price Elasticity of DemandDemand

Price Elasticity of Demand (Price Elasticity of Demand (ЄЄ Q,Q,pp))

– The responsiveness of quantity The responsiveness of quantity demanded of a commodity to changes demanded of a commodity to changes in its pricein its price

– Related to the slope, but concerned Related to the slope, but concerned with percentage changeswith percentage changes

6868

Impact of a Change in Supply & Impact of a Change in Supply & Therefore Price on the Quantity Therefore Price on the Quantity DemandedDemanded

S1

Quantity (pizzas per hour)

Pri

ce (

dolla

rs p

er

pizz

a)

10.00

20.00

30.00

40.00

Da

0 255 10 15 2013

5.00

S0

Large price change and small quantity change

An increasein supplybrings ...

… and a smallincrease in quantity

… a largefall in price...

6969

Impact of a Change Impact of a Change in Supply…in Supply…


Pric

e (d

olla

rs p

er p

izza

)

10.00

20.00

30.00

40.00

Db

0 255 10 15 2017

S1

15.00

S0

Small price change and large quantity change

An increasein supplybrings ...

… a smallfall in price...

… and a largeincrease in quantity

7070

Solution: Price Elasticity of Solution: Price Elasticity of DemandDemand

P

Qd

%

%PQ,

Percentage change in price

Percentage change in quantity demandedЄQ,P

The ratio of the two percentages is a

number without units.

Price Elasticity of Demand

7171

Price ElasticityPrice Elasticity ExampleExample

– Price of oil increases 10%Price of oil increases 10%– Quantity demanded decreases 1%Quantity demanded decreases 1%

1.%10

%1-PQ,

When calculating the price elasticity of demand, we often ignore the minus sign for % change in Q.

7272

TYPES OF ELASTICITY -Hypothetical Demand ElasticitiesTYPES OF ELASTICITY -Hypothetical Demand Elasticities

Product % Change in price (%P)

% Change in quantity demanded (%QD)

Elasticity (%QD/%P)

Insulin

+ 10%

0%

0 Perfectly inelastic

Basic Telephone service

+ 10%

-1%

.1 Inelastic

Beef

+ 10%

-10%

1.0 Unitarily elastic

Bananas

+ 10%

-30%

3.0Elastic

7373

Price Elasticity Ranges: Price Elasticity Ranges: Extreme Price ElasticitiesExtreme Price Elasticities

Quantity Demanded per Year(millions of units)

Pric

e

0

D

8

Perfect inelasticity, zero elasticity,no matter howmuch Pricechanges,Quantitystays the same; insulin

P0

P1

Quantity Demanded per Year(millions of units)

Pri

ce

0

Perfect elasticity, infinite elasticity,the slightest increasein price will lead to zero sales.

30D

P1

P1 isthe demand curve

7474

Price Elasticity RangesPrice Elasticity RangesSummary from TableSummary from Table

1PQ, ;%% PQ

1PQ, ;%% PQ

1PQ, ;%% PQ

Unit Elastic

Inelastic Demand

Elastic Demand

7575

Elasticity of DemandElasticity of Demand Calculating elasticityCalculating elasticity

or

or

Sum of prices/2

Change in P

Sum of quantities/2

Change in QЄQ,P

Always use

the mid-point

formula

ЄQ,P

Change in

Q(Q1 Q2)/2

Change in

P(P1 P2)/2

ЄQ,P

QAvg.Q

PAvg.P

7676

Calculating the Elasticity of Calculating the Elasticity of DemandDemand

9 10 11

19.50

20.50

D

Newpoint

Quantity (pizzas/hour)

Price (dollars/pizza)

20.00

Originalpoint

Elasticity = = 4Q /Qave

P /Pave

2/10

1/20=

ΔP=1

ΔQ=2

Qave =1/2(11+9)=10

Pave =1/2(20.50+19.50)=20

7777

Elasticity of Demand (mid-point)Elasticity of Demand (mid-point)

ЄQ,P =P = $1.00

P1 + P2 ($20.50 + $19.50)

2

P =5% = $20

Q = 2

Q1 + Q2 (9 + 11)

2

Q =20% = 10

Always use the mid-point formula for calculating elasticity

20%

5%= 4= ЄQ,P =

X 100

X 100

7878

Elasticity: ExampleElasticity: Example You are the consulting economist to the You are the consulting economist to the

Guelph transportation commission, Guelph transportation commission, The current fare is $.95 The current fare is $.95 There are 17,500 riders per day There are 17,500 riders per day For each $.10 increase in the fare, rider For each $.10 increase in the fare, rider

ship decreases by 10,000 riders per day.ship decreases by 10,000 riders per day. What is the price elasticity of demand at What is the price elasticity of demand at

the current fare? the current fare? Should fares be raised or lowered?Should fares be raised or lowered? What fare will maximize revenue? What fare will maximize revenue?

