Pub Econ Lecture 20 Optimal Taxation

8/3/2019 Pub Econ Lecture 20 Optimal Taxation

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Public Finance

Dr. Katie Sauer

Optimal Taxation


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In the absence of market failures, the market outcome is

the socially efficient outcome.

Taxes cause behavior changes.

Taxes reduce efficiency.


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Price

Quantity

Supply

Demand

Q

P

At Qt, the value to

buyers of the good

exceeds the cost ofproduction of the

good.

forgone transactions

Total surplus is not

maximized.

- inefficient

- Deadweight

Loss

Supply + tax

tax

Pt

Qt

Pp

Recall a tax on a good:


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The size of the Dead weight Loss depends on elasticity

and the size of the tax.

Given a stable demand curve, the deadweight loss islarger when supply is relatively elastic.

Given a stable supply curve, the deadweight loss is

larger when demand is relatively elastic.


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A higher elasticity means people are changing their

behavior more in response to the higher price (from the

tax). - fewer goods are produced and sold

- goods that arent produced, sold, or taxed do not

benefit anyone


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quantity

price

quantity

price

D

D

Inelastic Demand Elastic Demand

Pt

P1

Pt

P1

Qt Q1 Q1Qt

S

S + taxS + tax

Pp Pp

The DWL is larger when demand is more elastic.


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quantity

price

quantity

price

D

D

Inelastic Supply Elastic Supply

PtP1

Pt

P1

Qt Q1 Q1Qt

S

S + taxS + tax

Pp

Pp

The DWL is larger when supply is more elastic.

S


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As the size of a tax increases, the marginal deadweight

loss from the tax increases.

The deadweight loss rises more quickly than the size of

the tax.

StaxStax

Stax

S S S

D D D

P P P

QQQ


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Mathematical reason:

Deadweight loss is roughly a triangle.The area of a triangle is (1/2)(base)(height).

The height of the DWL triangle is the tax amount.

The base of the DWL triangle is the reduction inquantity sold.

When a tax is increased, both the base and height of the

DWL triangle increase.

So, when a tax is increased, DWL loss rises more than

the amount of the tax.


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The formula for calculating DWL:

!

P

QxxDWL

DS

DS 2

2

1X

LL

LL

S is elasticity of supply

D is elasticity of demand is the tax rate


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The appropriate elasticities to use are called thecompensated elasticities.

- reflect substitution effects only

Any government revenue raising has income effects.

The inefficiency of the tax comes from people changing

their behavior due to substitution effects.

In practice, we often use the uncompensated elasticites.

- easier


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DWL and efficient tax systems

1. Efficiency is affected by a markets preexisting

distortions

- DWL from negative externalities can becorrected with a tax.

- In markets other than perfect competition,

goods are underproduced relative to thecompetitive outcome a tax increases the

DWL.


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2. Progressive tax systems can be less efficient

Two types of workers: low wage, high wage

Levy a 20% payroll tax on everyone. (proportional)

Assuming all workers have the same elasticity of supply,

all workers reduce their hours by the same amount.

Because the high-wage worker has a higher marginalproduct of labor, society loses more efficiency when the

high-wage worker reduces hours.

- DWL will be larger in the high-wage market


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Suppose a progressive tax system:

0% tax on first $10,000 of income

60% tax on additional income

No real DWL in the low-wage labor market.

Higher tax rate on high-wage earners reduces their labor

supply even more than a 20% payroll tax.

- DWL rises faster than the tax rate

**The more you load taxes on a narrow base, the faster

DWL rises.**


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3. Smoothing Tax Rates

Because the marginal deadweight loss rises with the tax

rate, governments should not raise and lower taxes as

they need money.

Instead they should set a long-run tax rate that will, on

average, meet budgetary needs.

Efficiency in taxation over time is achieved by taxsmoothing.


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Ramsey Taxation(Optimal Commodity Taxation)

Frank Ramsey considered a government looking to

raise revenue by taxing different commodities.

He asked

How can a government raise a given amount ofrevenue with the least amount of distortion?


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His answer:

The government should set taxes across commodities so

that the ratio of marginal deadweight loss tomarginal revenue is equal across commodities.

P!!B

B

A

A

MR

MDWL

MR

MDWL


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MDWL is the marginal deadweight loss from increasing

the tax on good i .

MR is the marginal revenue raised from that tax increase.

is the value of additional government revenue.

- the value of having another dollar in the

governments hands relative to its next best use in

the private sector

- small means additional govt revenues

have little value relative to the value that

private individuals place on having that

money


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Think ofMDWL/MR as the marginal cost of taxation.

Think of as the marginal benefit of taxation.


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B

B

A

A

MR

MDWL

MR

MDWL"If

Then taxing good A causes more inefficiency per

dollar of revenue raised than taxing good B.

Reduce taxes on A and raise taxes on B.


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If commodity markets are competitive, we can express

the optimal commodity tax rate as:

PL

X

i

i 1* !

i is the elasticity of demand for commodity i.


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Two rules for setting optimal commodity taxes:

1. Elasticity Rule

if high elasticity of demand tax it at a lower rate

if low elasticity of demand tax it at a higher rate

DWL rises with elasticity.

2. Broad Base Rule

better to tax a wide variety of goods at a low rate

than tax a few goods at a high rate


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Optimal Income Taxes

In the US, income taxation is a much more importantsource of revenue than commodity taxation.

Goals:

- meet budgetary requirements for revenue

- minimize distortions due to taxes

- vertical equity

(raise revenue in a manner that maximizes the

nations social welfare function)


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In designing optimal income taxes, the government needs

to consider the effect of raising tax rates on the size of thetax base.

A tax on labor income:revenues raised = tax rate x tax base

Effects of increasing the tax rate:

- tax revenue for a given labor income will rise- workers reduce labor income tax base shrinks


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At low tax rates, the first effect dominates.

Laffer Curve:


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An optimal income tax system meets the following:

Set income tax rates across groups such that

P!!B

B

A

A

MR

MU

MR

MU

MUi

is the marginal utility of individual i.

MRi is the marginal revenue from taxing individual i.

is the value of additional government revenues.


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B

B

A

A

MR

MU

MR

MU"If

Reduce tax rates on A and raise tax rates on B.

(When A has more money MU falls.)


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Two factors to balance when setting optimal income taxes:

1. Vertical Equitysocial welfare is maximized when those who have

a high level of consumption (low MU) are taxed

more heavily than those with a low level of

consumption

miss the money less

2. Behavioral Response

as taxes on a group rise, individuals may respond

by earning less income additional taxes will

raise less revenue


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Tax-Benefit Linkages

Tax-benefit linkages can affect the equity and efficiencyof a tax.

payroll taxes finance social insurance programs


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Consider a workers comp program that is financed by a

payroll tax on employers.

- reduction demand for

labor

In equilibrium:

- lower wage

- reduced labor

- DWL


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But, workers comp benefits workers.

Workers do not need to be compensated in the wage forjob-related risk.

- willing to accept a lower wage


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S2benefits

L3

w3

- increase in supply of

labor

Equilibrium labor is

lower than original,

but higher than taxalone.

DWL is less.

If workers fully valued the benefit at its cost to employers

there would be no DWL.

Pub Econ Lecture 20 Optimal Taxation

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