Principles of Tax Analysis
© Allen C. Goodman, 2009
1
Lots of Different Taxes
Income/Business
Personal Income
Corporate Income
Value-Added
License
Consumption
Sales
Use
Motor Fuel
Alcoholic Beverage
Hotel/Motel
Restaurant Meals
Most economists
Telephone Call
Don’t like this one.
Gambling
Wealth
Property
Estate
Inheritance
Transfer
Why?
2
Lots of Different Taxes
Income/Business
Consumption
Wealth
Personal Inc.
Corporate Inc.
Value-Added
License
Sales
Use
Motor Fuel
Alcoholic Beverage
Hotel/Motel
Restaurant Meals
Telephone Call
Gambling
Property
Estate
Inheritance
Transfer
3
Lots of Different Taxes
Income/Business
Consumption
Wealth
Personal Inc.
Corporate Inc.
Value-Added
License
Sales
Use
Motor Fuel
Alcoholic Beverage
Hotel/Motel
Restaurant Meals
Telephone Call
Gambling
Property
Estate
Inheritance
Transfer
Why good?
Why bad?
4
Tax Incidence
• Who REALLY pays the tax
• If you buy something at the store, you give
$ to the clerk, and the store pays $ to the
gov’t, but who really pays?
• If you rent an apartment and property
taxes in your city rise, what happens to the
rent that you pay? Who really pays?
5
Tax Incidence and Burden
• Progressive Tax
– Tax Burden/income ↑
as income ↑
• Proportional Tax
– Tax Burden/income
is constant as
income ↑
Tax
• Regressive Tax
– Tax Burden/income ↓
as income ↑
Income
6
Ave  Ray to origin
Mgl  slope
Progressive Tax
Average
Marginal
ΔT
T
• Progressive Tax
– Tax Burden/income ↑
as income ↑
– Slope of ray = T/Y
– Mgl Tax Rate =
ΔT/ΔY
• Example – Gas
Guzzler Tax
• Federal Income Tax
ΔY
Y
Tax
Mgl.
Tax
Rate
Ave.
Tax
Rate
T
Y1
Y2 Y3
Income
7
Ave  Ray to origin
Proportional Tax
Mgl  slope
Average
Marginal
ΔT
T
• Proportional Tax
– Tax Burden/income
constant as income ↑
– Slope of ray = T/Y
– Mgl Tax Rate =
ΔT/ΔY
Y
ΔY
Tax
• Example – Medicare
Tax
Y1
Y2 Y3
Income
8
Ave  Ray to origin
Mgl  slope
Regressive Tax
Average
Marginal
ΔT
T
• Regressive Tax
– Tax Burden/income ↓
as income ↑
– Slope of ray = T/Y
– Mgl Tax Rate =
ΔT/ΔY
ΔY
Y
Tax
Mgl.
Tax
Rate
• Example – FICA tax
for Social Security
Y1
Y2
Y3
Income
9
FICA and Medicare
FICA and Medicare Taxes
7000
FICA Tax - 2008
6000
FICA Tax - 2009
Taxes ($)
5000
Medicare Tax
4000
3000
2000
1000
0
0
20000
40000
60000
80000
100000
120000
Payroll Income
10
General Rules for Taxes
• Only way (legally) to avoid taxes is to
change behavior.
• The more that one agent can avoid the tax
– the less is collected
– the more someone else pays
11
Efficient
Quantity!
WHY?
Taxes and Efficiency
• Excise Tax
– Tax on a particular
good.
– Look at a unit (as
oppose to percentage)
tax.
D
S
$
P0
• Partial eq’m analysis
looks at a single
market.
Q0
12
Q
Taxes and Efficiency
• Excise Tax
– Tax on a particular good.
– Look at a unit (as oppose to
percentage) tax.
• $1 Tax Collected on
DEMANDERS
D
S
$
Why is this treated
as a downward shift?
P0
3.0
Suppose you buy gasoline at $3.00 per
gallon.
$1
Your state imposes a $1.00/gallon tax.
You keep your receipts and pay tax.
You demand based on $2.00 per gallon,
because you know you’ll have to pay an
additional $1.00. Your demand curve shifts
DOWN by $1.00.
Q0
13
Q
Taxes and Efficiency
• Excise Tax
– Tax on a particular
good.