7979

Total Revenue and Total Revenue and ElasticityElasticity

Total Revenue =

Price Per GoodX

# of Goods Sold

TR = P X Q

Total Revenue =

Price Per GoodX

# of Goods Sold

TR = P X Q

Assumption : Costs are constantAssumption : Costs are constant

8080

5555 110110

.55.55

1.101.10

3.003.00

(dol

lars

)(d

olla

rs)

Maximum total revenue

When demandis inelastic, price cut decreasestotal revenue

Unitelastic

Elasticdemand

QuantityQuantity

Inelastic demand

00

When demand is elastic, price cut increases total revenue

To

tal R

eve

nue

To

tal R

eve

nue

Pri

ceP

rice

0 550 55 110110

Ela

sti

cit

y a

nd

Tota

l Ela

sti

cit

y a

nd

Tota

l R

even

ue

Reven

ue

QuantityQuantity

.80

8181

Relationship Between PriceRelationship Between PriceElasticity of Demand and Total RevenuesElasticity of Demand and Total Revenues

InelasticInelastic ((ЄQ,P < < 1) 1) TR TR TR TR

Unit-elasticUnit-elastic ((ЄQ,P = 1) = 1) No change No change No No

change change Elastic Elastic ((ЄQ,P > 1) > 1) TR TR TR TR

Price Elasticity Effect of Price Change

of Demand on Total Revenues (TR)

Price PriceDecrease Increase

Note: It is possible to classify elasticity by Note: It is possible to classify elasticity by

observing the change in revenue from a price observing the change in revenue from a price

changechange

8282

QuestionQuestion• 2 drivers - Tom & Jerry each drive 2 drivers - Tom & Jerry each drive

to to a gas station. to to a gas station. • Before looking at the price, each Before looking at the price, each

places an order. places an order. • Tom says, “I’d like 10 litres of gas”. Tom says, “I’d like 10 litres of gas”. • Jerry says, “I’d like $10 of gas”.Jerry says, “I’d like $10 of gas”.• What is each driver’s price What is each driver’s price

elasticity of demand?elasticity of demand?

8383

Determinants ofDeterminants ofPrice Elasticity of DemandPrice Elasticity of Demand

Existence of substitutesExistence of substitutes– Goods are more price elastic if substitutes Goods are more price elastic if substitutes

existexist

Share of budgetShare of budget– Goods are more price elastic when a Goods are more price elastic when a

consumer’s expenditure on the good is large consumer’s expenditure on the good is large (in dollar terms or relatively)(in dollar terms or relatively)

NecessityNecessity– Goods are less price elastic when seen as a Goods are less price elastic when seen as a

necessitynecessity

8484

Market and Brand Market and Brand ElasticitiesElasticities

Market and Brand Elasticities are Market and Brand Elasticities are not equalnot equal– Although a water addict is very price Although a water addict is very price

inelastic to the price of bottled water in inelastic to the price of bottled water in general, he/she would quickly switch to general, he/she would quickly switch to another brand if only 1 brand of water another brand if only 1 brand of water increased in priceincreased in price

– GENERALLY, Brand price elasticity of GENERALLY, Brand price elasticity of demand is higher than market price demand is higher than market price elasticity of demandelasticity of demand

8585

Qd = a – bp

a,b are positive constants p is price

-b is the slopea/b is the choke price (price at which nothing is sold)

8686

the elasticity is

Q,P = (Q/p)(p/Q) …definition… = -b(P/Q)

Since the slope of the graph is –b.Therefore…elasticity falls from 0 to - along the linear demand curve, but slope is constant.

if Qd = 400 – 10p, and p = 30, Q,P = (-10)(30)/(100) = -3 "elastic"

8787

D

Quantity per Period (billions of minutes)

Pric

e pe

r M

inut

e ($

)

0

.10

.20

.30

.40

.50

.60

.70

.80

.90

1.00

1.10

1 2 3 4 5 6 7 8 9 10 11

Elastic (ЄQ,P > 1)

Inelastic (ЄQ,P < 1)

Unit-elastic (ЄQ,P = 1)

Changes in Elasticity Along a Changes in Elasticity Along a Linear DemandLinear Demand

8888

The Relationship Between Price Elasticity of The Relationship Between Price Elasticity of Demand andDemand andTotal Revenues for Cellular Phone ServiceTotal Revenues for Cellular Phone Service

$1.10$1.10 0 0

1.001.00 1 1

.90.90 2 2

.80.80 3 3

.70.70 4 4

.60.60 5 5

.50.50 6 6

.40.40 7 7

.30.30 8 8

.20.20 9 9

.10.10 1010

Quantity Total Elasticity Price Demanded Revenue ЄQ,P

21.000

6.333

3.400

2.143

1.144

1.000

.692

.467

.294

.158

Elastic

Inelastic

Unit-elastic

00

1.01.0

1.81.8

2.42.4

2.82.8

3.03.0

3.03.0

2.82.8

2.42.4

1.81.8

1.01.0

8989

Qd = Ap

= elasticity of demand and is negative p = price A = constant

Elasticity is constant, but the slope of demand falls from 0 to -.

