application: the costs of taxation

C H A P T E R

Application: Application: The Costs of TaxationThe Costs of Taxation

应用：赋税的代价应用：赋税的代价

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In this chapter, In this chapter, look for the answers to these look for the answers to these questions:questions: How does a tax affect consumer surplus, producer surplus, and total surplus?

What is the deadweight loss of a tax?

What factors determine the size of this deadweight loss?

How does tax revenue depend on the size of the tax?

税收怎样影响消费者剩余，生产者剩余和总剩余？

什么是税收的无谓损失？决定无谓损失大小的因

素有哪些？

税收规模如何影响税收收入？

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APPLICATION: THE COSTS OF TAXATION 3

Review from Chapter 6 A tax

drives a wedge between the price buyers pay and the price sellers receive.

raises the price buyers pay and lowers the price sellers receive.

reduces the quantity bought & sold.

These effects are the same whether the tax is imposed on buyers or sellers, so we do not make this distinction in this chapter.

税收在买者支付的价格和卖

者得到的价格之间打入一个契子

提高了买者为该物品支付的价格，降低了卖者从该物品得到的价格

减少了购买与销售的数量

无论是对买者还是卖者征税，结果都一样。因此本章我们不做这种区分


QT

The Effects of a Tax税收效应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


The Effects of a TaxP

Q

D

S

Revenue from tax: $T x QT

PS

PB

PE

QEQT

Size of tax = $T


The Effects of a Tax 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.

下面我们应用福利经济学来衡量从税收中得到的收益与损失

我们计算有税收与没有税收时的消费者剩余，生产者剩余，税收收入以及总剩余

税收能为对公众有利的服务提供资金支持（比如教育，公路，警察），因此我们把它算入总剩余



Q

D

S

Without a tax,

PE

QEQT

A

B C

D E

F

CS = A + B + C

PS = D + E + F

Tax revenue = 0

Total surplus= CS + PS= A + B + C + D + E + F



Q

D

S

PS

PB

QEQT

A

B C

D E

F

CS = A

PS = F

Tax revenue = B + D

Total surplus= A + B + D + F

With the tax,

The tax reduces total surplus by C + E



Q

D

S

PS

PB

QEQT

A

B C

D E

F

C + E is called the deadweight loss (DWL) of the tax, the fall in total surplus that results from a market distortion, such as a tax.


About the Deadweight LossP

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.

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 taxAnalysis of tax

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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


Answers to AAnswers to A

12

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


Answers to BAnswers to B

13

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


What Determines the Size of the DWL?

Which goods or services should govt tax to raise the revenue it needs?

One answer: those with the smallest DWL.

When is the DWL small vs. large? Turns out it depends on the price elasticities of supply and demand.

Recall: The price elasticity of demand (or supply) measures how much QD (or QS) changes when P changes.

政府应该对哪些物品或服务征税以获得它需要的税收收入？

答案：无谓损失最小的物品或服务

无谓损失什么时候大？什么时候小？这取决于需求弹性和供给弹性

复习：需求价格弹性（或供给价格弹性）衡量需求（或供给）对价格变动的反应程度


When supply is inelastic,

it’s harder for firms to leave the market when the tax reduces PS.

So, the tax only reduces Q a little,

and DWL is small.

When supply is inelastic,

it’s harder for firms to leave the market when the tax reduces PS.


and DWL is small.

DWL and the Elasticity of Supply

P

Q

D

S

Size of tax


DWL and the Elasticity of Supply

P

Q

D

S

Size of tax

The more elastic is supply,

the easier for firms to leave the market when the tax reduces PS,

the greater Q falls below the surplus-maximizing quantity,

the greater the DWL.

The more elastic is supply,

the easier for firms to leave the market when the tax reduces PS,

the greater Q falls below the surplus-maximizing quantity,

the greater the DWL.


DWL and the Elasticity of Demand

P

Q

D

S

Size of tax

When demand is inelastic,

it’s harder for consumers to leave the market when the tax raises PB.


and DWL is small.

When demand is inelastic,

it’s harder for consumers to leave the market when the tax raises PB.


and DWL is small.


DWL and the Elasticity of Demand

P

Q

D

S

Size of tax

The more elastic is demand,

the easier for buyers to leave the market when the tax increases PB,

the more Q falls below the surplus-maximizing quantity,

and the greater the DWL.

The more elastic is demand,

the easier for buyers to leave the market when the tax increases PB,

the more Q falls below the surplus-maximizing quantity,

and the greater the DWL.