– Look at a unit (as
oppose to percentage)
tax.
D
S
$
D'
P1
P0
3.0
Total Revenue
$1
• $1 Tax Collected on
DEMANDERS
Who Pays?
Q1 Q0
14
Q
Taxes and Efficiency
• Excise Tax
– Tax on a particular
good.
– Look at a unit (as
oppose to percentage)
tax.
D
S
$
P1
Con.
P0
3.0
DW
Prod.
$1
• $1 Tax Collected on
DEMANDERS
What’s DW$
Q1 Q0
15
Q
EXACTLY the
same result.
Suppose the $1 is on Suppliers?
• Excise Tax
– Tax on a particular
good.
– Look at a unit (as
oppose to
percentage) tax.
D
S
$
P1
P0
3.0
Cons.
Total RevenueDW
Prod.
• $1 Tax Collected
on SUPPLIERS
Who Pays?
Q1 Q0
16
Q
If result is same …
• Why do we usually collect sales taxes
from the sellers?
• Do we ever try to collect it from the
buyers?
• What happens when we do?
17
Important Concepts!
• DW loss relates to the change in quantity. Remember,
we saw that efficiency related to quantity. The more
behavioral change that a tax makes, the more DW loss.
• Incidence relates to elasticity of demand and supply.
Remember elasticity addresses whether quantity
changes a little or lot. If you can change your behavior a
lot, and avoid the tax, its incidence on you is small.
• If you can’t change your behavior and avoid it, its
incidence is a lot! Does it matter how we collect the tax?
18
Another Gas Tax Example S'
• Suppose that Southfield
puts a $1/gallon tax on
gas.
• Let’s look at demand and
supply.
• Why did I draw demand
and supply like I did.
Who Pays?
Price ↑ a little;
Quantity ↓ a lot
Most is paid by
producers.
S
$
$1
P1
Consumer
P0
Total (yellow)
D
by producer
Q1
Q0
19
Quantity
Another Gas Tax Example S'
• Suppose that the US
puts a $1/gallon tax on
gas.
• Let’s look at demand and
supply.
• Why did I draw demand
and supply like I did.
Who Pays?
S
$
P1
$1
Tax
Collected
P0
D
Price ↑ a lot;
Quantity ↓ a little
Most is paid by
consumers.
WHY?
Q1
Q0
20
Quantity
Excess Burden – Gen’l Eq’m
Other Goods
• Previously, we looked
only at a single market.
Even if a tax doesn’t
change quantity in a
given market it may
change behavior in other
markets.
• We can’t measure U1 – U2,
but we CAN, in principle,
measure the cost in $ of
this excess burden.
U1
U2
U0
Excess
Burden
21
Gasoline
Even if Q doesn’t change! – Gen’l Eq’m
Other Goods
• Previously, we looked
only at a single market.
Even if a tax doesn’t
change quantity in a
given market (again,
suppose it’s gasoline) it
may change behavior in
other markets.
• Again we can’t measure
U1 – U2, but we CAN, in
principle, measure the cost
in $ of this excess burden,
even though the amount of
gas did not change.
U0
U1
U2
22
Gasoline
WHO
REALLY
PAYS?
Tax Incidence
© Allen C. Goodman, 2009
23
What has been happening
• Over time, the share of output generated
from the relatively less cyclically sensitive
service-producing industries has risen
modestly in comparison with relatively
larger cyclically sensitive goods-producing
industries.
• So, as the share of services has risen the
share (and possibly the amount) of goodsbased sales taxes has fallen.
24
Sources of State Revenues
• Go to Spreadsheet
All States
http://www.census.gov/compendia/statab/cats/state_local_govt_finances_employment/state_government_finances.html25
Where does Michigan stand?
• Go to Spreadsheet.
http://www.census.gov/compendia/statab/cats/state_local_govt_finances_employment/state_government_finances.html26
Why
drawn like
this?
Short-Run and Long-Run Impacts
D
$
• Look at SR
supply
elasticities?
• Look at SR
demand
elasticities?
• What is impact of
6% tax on
services?
S'
S
P2
P1
Total Tax Rev.
DW is small
Total Sales
Q2 Q1
Quantity
27
Supply
more elastic
Long-Run Impacts
D
$
• Look at LR
supply
elasticities?