In another form, ifLn(Qd)=μLN(P),

μ= Price Elasticity of Demand

9090

Quantity

Price

0 Q

P • Observed price and quantity

Constant elasticity demand curve

Linear demand curve

Example: A Constant Elasticity versus a Linear Demand Curve

9191

Elasticity of SupplyElasticity of Supply

Calculating elasticityCalculating elasticity

or

or

Sum of prices/2

Change in P

Sum of quantities/2

Change in QЄQs,P

Always use

the mid-point

formula

ЄQs,P

Change in Q(Q1 Q2)/2

Change in P(P1 P2)/2

ЄQs,P

QAvg.Q

PAvg.P

9292

How a Change in Demand Changes How a Change in Demand Changes Price and QuantityPrice and Quantity


Pri

ce (

dolla

rs p

er p

izza

)

10.00

40.00

D0

0 255 10 15 20

Sa Large price change and small quantity change

… a largeprice rise...

20.00

D1

30.00

13

An increasein demandbrings ...

… and a smallquantity increase

9393

How a Change in Demand Changes Price and How a Change in Demand Changes Price and QuantityQuantity


Pri

ce (

dolla

rs p

er

pizz

a)

10.00

30.00

40.00

D0

0 255 10 15 20

Sb

Small price change and large quantity change

… a smallprice rise...

20.00

D1

An increasein demandbrings ...

21.00

… and a largequantity increase

9494

Elasticity of SupplyElasticity of Supply Elasticity of supply rangesElasticity of supply ranges

– (from) (from) Perfectly ElasticPerfectly Elastic Supply Supply Quantity supplied falls to 0 when there is any Quantity supplied falls to 0 when there is any

decrease in pricedecrease in price

– (to) (to) Perfectly InelasticPerfectly Inelastic Supply Supply Quantity supplied is constant no matter what Quantity supplied is constant no matter what

happens to pricehappens to price

Notice: There is no total revenue test for supply since price and quantity are directly related

9595

Supply Elasticity Supply Elasticity Ranges Ranges

Pric

e

Quantity

SElasticity of supply = 0

0

Quantity supplied is the same for any

price!

Pric

eP

rice

QuantityQuantity

SS

Elasticity of supply =

00

Suppliers will offerANY quantity at this

price

9696

Elasticity of Supply: Elasticity of Supply: Depends On:Depends On:

1. Resource substitution possibilities, -The more unique the resource, the more

inelastic the supply.

2. Time frame for the supply decision, Momentary supply Long-run supply Short-run supply

- Typically, the longer producers have to adjust to a price change, the more elastic is supply.

9797

Long-Run Elasticity of Long-Run Elasticity of DemandDemand Elasticities can vary in the short run (when major Elasticities can vary in the short run (when major changes cannot be made) and the long run.changes cannot be made) and the long run.

-For most goods, elasticity of demand is greater in -For most goods, elasticity of demand is greater in the long run (curves are “flatter”)the long run (curves are “flatter”)

-People are more able to adjust to changes over -People are more able to adjust to changes over time (slowly switch consumption)time (slowly switch consumption)

-For essential durable goods (ie: Cars), long-run -For essential durable goods (ie: Cars), long-run demand elasticity is less (curves are “steeper”)demand elasticity is less (curves are “steeper”)

-People can change their purchases or suppliers -People can change their purchases or suppliers now, but eventually they have to buy new goods now, but eventually they have to buy new goods as old ones breakas old ones break

9898

Long-Run Elasticity of Long-Run Elasticity of SupplySupply Elasticities can vary in the short run (when major Elasticities can vary in the short run (when major changes cannot be made) and the long run.changes cannot be made) and the long run.

-For most goods, elasticity of supply is greater in the -For most goods, elasticity of supply is greater in the long run (curves are “flatter”)long run (curves are “flatter”)

-Firms are more able to adjust to changes over time -Firms are more able to adjust to changes over time (slowly switch production)(slowly switch production)

-For reusable goods (ie: Aluminum), long-run supply -For reusable goods (ie: Aluminum), long-run supply elasticity is less (curves are “steeper”)elasticity is less (curves are “steeper”)

-People resell their stock when prices go up, but -People resell their stock when prices go up, but eventually their stock runs outeventually their stock runs out

9999

S2

Quantity Supplied per Period

Pri

ce p

er

Un

it

S1

Qe

Pe

P1

As time passes, thesupply curve rotatesto S2 and then to S3and quantity suppliedrises first to Q1 and then to Q2

