Elasticity and its Application

EconomicsP R I N C I P L E S O FP R I N C I P L E S O F

N. Gregory N. Gregory MankiwMankiw

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ELASTICITY AND ITS APPLICATION 2

Calculating Percentage Changes• So, we instead use the midpoint method:

end value – start valuemidpoint

x 100%

The midpoint is the number halfway between the start & end values, the average of those values.

It doesn’t matter which value you use as the “start” and which as the “end” – you get the same answer either way!

ELASTICITY AND ITS APPLICATION 3

Calculating Percentage Changes• Using the midpoint method, the % change

in P equals

$250 – $200$225

x 100% = 22.2%

The % change in Q equals

12 – 810

x 100% = 40.0%

The price elasticity of demand equals

40/22.2 = 1.8

A C T I V E L E A R N I N G A C T I V E L E A R N I N G 11

Calculate an elasticityCalculate an elasticity

4

Use the following information to calculate the price elasticity of demand for hotel rooms:

if P = $70, Qd = 5000

if P = $90, Qd = 3000

A C T I V E L E A R N I N G A C T I V E L E A R N I N G 11

AnswersAnswers

5

Use midpoint method to calculate % change in Qd

(5000 – 3000)/4000 = 50%

% change in P

($90 – $70)/$80 = 25%

The price elasticity of demand equals50%25%

= 2.0

ELASTICITY AND ITS APPLICATION 6

Price Elasticity and Total Revenue

• If demand is elastic, then price elast. of demand > 1 % change in Q > % change in P

• The fall in revenue from lower Q is greater than the increase in revenue from higher P, so revenue falls.

Revenue = P x Q

Price elasticity of demand

=Percentage change in QPercentage change in P

ELASTICITY AND ITS APPLICATION 7

Price Elasticity and Total RevenueElastic demand(elasticity = 1.8) P

Q

D$200

12

If P = $200, Q = 12 and revenue = $2400.

When D is elastic, a price increase causes revenue to fall.

$250

8

If P = $250, Q = 8 and revenue = $2000.

lost revenue due to lower Q

increased revenue due to higher P

Demand for your websites

ELASTICITY AND ITS APPLICATION 8

Price Elasticity and Total RevenueNow, demand is inelastic: elasticity = 0.82 P

Q

D

$200

12

If P = $200, Q = 12 and revenue = $2400. $250

10

If P = $250, Q = 10 and revenue = $2500.

When D is inelastic, a price increase causes revenue to rise.

lost revenue due to lower Q

increased revenue due to higher P

Demand for your websites

Supply, Demand, and Government Policies

EconomicsP R I N C I P L E S O FP R I N C I P L E S O F

N. Gregory N. Gregory MankiwMankiw

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A C T I V E L E A R N I N G A C T I V E L E A R N I N G 11

Price controlsPrice controls

40

50

60

70

80

90

100

110

120

130

140

50 60 70 80 90 100 110 120 130Q

PS

0

The market for hotel rooms

D

Determine effects of:

A. $90 price ceiling

B. $90 price floor

C. $120 price floor

10

A C T I V E L E A R N I N G A C T I V E L E A R N I N G 11

A. $90 price ceilingA. $90 price ceiling

40

50

60

70

80

90

100

110

120

130

140

50 60 70 80 90 100 110 120 130Q

PS

0

The market for hotel rooms

D

The price falls to $90.

Buyers demand 120 rooms, sellers supply 90, leaving a shortage.

shortage = 30

Price ceiling

11

A C T I V E L E A R N I N G A C T I V E L E A R N I N G 11

B. $90 price floorB. $90 price floor

40

50

60

70

80

90

100

110

120

130

140

50 60 70 80 90 100 110 120 130Q

PS

0

The market for hotel rooms

D

Eq’m price is above the floor, so floor is not binding.

P = $100, Q = 100 rooms. Price floor

12

A C T I V E L E A R N I N G A C T I V E L E A R N I N G 11

C. $120 price floorC. $120 price floor

40

50

60

70

80

90

100

110

120

130

140

50 60 70 80 90 100 110 120 130Q

PS

0

The market for hotel rooms

D

The price rises to $120.

Buyers demand 60 rooms, sellers supply 120, causing a surplus.

surplus = 60

Price floor

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A C T I V E L E A R N I N G A C T I V E L E A R N I N G 22

Effects of a taxEffects of a tax

40

50

60

70

80

90

100

110

120

130

140

50 60 70 80 90 100 110 120 130Q

PS

0

The market for hotel rooms

D

Suppose govt imposes a tax on buyers of $30 per room.