Elasticity and the DWL of a taxElasticity and the DWL of a tax

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

A. Breakfast cereal or sunscreen?

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

C. Groceries or meals at fancy restaurants?

下面各组物品中，对哪种物品征税的无谓损失更大？A. 谷类早餐还是

防晒霜？B. 短期的宾馆住

房还是长期的宾馆住房？

C. 普通食品还是高档餐馆的用餐？

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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 AnswersAnswers

A. Breakfast cereal or sunscreen

From Chapter 5: Breakfast cereal has more close substitutes than sunscreen, so demand for breakfast cereal is more price-elastic than demand for sunscreen.

So, a tax on breakfast cereal would cause a larger DWL than a tax on sunscreen.

A.谷类早餐还是防晒霜

我们在第五章已经知道：谷类早餐相对于防晒霜有更多相近的替代品，谷类早餐的需求价格弹性要大于防晒霜的需求价格弹性

因此，对谷类早餐征税造成的无谓损失要大于对防晒霜征税造成的无谓损失

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B. Hotel rooms in the short run or long run

From Chapter 5: The price elasticities 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.

B. 短期的宾馆住房还是长期的宾馆住房

我们在第五章已经知道：长期宾馆住房的需求弹性和供给弹性都要大于短期宾馆住房

因此，对长期的宾馆住房征税所造成的无谓损失要大于对短期的宾馆住房征税造成的无谓损失

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C. Groceries or meals at fancy restaurants

From Chapter 5: 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.

C.普通食品还是高档餐馆的用餐

我们在第五章已经知道：普通食品是必需品，其需求的价格弹性要低于高档餐馆用餐的需求弹性

因此，对高档餐馆用餐征税造成的无谓损失要大于对普通食品征税造成的无谓损失

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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?

政府需要增加税收收入来支付对学校，警察等的支出。为达到这个目的，政府既可以对普通食品征税也可以对高档餐馆的用餐征税

应该对哪个征税？

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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’s the biggest source of govt revenue.

For the typical worker, the marginal tax rate (the tax on the last dollar of earnings) is about 40%.

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

一个更大的政府能提供更多的服务，但这需要更高的税收，而税收会带来无谓损失

税收带来的无谓损失越大，对小政府的呼声就越大

对劳动收入征收尤其重要：它是政府收入的最大来源

对一个典型的工作者而言，边际税率（对最后一美元收入的征税）高达 40%.

这种税收的无谓损失有多大？它取决于弹性……



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.

如果劳动的供给是缺乏弹性的，那无谓损失比较小

一些经济学家认为劳动供给是缺乏弹性的，以至于大部分工人在无论工资高低情况下都会选择全职工作



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 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.

另外一些经济学家认为劳动税高度扭曲了劳动市场，因为一部分工人的劳动供给富有弹性，对激励做出反应较大：许多工人可以调整他们的工作

时间比如：加班工作

许多家庭有第二个赚钱人，他们根据情况决定是否要工作以及工作多少时间

许多老年人根据他们的工作来选择何时退休

一些人从事“地下经济”来逃避高税收


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? We explore this next….

政策制定者经常提高或降低税收

当税收变动时，无谓损失的变动情况如何？我们接下来考虑这个问题……


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

DWL and the Size of the TaxP

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 and the Size of the Tax

DWL

Tax size

Summary

When a tax increases, DWL rises even more.

Implication

When 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.

Implication

When 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

Revenue and the Size of the TaxP

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.拉弗曲线：揭示了税收规模与税收收入之间的关系

Revenue and the Size of the Tax

Tax size

Tax revenue

The Laffer curve

CHAPTER SUMMARYCHAPTER 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 govt.

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.

一种物品的税收使该物品买者与卖者的福利减少了，而且，消费者剩余和生产者剩余的减少常常超过了政府筹集到的收入。

总剩余 --- 消费者剩余，生产者剩余和税收收入之和 --- 的减少被称为税收的无谓损失

税收带来无谓损失是因为它使买者少消费，使卖者少生产，而且这种行为变动使市场规模缩小到使总剩余最大化的水平之下

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CHAPTER SUMMARYCHAPTER SUMMARY 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.

由于需求价格弹性和供给价格弹性衡量买者与卖者对价格变动的反应程度，因此，弹性越大意味着无谓损失越大

税收规模的增大可能使税收的无谓损失增加的更多

税收收入起初随着税收规模的扩大而增加，但如果税收规模达到足够大时，税收收入就会开始下降

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application: the costs of taxation

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