Chapter 3

Applying the Supply-and-

Demand Model

Applying supply and demand

model

1. shapes matter

2. sensitivity of quantity demanded to price

3. sensitivity of quantity supplied to price

4. sensitivity is different in long run than in

the short run

5. effects of a sales tax

Questions

1. electric power: why did price shoot up in

2000?

2. inelastic: can demand be everywhere

inelastic?

What-if questions

how do equilibrium price and quantity

change when an underlying factor changes?

use graphs to predict qualitative effects of

changes: direction of change

need to know shape of demand and supply

curves to determine quantitative change:

amount equilibrium quantity and price

change

Shapes of demand and supply

curves matter

supply shock (25 increase in price of hogs)

effect on Canadian processed pork depends

on shape of demand curve

supply shock causes supply curve of pork to

shift left from S

1

to S

2

p, $ per kg

215 2201760

Q, Million kg of pork per year

3.55

3.30

S

1

D

1

S

2

e

1

e

2

Pork demand and supply curves

If the demand curve is horizontal

p, $ per kg

2202051760

Q, Million kg of pork per year

3.30

S

1

S

2

D

3

e

1

e

2

If the demand curve is vertical

p, $ per kg

2201760

Q, Million kg of pork per year

3.675

3.30

S

1

S

2

D

2

e

1

e

2

-49.5-150Horizontal

82.5037.5Vertical

37.25-525Actual:

Downward slope

R, $million/ yearQ, million kg/yearp, cents/kg

Demand Curve

Review: Electric power

Why did Californias wholesale electric

power rates suddenly shoot up in 2000?

Answer

demand increased 5% more than expected

limited capacity short-run supply nearly

vertical

price per kWh

Quantity, million kWh per year

D

1

D

2

S

p

1

p

2

p*

S*

Elasticity of demand

summarize sensitivity of the quantity

demanded to price in a single statistic: price

elasticity of demand:

%change in quantity demanded /

%change in price /

Q Q

p p

= =

/

/

Q Q Q p

p p pQ

= =

Linear demand curve

linear demand: Q = a bp

elasticity of demand:

pork demand curve: Q = 286 20p

d

d

Q p Q p p

b

p Q p Q Q

= = =

3.30

20 0.3

220

Q p p

b

p Q Q

= = = =

Interpretation of pork demand

elasticity

1% increase in price of pork leads to an %

= -0.3% change in the quantity demanded

quantity falls less than in proportion to price

negative price elasticity, -0.3, is consistent

with Law of Demand

Types of elasticities

elastic: the quantity demanded changes

more than in proportion to a change in price

inelastic: the quantity demanded changes

less than in proportion to a change in price

elasticity of demand varies along most

linear demand curves

Figure 3.2 Elasticity Along the Pork Demand Curve

p, $ per kg

a/2 = 143a/5 = 57.2

D

a = 286220

Q, Million kg of pork per year

0

11.44

a/b = 14.30

3.30

a/(2b) = 7.15

Elastic: < 1

= 4

Unitary: = 1

= 0.3

Inelastic: 0 > > 1

Perfectly

inelastic

Perfectly elastic

Downward-sloping linear

demand curve

perfectly elastic ( is -) where demand

curve hits vertical axis

unitary elasticity at midpoint:

p = a/(2b) and Q = a/2

therefore, = -bp/Q = -b(a/[2b])/(a/2) = -1

perfectly inelastic ( = 0) where demand

curve hits quantity axis

= -bp/Q = -b0/Q = 0

Constant elasticity demand

curves

elasticity same at every point along curve

smooth curves:

Q = Ap

, or,

vertical demand curve: perfectly inelastic

( = 0) everywhere: essential good

horizontal demand curve: perfectly elastic

(-): perfect substitutes

Constant Elasticity Demand Curves

Figure 3.3c Individuals Demand for Insulin

*

p, Price of

insulin dose

* Q, Insulin

doses per day

p

Q

Prove constant elasticity

demand function: Q = Ap

1

1

d

elasticity

d

Q p p

Ap

p Q Q

p p

Ap

Ap p

= =

= = =

Solved problem

Is it possible that a demand curve is

inelastic everywhere?

restatement: Does the assumption that a

demand curve is everywhere inelastic

contradicts some known fact?