Find new Q, PB, PS, and incidence of tax.

A C T I V E L E A R N I N G A C T I V E L E A R N I N G 22

AnswersAnswers

40

50

60

70

80

90

100

110

120

130

140

50 60 70 80 90 100 110 120 130Q

PS

0

The market for hotel rooms

D

Q = 80

PB = $110

PS = $80

Incidencebuyers: $10sellers: $20

Tax

PB =

PS =

Consumers, Producers, and the Efficiency of Markets

EconomicsP R I N C I P L E S O FP R I N C I P L E S O F

N. Gregory N. Gregory MankiwMankiw

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17

05

10152025

303540

4550

0 5 10 15 20 25

P

Q

demand curve

A. Find marginal buyer’s WTP at Q = 10.

B. Find CS for P = $30.

Suppose P falls to $20.How much will CS increase due to… C. buyers entering

the marketD. existing buyers paying

lower price

$

A C T I V E L E A R N I N G A C T I V E L E A R N I N G 11

Consumer surpConsumer surpluslus

A C T I V E L E A R N I N G A C T I V E L E A R N I N G 11

AnswersAnswers

18

05

10152025

303540

4550

0 5 10 15 20 25

P$

Q

demand curve

A. At Q = 10, marginal buyer’s WTP is $30.

B. CS = ½ x 10 x $10 = $50

P falls to $20.

C. CS for the additional buyers = ½ x 10 x $10 = $50

D. Increase in CS on initial 10 units= 10 x $10 = $100

0

5

1015

20

25

30

3540

45

50

0 5 10 15 20 25

P

Q

supply curve

A. Find marginal seller’s cost at Q = 10.

B. Find total PS for P = $20.

Suppose P rises to $30.Find the increase in PS due to… C. selling 5

additional unitsD. getting a higher price

on the initial 10 units19

A C T I V E L E A R N I N G A C T I V E L E A R N I N G 22

Producer surplusProducer surplus

A C T I V E L E A R N I N G A C T I V E L E A R N I N G 22

AnswersAnswers

0

5

1015

20

25

30

3540

45

50

0 5 10 15 20 25

P

Q

supply curve

A. At Q = 10, marginal cost = $20

B. PS = ½ x 10 x $20 = $100

P rises to $30.

C. PS on additional units= ½ x 5 x $10 = $25

D. Increase in PS on initial 10 units= 10 x $10 = $100

20

Application: The Costs of Taxation

EconomicsP R I N C I P L E S O FP R I N C I P L E S O F

N. Gregory N. Gregory MankiwMankiw

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A C T I V E L E A R N I N G A C T I V E L E A R N I N G 11

Answers to AAnswers to A

22

D

S

CS = ½ x $200 x 100= $10,000

0

50

100

150

200

250

300

350

400

0 25 50 75 100 125

P

Q

$

Total surplus= $10,000 + $10,000= $20,000

PS = ½ x $200 x 100= $10,000

P =

The market for airplane tickets

A C T I V E L E A R N I N G A C T I V E L E A R N I N G 11

Answers to BAnswers to B

23

D

S

CS = ½ x $150 x 75= $5,625

0

50

100

150

200

250

300

350

400

0 25 50 75 100 125

P

Q

$

Total surplus = $18,750

PS = $5,625

Tax revenue= $100 x 75= $7,500

DWL = $1,250

PS =

PB =

A $100 tax on airplane tickets

Application:International Trade

EconomicsP R I N C I P L E S O FP R I N C I P L E S O F

N. Gregory N. Gregory MankiwMankiw

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A C T I V E L E A R N I N G A C T I V E L E A R N I N G 11

Analysis of tradeAnalysis of trade

25

Without trade,PD = $3000, Q = 400

In world markets, PW = $1500

Under free trade, how many TVs will the country import or export?

Identify CS, PS, and total surplus without trade, and with trade.

P

Q

D

S

$1500

200

$3000

400 600

Plasma TVs

A C T I V E L E A R N I N G A C T I V E L E A R N I N G 11

AnswersAnswers

26

Under free trade, domestic

consumers demand 600

domestic producers supply 200

imports = 400

P

Q

D

S

$1500

200

$3000

600

Plasma TVs

imports

A C T I V E L E A R N I N G A C T I V E L E A R N I N G 11

AnswersAnswers

27

Without trade, CS = APS = B + CTotal surplus

= A + B + C

With trade, CS = A + B + DPS = CTotal surplus

= A + B + C + D

P

Q

D

S

$1500

$3000

Plasma TVs

A

B D

C

gains from trade

imports