Taxation and income
distribution
Today: Some basic tax theory
Begin Unit 4

Today
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
Parts of chapter 14
An introduction to some basic theories related to
taxation
Taxation


Taxes are typically used to finance public
projects
Deadweight loss comes with most forms of
taxation

This will be discussed in next lecture
Taxation and income distribution

The US federal tax system has been set up
so that people with high incomes have higher
average tax rates

Do people consume more leisure with high
marginal tax rates?
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Usually yes
Public project financing

People with high tax rates probably have high
willingness to pay for many public projects
Taxation and income distribution
Table 14.3 Average federal tax rates and share of federal taxes by
income quintile (2006)
Income Category
Average Federal
Tax Rate
Share of
Federal Taxes
Lowest Quintile
5.6%
1.1%
Second Quintile
12.1
5.2
Third Quintile
15.7
10.3
Fourth Quintile
19.8
19.0
Highest Quintile
26.5
64.2
All Quintiles
21.6
100.0
Top 1%
31.2
21.3
Source: Congressional Budget Office [2004]. These figures are based
on projections that rely on assumptions about inflation and income
growth. They include all tax law as of 2001.
Some terminology

Statutory incidence

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Who legally has to pay for the tax
Economic incidence

How much does real income change to all parties
due to a tax?
Some terminology

Lump sum tax
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
Proportional tax
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Average tax rate is independent of income
Progressive tax
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
A tax that has to be paid no matter how a person
behaves
Average tax rate increases with income
Regressive tax

Average tax rate decreases with income
Some terminology

Unit tax


A tax that is paid per unit of a good
Ad valorem tax
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A tax that is a percentage of the purchase price
Partial equilibrium models

With partial equilibrium models, only one
market is examined at any one time


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Ignores possible spillover effects
Usually easier to analyze than general equilibrium
models
Two types of taxes analyzed


Unit tax
Ad valorem tax
Unit tax

You have likely seen unit taxes before



Econ 1 (or equivalent)
Econ 100A/B (or equivalent)
Either the buyer or seller pays a given dollar
amount for each unit sold or purchased
$
2.60
Before Tax
After Tax
Partial
Equilibrium
Models
2.40
Consumers Pay
$1.20
$1.40
2.20
Suppliers Receive
$1.20
$1.00
S1
2.00
S0
1.80
1.60
1.40
1.20
1.00
0.80
D1
D0
0.60
0
1
2
3
4
5
6
7
Quantity 8
Ad valorem taxes

Assume that the consumer pays an ad
valorem tax


Example: 6% sales tax (of the net price) imposed
on the consumer
The ad valorem tax shifts the demand curve
by the same percentage (relative to the
horizontal axis)
Price per pound of food
Ad valorem taxes
Sf
Pr
P0
Pm
Df
Df’
Qr
Q0
Qm
Pounds of food
per year
Tax on gross price? …or net price?

A tax on the gross price (paid by consumers)
lowers the willingness to pay by the
percentage of the tax

Example


25% tax of gross price when demand is P = 4000 – 20Q
New demand after tax is P = (1 – 0.25) (4000 – 20Q)

P = 3000 – 15Q
Tax on gross price? …or net price?

A tax on the net price (paid by consumers) is
more complicated

You need to find the new demand such that when
the tax is added, you get the new demand
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Example

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25% tax of net price when demand is P = 4000 – 20Q
WTP with the tax is 5/4 of WTP without the tax
In other words, WTP without the tax is 4/5 the WTP with the
tax
New demand after the tax is P = (4/5) (3000 – 20Q), which
leads to P = 3200 – 16Q
Other types of taxes
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Taxes from working

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Capital taxes
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Income tax
Social Security tax
Hospital insurance tax (Medicare)
Problem: Mobility of capital may move capital out
of the country with taxation
Taxes on profits


Accounting profits
Economic profits
Summary


High income people pay a higher percentage
of their income in taxes
Different forms of taxation exist


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Unit tax
Ad valorem tax
Taxes on wages
Capital taxes
Profit taxes
Problem: Ad valorem tax
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Supply: P = Q
Demand: P = 1710 – Q
What is the equilibrium in the absence of a
tax?
What is the equilibrium if there is a 10% tax
of the gross price?
No taxes

Set Q = 1710 – Q


Q = 855
Since P = Q from the supply curve, P = 855
With a tax

A tax on the gross price implies that the
willingness to pay goes down by 10% for
each unit


New demand is P = 1539 – 0.9Q
Set Q = 1539 – 0.9Q

Q = 810
With a tax

What about price?

Price without the tax is 810


This is the price that suppliers receive
Price with tax is 810/0.9 = 900

This is the price that consumers pay
Inevitable: Death and…