topic 8 ： taxation(1)- positive principles of taxation
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Topic 8 ： Taxation(1)- Positive Principles of Taxation
Taxes• The government levies taxes on many goods
& services to raise revenue to pay for national defense, public schools, etc.
• The government can make buyers or sellers pay the 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.
S1
E
EXAMPLE : The Market for Pizza
Equilibriumwithout tax
P
Q
D1
$10.00
500
A Tax on Buyers
Effects of a $1.00 per unit tax on buyers
D1
$10.00
500430
P
Q
D2
$11.00
$9.00
Tax
470
• Without tax consumers would buy 430 pizzas if the price is $11.• For consumers it does not matter if the increase in price is due to price itself or tax.• If the market price is $10 but consumers have to pay $1 in tax then at P=$10 they would demand as much as at P=$11 without tax.•The same is true for any price.•Hence, $1 tax would shift the demand curve down to the left by vertical distance $1.
S1
D1
$10.00
500430
A Tax on BuyersA tax on buyers shifts the D curve down by the amount of the tax.
A tax on buyers shifts the D curve down by the amount of the tax.
P
QD2
$11.00PB =
$9.50PS =
Tax
Effects of a $1.50 per unit tax on buyers
The price buyers pay rises, the price sellers receive falls, equilibrium Q falls.
The price buyers pay rises, the price sellers receive falls, equilibrium Q falls.
Etb
430
S1
how the burden of a tax is shared among market participants
P
Q
D1
$10.00
500
D2
$11.00PB =
$9.50PS =
Tax
Because of the tax, buyers pay $1.00 more,
sellers get $0.50 less.
Because of the tax, buyers pay $1.00 more,
sellers get $0.50 less.
Etb
S1
A Tax on Sellers
A tax on sellers shifts the S curve up by the amount of the tax.
A tax on sellers shifts the S curve up by the amount of the tax.
P
Q
D1
$10.00
500
S2
430
$11.00PB =
$9.50PS =
Tax
Effects of a $1.50 per unit tax on sellers
The price buyers pay rises, the price sellers receive falls, equilibrium Q falls.
The price buyers pay rises, the price sellers receive falls, equilibrium Q falls.
Ets
S1Ets
Etb
E
What matters is this:A tax drives a wedge between the price buyers pay and the price sellers receive.
P
Q
D1
$10.00
500430
$9.50
$11.00PB =
PS =
Tax
Conclusion: The effects on P and Q, and the tax incidence are the same whether the tax is imposed on buyers or sellers!
incidence 发生率； 影响范围wedge 楔形物
Elasticity and Tax IncidenceCASE 1: Supply is more elastic than demand
P
QD
S
Tax
Buyers’ share of tax burden
Sellers’ share of tax burden
Price if no tax
PB
PS
In this case, buyers bear most of the burden of the tax.
In this case, buyers bear most of the burden of the tax.
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
PB
PS
In this case, sellers bear most of the burden of the tax.
In this case, sellers bear most of the burden of the tax.
• Conclusion:• If buyers’ price elasticity > sellers’ price elasticit
y, buyers can more easily leave the market when the tax is imposed, so buyers will bear a smaller share of the burden of the tax than sellers.
• If sellers’ price elasticity > buyers’ price elasticity, the reverse is true.
CASE STUDY: Who Pays the Luxury Tax?
• 1990: Congress of USA adopted a luxury tax on yachts, private airplanes, furs, expensive cars, etc.
• Goal of the tax: to raise revenue from those who could most easily afford to pay – wealthy consumers.
• But who really pays this tax?
The market for yachts
P
Q
D
S
Tax
Buyers’ share of tax burden
Sellers’ share of tax burden
PB
PS
Demand is price-elastic. Demand is price-elastic.
In the short run, supply is inelastic. In the short run, supply is inelastic.
Hence, companies that build yachts pay most of the tax.
Hence, companies that build yachts pay most of the tax.
Review• A tax is a wedge between the price buyers pay
and the price sellers receive. • A tax raises the price buyers pay and lowers th
e price sellers receive. • A tax reduces the quantity bought & sold. • These effects are the same whether the tax is i
mposed on buyers or sellers, so we do not make this distinction in this chapter.
QT
The Effects of a Tax P
Q
D
S
Eq’m with no tax: price = PE quantity = QE
PS
PB
PE
QE
Eq’m with tax = $T per unit:
Sellers receive PS
Quantity = QT
Buyers pay PB
Size of tax = $T
P
Q
D
S
Revenue from tax: $T x QT
PS
PB
PE
QEQT
Size of tax = $T
• Next, we apply welfare economics to measure the 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.
P
Q
D
S
Without a tax,
PE
QEQT
A
B C
D E
F
CS = A + B + CPS = D + E + FTax revenue = 0Total surplus
= CS + PS= A + B + C + D + E + F
P
Q
D
S
PS
PB
QEQT
A
B C
D E
F
CS = APS = FTax revenue = B + DTotal surplus
= A + B + D + F
With the tax,
The tax reduces total surplus by C + E
P
Q
D
S
PS
PB
QEQT
A
B C
D E
F
C + E is called the deadweight loss (DWL 无谓损失 ) of the tax, the fall in total surplus that results from a market distortion, such as a tax.
