20121224095330318

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Topic 8：Taxation(1)-Positive Principles of Taxation

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Taxes• The government levies taxes on many goods &

services to raise revenue to pay for nationaldefense, public schools, etc.

• The government can make buyers or sellers paythe tax.

• The tax can be a percentage of the good’s

price, or a specific amount for each unit sold. – For simplicity, we analyze per-unit taxes only.

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S 1

EXAMPLE : The Market for Pizza

Equilibrium

without tax

P

Q

D 1

$10.00

500

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A Tax on Buyers

Effects of a $1.00 per unit tax on buyers

D 1

$10.00

500430

P

Q

D 2

$11.00

$9.00

Tax

470

• Without tax consumerswould buy 430 pizzas if theprice is $11.• For consumers it does notmatter if the increase in priceis due to price itself or tax.• If the market price is $10 butconsumers have to pay $1 intax then at P=$10 they would

demand as much as at P=$11without tax.•The same is true for any price.•Hence, $1 tax would shift thedemand curve down to the left

by vertical distance $1.

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S 1

D 1

$10.00

500430

A Tax on Buyers

A tax onbuyers shiftsthe D curvedown by the

amount of thetax.

P

Q

D 2

$11.00P B =

$9.50P S =

Tax

Effects of a $1.50 per

unit tax on buyers

The pricebuyers payrises, theprice sellersreceive falls,equilibrium

Q falls.

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430

S 1

how the burden of a tax is shared among

market participantsP

Q

D 1

$10.00

500

D 2

$11.00P B =

$9.50P S =

Tax

Because

of the tax,

buyers pay$1.00 more,

sellers get

$0.50 less.

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S 1

A Tax on Sellers

A tax on sellersshifts the S curve up by theamount of the

tax.

P

Q

D 1

$10.00

500

S 2

430

$11.00P B =

$9.50P S =

Tax

Effects of a $1.50 per

unit tax on sellers

The price

buyers pay

rises, the pricesellers receive

falls,

equilibrium Q

falls.

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S 1

What matters isthis:

A tax drivesa wedgebetween theprice buyerspay and theprice sellersreceive.

P

Q

D 1

$10.00

500430

$9.50

$11.00P B =

P S =

Tax

The effects on P and Q , and the tax incidence

are the same whether the tax is imposed onbuyers or sellers!

incidence发生率；影响范围 wedge楔形物

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Elasticity and Tax Incidence

CASE 1: Supply is more elastic than demandP

Q

D

S

Tax

Buyers’ share

of tax burden

Sellers’ share

of tax burden

Price if no tax

P B

P S

In this case,

buyers bear

most of the

burden of

the tax.

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CASE 2: Demand is more elastic than supply

P

Q

D

S

Tax

Buyers’ share

of tax burden

Sellers’ share

of tax burden

Price if no tax

P B

P S

In this case,

sellers bear

most of the

burden of the tax.

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• If buyers’ price elasticity > sellers’ priceelasticity, buyers can more easily leave themarket when the tax is imposed, so buyers willbear a smaller share of the burden of the tax

than sellers.• If sellers’ price elasticity > buyers’ price

elasticity, the reverse is true.

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CASE STUDY: Who Pays the Luxury Tax?

• 1990: Congress adopted a luxury tax on yachts,private airplanes, furs, expensive cars, etc.

•

Goal of the tax: to raise revenue from thosewho could most easily afford to pay – wealthy consumers.

• But who really pays this tax?

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The market for yachts

P

Q

D

S

Tax

Buyers’ share

of tax burden

Sellers’ share

of tax burden

P B

P S

Demand isprice-elastic.

In the short run,supply is inelastic.

Hence,companiesthat build

yachts paymost of the tax.

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Review

• A tax is a wedge between the price buyers payand the price sellers receive.

•

A tax raises the price buyers pay and lowers theprice sellers receive.

• A tax reduces the quantity bought & sold.

• These effects are the same whether the tax is

imposed on buyers or sellers, so we do notmake this distinction in this chapter.

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Q T

The Effects of a Tax P

Q

D

S

Eq’m with no tax:

price = P E

quantity = Q E

P S

P B

P E

Q E

Eq’m withtax = $T per unit:

Sellers receive P S

Quantity = Q T

Buyers pay P B

Size of tax = $T

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P

Q

D

S

Revenue from tax:$T x Q T

P S

P B

P E

Q E Q T

Size of tax = $T

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• Next, we apply welfare economics to measurethe gains and losses from a tax.

• We determine consumer surplus (CS),producer surplus (PS), tax revenue,and total surplus with and without the tax.

• Tax revenue can fund beneficial services

(e.g . education, roads, police)so we include it in total surplus.

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P

Q

D

S

Without a tax,

P E

Q E Q T

A

B CD E

F

CS = A + B + C

PS = D + E + F

Tax revenue = 0

Total surplus= CS + PS

= A + B + C+ D + E + F

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P

Q

D

S

P S

P B

Q E Q T

A

B CD E

F

CS = A

PS = F

Tax revenue

= B + DTotal surplus

= A + B+ D + F

With the tax,

The tax reducestotal surplus by

C + E

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P

Q

D

S

P S

P B

Q E Q T

A

B CD E

F

C + E is called thedeadweight loss (DWL无谓损失) of the tax, the fall in

total surplus thatresults from amarket distortion,such as a tax.

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P

Q

D

S

P S

P B

Q E Q T

Because of the tax,

the units betweenQ T and Q E are notsold.

The value of these

units to buyers isgreater than the costof producing them,

so the tax preventssome mutuallybeneficial trades.