Answer

1. assume that a demand curve is everywhere

inelastic, and determine the properties of

that demand curve:

if demand curve is perfectly inelastic, quantity

doesn't change as price increases so revenue

rises in proportion to price

as the price rise, the amount consumers spend

grows without limit

Answer (cont.)

2. check whether those properties violate a

known fact:

consumers cannot spend an infinite amount

on a single good: They don't have unlimited

wealth

therefore, a demand curve cannot be

everywhere inelastic (at a high enough

price, the demand must be elastic)

Solved problem

Will a profit-maximizing monopoly ever

operate in the inelastic section of its demand

curve?

restatement: Can a monopoly make more

money operating in a different section of its

demand curve?

Answer

1. show what happens to its revenue if the monopoly

raises its price and it is in the inelastic section of

its demand curve: quantity falls less than in

proportion to price, so revenue rises

2. discuss what happens to profit: cost falls with

quantity, so profit rises

3. conclude: monopoly raises its price when in the

inelastic section section of its demand curve until

its no longer in that section

Income elasticity of demand

% change in quantity demanded

% change in income

/

/

Q Q Q Y

Y Y Y Q

=

= =

Pork income elasticity of demand

pork demand function is

Q = 171 20p + 20p

b

+ 3p

c

+ 2Y

so pork income elasticity is

at Q = 220 and Y = 12.5

= 2 x 12.5/220 = 0.114

2

Q Y Y

Y Q Q

= =

Cross-price elasticity of demand

how quantity of one good changes as price

of another good increases

%change in quantity demanded

%change in price of another good

/

/

o

o o o

Q Q Q p

p p p Q

= =

Negative cross-price elasticity

as the other goods price increases, people

buy less of this good

demand curve shifts to the left

example: as price of cream rises, people

consume less coffee (cross-price elasticity

is negative)

Positive cross-price elasticity

as the price of the other good increases,

people buy more of this good

demand curve shifts to the right

example: demand for a Camry rises as the

price of a Taurus increases

Pork-beef example

pork demand function is

Q = 171 20p + 20p

b

+ 3p

c

+ 2Y

so cross-price elasticity of demand for pork

and the the price of beef is

at Q = 220 and p

b

= $4 per kg, cross-price

elasticity is 20 x 4/220 = 0.364

20

o b

o

Q p p

p Q Q

=

Price elasticity of supply

/

/

%change in quantity supplied

%change in price

Q Q Q p

p p pQ

=

= =

Sign of elasticity of supply

if supply curve slopes upward, p/Q > 0,

then > 0

if supply curve slopes downward, p/Q >

0, then < 0

supply curve is elastic if > 1

supply curve is inelastic if 0 < 1

Pork supply elasticity

pork supply curve is

Q = 88 + 40p

so pork supply elasticity is

as price of pork increases by 1%, the quantity

supplied rises by nearly two-thirds of a percent

3.30

40 0.6

220

Q p

p Q

= = =

Figure 3.4 Elasticity Varies Along Linear Pork Supply Curve

p, $ per kg

220 260176

S

0.71

0.66

0.6

0.5

300

Q, Million kg of pork per year

0

3.30

2.20

4.30

5.30

Constant Elasticity Supply Curves

Long run versus short run

SR and LR elasticities may differ

substantially

gasoline demand elasticities:

SR elasticity = -0.35

5-year intermediate-run elasticity = -0.7

10-year, LR elasticity = -0.8

if a good can be easily stored, SR demand

curve may be more elastic than LR curve

OPEC restricts output

according to news reports 1/17/01, OPEC

planned to reduce its quantity of oil by 5%

how would the price change in SR and LR?

p/p = (Q/Q)/

= -5%/(-0.35) = 14.3% (SR)

= -5%/(-0.7) = 7.1% (intermediate run)