P
Q
D
S
PS
PB
QEQT
Because of the tax, the units between QT and QE are not sold. The value of these units to buyers is greater than the cost of producing them,so the tax prevents some mutually beneficial trades.
AA CC TT II VV E LE L EE AA RR NN II NN G G 11: : Analysis of taxAnalysis of tax
A. Compute CS, PS, and total surplus without a tax.
B. If $100 tax per ticket, compute CS, 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
AA CC TT II VV E LE L EE AA RR NN II NN G G 11: : Answers to AAnswers 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
AA CC TT II VV E LE L EE AA RR NN II NN G G 11: : Answers to BAnswers 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 = $20000-$18750=$1,250
PS =
PB =
A $100 tax on airplane tickets
What Determines the Size of the DWL?
• Which goods or services should government tax to raise the revenue it needs? – One answer: those with the smallest DWL.
• When is the DWL small vs. large? – It depends on the price elasticity
of supply and demand.
Recall: The price elasticity of demand (or supply) measures how much QD (or QS) changes when P changes.
the DWL of a tax is small.
When supply is inelastic,
DWL and the Elasticity of SupplyP
Q
D
S
Size of tax
The more elastic is supply, the larger is the DWL.
P
Q
D
S
Size of tax
the DWL of a tax is small.
DWL and the Elasticity of Demand
When demand is inelastic,
P
Q
D
S
Size of tax
P
Q
D
S
Size of tax
The more elastic is demand, the larger isthe DWL.
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 and sellers respond to changes in price,and therefore determines how much the tax distorts the market outcome.
AA CC TT II VV E LE L EE AA RR NN II NN G G 22: : Elasticity and DWL of a taxElasticity and DWL of a taxWould the DWL of a tax be larger if the tax were onA. Rice Krispies or sunscreen?B. Hotel rooms in the short run or hotel rooms i
n the long run?C. Groceries or meals at fancy restaurants?
AA CC TT II VV E LE L EE AA RR NN II NN G G 22: : AnswersAnswersA. Rice krispies or sunscreen• Rice krispies has many more close substitutes t
han sunscreen, so demand for rice krispies is more price-elastic than demand for sunscreen.
• So, a tax on rice krispies would cause a larger DWL than a tax on sunscreen.
AA CC TT II VV E LE L EE AA RR NN II NN G G 22: : AnswersAnswersB. Hotel rooms in the short run or long run• The price elasticity of demand and supply
for hotel rooms are larger in the long run than in the short run.
• So, a tax on hotel rooms would cause a larger DWL in the long run than in the short run.
AA CC TT II VV E LE L EE AA RR NN II NN G G 22: : AnswersAnswersC. 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 a larger DWL than a tax on groceries.
AA CC TT II VV E LE L EE AA RR NN II NN G G 33: : Discussion questionDiscussion question• The government must raise tax revenue
to pay for schools, police, etc. To do this, it can either tax groceries or meals at fancy restaurants.
• Which should it tax?
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’s t
he biggest source of government revenue. • For many workers, the marginal tax rate (the tax on th
e last dollar of earnings) is almost 50%. • How big is the DWL from this tax?
It depends on elasticity….
• If labor supply is inelastic, then this DWL is small.
• Some economists believe labor supply is inelastic, arguing that most workers work full time regardless of the wage.
•Other economists believe labor taxes are highly distorting because some groups of workers have elastic 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 w
hether and how much to work. – Many elderly choose when to retire based on the wag
e they earn.– Some people work in the “underground economy” to
evade high taxes.
discretion 判断力evade 逃避
The Effects of Changing the Size of the Tax
• Policymakers often change taxes, raising some and lowering others.
• What happens to DWL and tax revenue when taxes change?
Q2 Q1
DWL and the Size of the TaxP
Q
D
S
causes the DWL to more than double.
Doubling the tax 2T T
Initially, the tax is T per unit.
initial DWL
new DWL
Q3
P
Q
D
S
Q1
3T Tcauses the DWL to more than triple.
Tripling the tax
Initially, the tax is T per unit.
initial DWL
new DWL
DWL
Tax size
SummaryWhen a tax increases, DWL rises even more.
ImplicationWhen tax rates are low, 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.
ImplicationWhen tax rates are low, 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.
Q2
Revenue and the Size of the TaxP
Q
D
S
Q1
PB
PS
PB
PS
2T T
When the tax is small, increasing it causes tax revenue to rise.
Q3
P
Q
D
S
Q2
PB
PS
PB
PS
3T 2TWhen the tax is larger, increasing it causes tax revenue to fall.
The Laffer curve shows the relationship between the size of the tax and tax revenue.
Tax size
Tax revenue
The Laffer curve
SUMMARY
• A tax on a good reduces the welfare of buyers and sellers. This welfare loss usually exceeds the revenue the tax raises for the government.
• The fall in total surplus (consumer surplus, producer surplus, and tax revenue) is called the deadweight loss (DWL) of the tax.
• A tax has a DWL because it causes consumers to buy less and producers to sell less, thus shrinking the market below the level that maximizes total surplus.
• The price elasticities of demand and supply measure how much buyers and sellers respond to price changes. Therefore, higher elasticities imply higher DWLs.
• An increase in the size of a tax causes the DWL to rise even more.
• An increase in the size of a tax causes revenue to rise at first, but eventually revenue falls because the tax reduces the size of the market.