• Look at LR
demand
elasticities?
• What is impact of
6% tax on
services?
S''
S'
S
D''
Demand
more
elastic
P2
P1
Tot. Tax Rev.
Tot Sales
Q2 Q1
Quantity
28
Long-Run Impacts
D
$
• What is net impact
as drawn?
• P3 < P2 because
demand is more
P3
elastic
• TR? Depends on
whether price ↑
(leading to ↑ in tax
per unit) by greater
% than quantity ↓.
S''
S'
S
D''
P2
P1
Tot. Tax
Tax Rev.
Rev.
New
Tot Sales
Q3 Q2 Q1
Quantity
29
A Model of a Michigan Service Tax
1 = goods produced nationally– examples?
2 = goods produced locally – examples?
T = Taxes Collected by Michigan
T = National sector taxes + Local Sector taxes
+
-
T = t1 p1 Q1 (t1, t2, p1, p2, y) + t2 p2 Q2 (t1, t2,
+
- +
p1, p2, y)
What happens if we
y = p1 Q1 + p2 Q2
establish (increase) taxes
on local goods, services?
30
What will the Full Impact of a tax on
local goods be?
• Lots of things happen!!
• Prices of local goods ,   in quantity
demanded of local goods.
•  in demand for national goods.
• What will be the TAX IMPACT and who will
pay it?
31
What will the Full Impact of a tax on
local goods be?
dT/dt2 = p2 Q2 + t2 p2 (dQ2/dt2) + t2 p2 (dQ2/dp2 ) (dp2/dt2 ) + t1
p1 (dQ1/dt2 )
Less Sold! But it
Is now taxed.
Higher prices,
Less sold.
More taxes on
Substitutes.
32
What will the Full Impact of a tax on
local goods be?
dT/dt2 = p2 Q2 + t2 p2 (dQ2/dt2) + t2 p2 (dQ2/dp2 ) (dp2/dt2 ) + t1
p1 (dQ1/dt2 )
dT/dt2 = p2 Q2 + t2 (dQ2/dt2 ) (Q2/Q2) p2 + (Q2/Q2)(p2/p2) t2 p2
(dQ2/dp2 ) (dp2/dt2 ) + (t2/t2) (Q1/Q1) t1 p1 (dQ1/dt2)
dT/dt2 = p2 Q2 + dQ2/dt2 (t2 /Q2) (p2 Q2) + p2 Q2 [(dQ2/dp2)
(p2/Q2)] [(dp2/dt2) (t2/p2)] + (t1/t2)(p1Q1) (dQ1/dt2) (t2/Q1)
dT/dt2 = p2 Q2 + Elas Q2t2 (p2 Q2) + p2 Q2 (Elas Q2p2) (Elas
p2t2) + (t1/t2)(p1Q1) (Elas Q1t2)
dT/dt2 = p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+ p1Q1
(t1/t2) (Elas Q1t2)
33
A Model of the Service Tax
+ or - ?
+ or - ?
+ or - ?
dT/dt2 = p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+
p1Q1 (t1/t2) (Elas Q1t2)
+ or - ?
KEY POINT --- There are LOTS of Impacts!
34
t2 = 0.06
A 6% Service Tax
This is a
one UNIT
 in tax.
We want
0.06 of that.
dT/dt2 = p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+
p1Q1 (t1/t2) (Elas Q1t2)
0.06* (dT/dt2) = 0.06 * p2 Q2 (1 + Elas Q2t2 + Elas Q2p2
Elas p2t2)+ 0.06 * t1p1Q1 (Elas Q1t2)
Elas Tt2 = s2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2) + s1 *
Elas Q1t2 ; s1 = t1p1Q1/T; s2 = t2p2Q2/T.
35
t2 = 0.06
A 6% Service Tax
dT/dt2 = p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+
p1Q1 (t1/t2) (Elas Q1t2)
6% of original sales of Q2
0.06* (dT/dt2) = 0.06 * p2 Q2 (1 + Elas Q2t2 + Elas Q2p2
Elas p2t2)+ 0.06 * p1Q1 (t1) (Elas Q1t2)
Change in sales of Q1
Elas Tt2 = s2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2) + s1 *
Elas Q1t2 ; s1 = t1p1Q1/T; s2 = t2p2Q2/T.
36