Supply Elasticity and the Long Supply Elasticity and the Long RunRun

(most non-durable, (most non-durable, non-essential goods)non-essential goods)

S3

Q2Q1

100100

How Long is the Long Run?How Long is the Long Run? There is no set amount of time that puts a There is no set amount of time that puts a

market into the long runmarket into the long run– The long run could be a week or a yearThe long run could be a week or a year

The long run is how long a consumer or The long run is how long a consumer or firm takes to fully adjust to a price changefirm takes to fully adjust to a price change– Time required to make major changes Time required to make major changes – Ie) Give up Pepsi Vanilla, Build more cost Ie) Give up Pepsi Vanilla, Build more cost

efficient Pepsi factory, secure a US Pepsi efficient Pepsi factory, secure a US Pepsi Vanilla supplierVanilla supplier

The short run is anything shorter than the The short run is anything shorter than the long runlong run

101101

Cross Price Elasticity of Cross Price Elasticity of DemandDemand

We’ve seen already that demand is affected by the We’ve seen already that demand is affected by the price of substitutes and complimentsprice of substitutes and compliments– An increase in the price of a substitute increases An increase in the price of a substitute increases

demanddemand– An increase in the price of a complement decrease An increase in the price of a complement decrease

demanddemand This effect can be measured using cross price This effect can be measured using cross price

elasticityelasticity If the cross price elasticity is zero, the good is If the cross price elasticity is zero, the good is

neither a complement nor a substituteneither a complement nor a substitute

102102

Change in Price of Y

----------------------------

(Py1 + Py2)/2

/

Cross Price Elasticity of Cross Price Elasticity of DemandDemand

Percentage change in price of Y

Percentage change in quantity demanded of X

Qi,Pj

Є

Є Qi,Pj = Change in X

---------------

(X1 + X2)/2

Substitutes – Positive Cross Price Elasticity

Compliments – Negative Cross Price Elasticity

103103

Cross Price Elasticity of Demand Cross Price Elasticity of Demand ExampleExample

““Recent cat attacks have prompted cat Recent cat attacks have prompted cat owners to buy guns for self-defense”owners to buy guns for self-defense”

Originally, 2 Econ students owned a cat. After the Originally, 2 Econ students owned a cat. After the price of guns went from $100 to $200, only 1 Econ price of guns went from $100 to $200, only 1 Econ student owned a cat.student owned a cat.

Calculate the cross-price elasticity of demandCalculate the cross-price elasticity of demand

104104

Cross-Price ElasticityCross-Price Elasticity

ЄQ,P =P = $100

P1 + P2 ($100 + $200)

2

PJ =66% = $150

Q = -1

Q1 + Q2 (2 + 1)

2

Qi =-66% = 1.5

Are cats and guns substitutes or compliments?

-66%

66%= -1= ЄQi,Pj =

X 100

X 100

105105

Income Elasticity of DemandIncome Elasticity of Demand

Income Elasticity of demand refers Income Elasticity of demand refers to a HORIZONTAL SHIFT in the to a HORIZONTAL SHIFT in the demand curve resulting from an demand curve resulting from an income changeincome change

Price elasticity of demand refers to Price elasticity of demand refers to a MOVEMENT ALONG THE a MOVEMENT ALONG THE DEMAND CURVE in response to a DEMAND CURVE in response to a price changeprice change

106106

Change in M

----------------------------

(M1 + M2)/2

/

Income Elasticity of Income Elasticity of DemandDemand

Percentage change in income

Percentage change in quantity demandedQ,I

Є

Є Q,I= Change in Q

---------------

(Q1 + Q2)/2

Normal Good – Positive Shift/Elasticity

Inferior Good – Negative Shift/Elasticity

107107

Income Elasticity of Demand ExampleIncome Elasticity of Demand Example In New Zealand, the average family will own 4 In New Zealand, the average family will own 4

Toyotas in their lifetime.Toyotas in their lifetime. If average Kiwi family income rose from $140K to If average Kiwi family income rose from $140K to

$160K a year, the average Kiwi family would own 2 $160K a year, the average Kiwi family would own 2 Toyotas over their lifetimeToyotas over their lifetime

Calculate Income Elasticity of Demand for Toyotas Calculate Income Elasticity of Demand for Toyotas in New Zealand.in New Zealand.

Are Toyotas normal or inferior goods in New Are Toyotas normal or inferior goods in New Zealand?Zealand?

108108

Income Elasticity of DemandIncome Elasticity of Demand

ЄQ,I =I = $20K

I1 + I2 ($140K + $160K)

2

I =13.3% = $150K

Q = -2

Q1 + Q2 (4 + 2)

2

Q =-66% = 3

In New Zealand, are Toyotas normal or inferior goods?Guess which brand is the luxury car.

-66%

13.3%= -5= ЄQi,Pj =

X 100

X 100

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