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A C T I V E L E A R N I N G 1:

Analysis of tax

A. ComputeCS, PS, andtotal surpluswithout a tax.

B. If $100 taxper ticket,computeCS, PS,

tax revenue,total surplus,and DWL.

D

S

0

50

100

150

200

250

300

350

400

0 25 50 75 100 125

P

Q

$

The market for airplane tickets

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Answers to A

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

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Answers to B

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

P S =

P B =

A $100 tax onairplane tickets

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What Determines the Size of the DWL?

• Which goods or services should government taxto raise the revenue it needs?

– One answer: those with the smallest DWL.

• When is the DWL small vs. large? – It depends on the price elasticities

of supply and demand.

Recall:The price elasticity of demand (or supply)measures how much Q D (or Q S ) changeswhen P changes.

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the DWL of atax is small.

When supplyis inelastic,

DWL and the Elasticity of SupplyP

Q

D

S

Sizeof tax

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The more elasticis supply, the

larger is the DWL.

P

Q

D

S

Sizeof tax

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the DWL of atax is small.

DWL and the Elasticity of Demand

When demandis inelastic,

P

Q

D

S

Sizeof tax

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P

Q

D

S

Sizeof tax

The more elasticis demand, the

larger isthe DWL.

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Why Elasticity Affects the Size of DWL

• A tax distorts the market outcome:consumers buy less, producers sell less,market Q is below the surplus-maximizing Q .

• Elasticity measures how much buyers andsellers respond to changes in price,

and therefore determines how much the

tax distorts the market outcome.

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Elasticity and DWL of a tax

Would the DWL of a tax be larger if thetax were on

A. Rice Krispies or sunscreen?

B. Hotel rooms in the short run or hotel rooms inthe long run?

C. Groceries or meals at fancy restaurants?

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Answers

A. Rice Krispies or sunscreen• Rice Krispies has many more close substitutes

than sunscreen, so demand for Rice Krispies ismore price-elastic than demand for sunscreen.

• So, a tax on Rice Krispies would cause a larger DWL than a tax on sunscreen.

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Answers

B.Hotel rooms in the short run or long run• The price elasticities of demand and supply

for hotel rooms are larger in the long run thanin the short run.

• So, a tax on hotel rooms would cause a larger DWL in the long run than in the short run.

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Answers

C.Groceries or meals at fancy restaurants• Groceries are more of a necessity and therefore

less price-elastic than meals at fancy restaurants.

• So, a tax on restaurant meals would cause alarger DWL than a tax on groceries.

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Discussion question

• The government must raise tax revenue topay for schools, police, etc. To do this, itcan either tax groceries or meals at fancy

restaurants.• Which should it tax?

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How Big Should the Government Be?

• A bigger government provides more services,but requires higher taxes, which cause DWLs.

• The larger the DWL from taxation,the greater the argument for smaller government.

• The tax on labor income is especially important; it’sthe biggest source of government revenue.

• For many workers, the marginal tax rate (the tax on thelast dollar of earnings) is almost 50%.

• How big is the DWL from this tax?It depends on elasticity….

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• If labor supply is inelastic, then this DWL is small.

• Some economists believe labor supply is

inelastic, arguing that most workers workfull time regardless of the wage.

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•Other economists believe labor taxes are highly

distorting because some groups of workers haveelastic supply and can respond to incentives:

– Many workers can adjust their hours,

e.g. by working overtime.

– Many families have a 2nd earner with discretion over

whether and how much to work.

– Many elderly choose when to retire based on the wage

they earn. – Some people work in the“underground economy” to

evade high taxes.

discretion判断力 evade逃避

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The Effects of Changing the Size of the Tax

• Policymakers often change taxes, raising someand lowering others.

• What happens to DWL and tax revenue whentaxes change?

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Q 2 Q 1

DWL and the Size of the TaxP

Q

D

S

causes the DWLto more than

double.

Doubling the tax 2T T

Initially, the tax isT per unit.

initial

DWL

newDWL

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Q 3

P

Q

D

S

Q 1

3T T causes the DWLto more thantriple.

Tripling the tax

Initially, the tax isT per unit.

initial

DWL

newDWL

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DWL

Tax size

Summary

When a tax increases,DWL rises even more.

Implication

When tax rates arelow, raising them

doesn’t cause much

harm, and lowering

them doesn’t bring much benefit.

When tax rates are

high, raising them is

very harmful, and

cutting them is very

beneficial.

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Q 2

Revenue and the Size of the TaxP

Q

D

S

Q 1

P B

P S

P B

P S

2T T

When thetax is small,increasing itcauses taxrevenue to rise.

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Q 3

P

Q

D

S

Q 2

P B

P S

P B

P S

3T 2T When thetax is larger,increasing itcauses tax

revenue to fall.

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The Laffer curve shows therelationshipbetween

the size of the taxand tax revenue.

Tax size

Taxrevenue

The Laffer curve

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SUMMARY

• A tax on a good reduces the welfare of buyersand sellers. This welfare loss usually exceedsthe revenue the tax raises for the government.

• The fall in total surplus (consumer surplus,

producer surplus, and tax revenue) is called thedeadweight loss (DWL) of the tax.

• A tax has a DWL because it causes consumersto buy less and producers to sell less, thus

shrinking the market below the level thatmaximizes total surplus.

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• The price elasticities of demand and supplymeasure how much buyers and sellers respond toprice changes. Therefore, higher elasticities implyhigher DWLs.

•

An increase in the size of a tax causes the DWL torise even more.

• An increase in the size of a tax causes revenue torise at first, but eventually revenue falls becausethe tax reduces the size of the market.

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