= -5%/(-0.8) = 6.3% (LR)

Predictions based on elasticities

knowing only the elasticities of demand and

supply, we can make accurate predictions

about the effects of a new tax and determine

how much of the tax falls on consumers

Two types of sales taxes

ad valorem tax (the sales tax): for every

dollar the consumer spends, the government

keeps a fraction,

specific (unit) tax: a specified amount, , is

collected per unit of output

Tax on consumer

pQ QT = Qspecific tax

(1 - )pQT = pQad valorem tax p

Firms after-tax

revenue

Total tax

revenue

Per unit tax

4 Questions about sales taxes

1. What effect does a specific sales tax have on

equilibrium prices and quantity?

2. Are sales taxes assessed on producers "passed

along" to consumers? (Do consumers pay entire

tax?)

3. Do equilibrium price and quantity depend on

whether the consumers or producers are taxed?

4. Do both types of sales taxes have the same effect

on equilibrium?

Specific tax

assume the specific tax is assessed on firms

at the time of sale

consumer pays p

government takes

seller receives p -

Question 1

What is the effect of a specific tax on the

equilibrium?

answer: See Figure 3.5 where we shift up

the after-tax supply curve

equilibrium price rises

equilibrium quantity falls

government collects tax revenues

Figure 3.5 Effect of a $1.05 Specific Tax on the Pork Market

Collected from Producers

p, $ per kg

Q

2

= 206 Q

1

= 220176

T

=

$216.3 million

Q, Million kg of pork per year

0

p

2

= 4.00

p

1

= 3.30

p

2

= 2.95

= $1.05

S

1

e

1

e

2

S

2

D

Sin taxes

because output falls after tax, governments

can use taxes to discourage "sin" activities

federal specific taxes have been used for:

cigarettes

alcohol

playing cards (in an earlier day)

Question 2

Who is hurt by the tax?

What is the incidence of the tax?

In-class problem

When a specific tax is imposed on pork,

what happens to prices? Price consumers

pay rises by

A. more than the tax

B. by the amount of the tax

C. by less than the tax

Price impact of tax

amount by which tax affects equilibrium

price depends on elasticities of supply and

demand

government raises tax by = - 0 =

price consumers pay increases by

p

=

Pork example

Figure 3.5 shows p = $4 - $3.30 = $0.70

demand elasticity: = -0.3

supply elasticity, = 0.6

= = $1.05

therefore:

0.6

($1.05) $0.70

0.6 ( 0.3)

p

= = =

Figure 3.5 Effect of a $1.05 Specific Tax on the Pork Market

Collected from Producers

p, $ per kg

Q

2

= 206 Q

1

= 220176

T

=

$216.3 million

Q, Million kg of pork per year

0

p

2

= 4.00

p

1

= 3.30

p

2

= 2.95

= $1.05

S

1

e

1

e

2

S

2

D

Tax incidence

incidence of a tax on consumers is share of

tax that consumers pay

p

=

Incidence of a tax on pork

figure 3.5 shows consumer incidence is

p/ = $0.70/$1.05 = 2/3

using elasticities, consumer incidence is

/( - ) = 0.6/(0.6 - [-0.3]) = 2/3

Restaurant tax incidence

estimated demand and supply for restaurant

meals (Brown 1980):

constant elasticity demand curve: = -0.188

constant elasticity supply curve: = 6.47

original equilibrium:

Q

1

= 8.14 billion meals per year

p

1

= $10.47 per meal ($1992)

Restaurant tax incidence

most of the incidence falls on consumers:

2 1

$11.44 - $10.47

= = = 97%

$1

6.47

= =97%

- 6.47 + 0.188

p p p

=

Overall effect of $1 meal tax

raises $8 billion in tax revenues

causes little drop in the number of

restaurant meals purchased

Specific gasoline taxes

federal range from nearly 11 and 20 per

gallon

state from 7 to 36 per gallon

Incidence of gas tax

0-wholesale price

+1+retail price

statefederal

1 increase in specific gasoline tax

Incidence ad valorem gas tax

ad valorem gas tax

CA, Georgia, IL, Indiana, Louisiana,

Michigan, Mississippi, NY

range up to 7% of retail price

tax rate from 0 to 5%

retail price 3.6

wholesale price 1.8.

Solved problem

if supply curve is perfectly elastic,

what is the effect of a $1 specific tax collected

from producers on equilibrium price and

quantity, and

what is the incidence on consumers?

why?

[for simplicity, assume demand is a

downward-sloping straight line]

Restatement

what changes: specific tax, , goes from $0

to $1 per unit

this change affects equilibrium price and

quantity

use pretax and post-tax price to consumers

to determine the incidence of the tax

p, Price per unit

Q, Quantity per time period

p

2

p

2

- = p

1

D

e

1

e

2

S

1

S

2

Question 3

Does equilibrium depend on who is taxed?

Answer

no: equilibrium is same whether government

collects tax from firms or from consumers

in a competitive market

= $1.05

= 2.95

Figure 3.6 Effect of a $1.05 Specific Tax on Pork Collected from

Consumers

p, $ per kg

Q

2

= 206 Q

1

= 220176

= $216.3 million

Q, Million kg of pork per year0

p

2

= 4.00

p

1

= 3.30

p

2

= $1.05

Wedge,

D

1

D

2

e

1

e

2

S

T

Question 4

How can an ad valorem and specific tax

have the same effect on equilibrium (in a

competitive market)?

Figure 3.7 A Comparison of an Ad Valorem and a Specific Tax

on Pork

p, $ per kg

Q

2

= 206 Q

1

= 220176

T

=

$216.3 million

Q

, Million kg of pork per year0

p

2

= 4.00

p

1

= 3.30

p

2

= 2.95

e

1

e

2

D

a

D

s

S

D

Luxury taxes

in 1990, an ad valorem tax was imposed on luxury

goods

tax was 10% of the amount over

$100,000 paid for yachts

$250,000 for private planes

$10,000 for furs and jewels

$30,000 for cars

objective: raise tax revenues without harming the

poor and middle class

Tax on automobiles

worked better than planned

expected: luxury tax would raise $25 million in 1991

and $1.5 billion over 5 years

actual: brought in $98.4 million in first year alone

most tax revenue came from sales of expensive,

foreign cars, whose sales fell

27%, Mercedes

10%, Lexus

few lost jobs for Americans except for auto

dealers

Taxes on other luxury goods

raised relatively little revenue

caused substantial loss of domestic output

and jobs

four bills brought before Congress within a

year to remove those taxes

in mid 1993, the taxes were revoked

Yacht tax harmed industry

substantially

in the first year sales of yachts costing over

$100,000 fell by 71%;

whereas, sales of unaffected less-expensive

yachts fell only 28% (due to the recession)

employment fell from 160,000 to 115,000

workers

loss in payroll taxes far outweighed the

increase in the luxury tax revenues

Yacht tax raised only $7 million

(well below the forecast)

Congressional analysts underestimated the

demand elasticity: ignored tax-avoiding

behavior and ability of consumers to

substitute

wealthy consumers escaped the boat tax by

buying yachts in the Bahamas

buying yachts that cost just under $100,000

(avoiding the luxury tax)

1 Shapes of demand and supply

curves matters

shapes determine the size of the effect

2 Elasticity of demand

= percentage change in quantity demanded

due to an increase in price divided by

percentage change in price

always negative due to the Law of Demand

3 Elasticity of supply

= percentage change in the quantity

supplied divided by the percentage change

in price

may have any sign, but commonly positive

(upward-sloping supply curve)

4 LR and SR elasticities

frequently differ

usually more adjustment is possible in the

long run than in the short run

5 Sales taxes

common types of sales taxes: ad valorem and

specific

both types of taxes usually raise equilibrium price

and lower equilibrium quantity

tax incidence depends on demand and supply

elasticities

in competitive markets, effect of a tax on

equilibrium same whether collected from

consumers or producers