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TAXATION AND
INCOME
DISTRIBUTION
Incidence of Social security (SOC)
(COPY)

Who bears the burden? Is SOC direct or
indirect tax?

Determinants of incidence (pure PAYGO x
FF systems), backward shaped S

Incidence in general equil. models (GEM)
14-2
Vocabulary

Statutory Incidence
Economic Incidence
Tax Shifting
Partial (General) Equilibrium Models

Example: VAT in Czech R.






VAT agent – who runs the shop and sells goods (seller,
producer)
Consumer - me, you if buying something in shop of VAT
agent
Who is worse off? Me or seller?
14-3
Tax Incidence: General Remarks

Only people can bear taxes





Functional distribution of income (capitalists, labourer) (Q (CIT))
Size distribution of income (rich or poor)
Both sources (PRODUCERS – physical!) and uses
(CONSUMERS) of income should be considered
Incidence depends on how prices are determined (see later
MONOPOL, or time aspects – long or shor run), Labour Union…
Incidence depends on the disposition of tax revenues (what for the
taxes are collected)




Balanced-budget tax incidence (Net tax/transfer incidence)
Differential tax incidence (One tax is replaced by another tax)
Lump-sum tax incidence (One tax is replaced by head tax)
Absolute tax incidence (only one tax is changing, ceteris paribus – the
simplest analyses)
14-4
Tax Progressiveness (YES or NO) Can Be Measured in
Several Ways…

Average tax rate versus
marginal tax rate

Proportional tax system

Progressive tax system

Regressive tax system
Tax Liabilities under a hypothetical tax
system
Income
Tax
Average Marginal
Liability Tax Rate Tax Rate
$2,000
-$200
-0.10
0.2
3,000
0
0
0.2
5,000
400
0.08
0.2
10,000
1,400
0.14
0.2
30,000
5,400
0.18
0.2
14-5
… and unfortunately sometimes with different results. HOW
Progressive a Tax System is can be measured by:
1/change in ATR if I goes up for 1 OR
2/level of elasticity
v1 
T1
I1

I1  I 0
T0
I0
v2 
T1  T0
T0
I1  I 0
I0
14-6
Q: The tax proposal - everyone´s tax
liability will increase by 20 %

T = t*TaxBase

T´ = 1,2*T

calculate v1/v1´

calculate v2/v2´

discuss the impact on progressivity
14-7
Measuring How Progressive a Tax System is – A
Numerical Example (2 payers, poor 0 and rich 1)
v1 
T1
I1

T0
I0
v2 
I1  I 0

.00025 
1000  800
300
1000
200
800

.0003 
1000  800
360
1000
240
800
T1  T0
T0
I1  I 0
I0
2.0 
300  200
200
1000  800
800
2.0 
360  240
240
1000  800
800
14-8
Measuring of global progressivity - GINI
Properties of inequality metrics
The Gini coefficient satisfies four important principles:

Anonymity: it does not matter who the high and low
earners are (man, woman, children, maried…).

Scale independence: the Gini coefficient does not
consider the size of the economy (in dollars or in CZK),
the way it is measured, or whether it is a rich or poor
country on average (v1 does not meet).

Population independence: it does not matter how large
the population of the country is.

Transfer principle: if income (less than the difference), is
transferred from a rich person to a poor person the
resulting distribution is more equal.
14-9
Gini:
1
2
G 1  2
* [ y1 * n  y 2 * (n  1)  ... yn]
n n *y

n is number of units

y is income (ascending manner)
14-10
$
2.60
Partial
Equilibrium
Models
2.40
2.20
Before Tax
After
Tax
Consumers Pay
$1.20
$1.40
Suppliers Receive
$1.20
$1.00
S1
2.00
S0
1.80
1.60
1.40
1.20
1.00
0.80
D0
0.60
0
1
2
3
4
5
6
D1
7
14-118
Quantity
$
2.6
SX
2.4
2.2
2
S
1.8
1.6
1.4
1.2
1
Perfectly
Inelastic
D ’
Supply X
0.8
DX
0.6
0
1
2
3
4
5
6
7
14-12 8
Quantity
$
2,6
2,4
2,2
2
S
1,8
1,6
Perfectly
Elastic
Supply
1,4
SX
1,2
1
0,8
DX’
DX
0,6
0
1
2
3
4
5
6
7
14-138
Quantity
$
2,6
2,4
2,2
2
DX
1,8
DX’
1,6
1,4
1,2
1
DX’´ˇ
SX
0,8
0,6
0
1
2
3
4
5
6
7
8
14-14
Quantity
Tobacco tax (or green tax reform) paradox

MoF really wants: get some additional money
for public budget (but it means no or only
small change in consumption). (inelastic d)

On the other side he says to the public to
justify - legitimize the new tax: smoking is
unhealthy and it is necessary to eliminate this
bad habit (it means a large decrease of
consumption). (elastic d)

Paradox…
14-15
Absolutely elastic D

Tax T1 on consumers plus absolutely elastic
demand

Tax T2 on producer plus absolutely elastic
demand

maximum pressure of consumers to producers
to preserve effective price unchanged. Tax is
shifted on producers. T1 and T2 are
equivalent taxes
14-16
Absolutely inelastic D (tobacco)

similar graphic analysis as above

We can sum up: there is a minimum pressure
of consumers to produces to preserve
effective price unchanged. Tax is shifted on
consumers. T1 (consumers) and T2
(producers) are equivalent taxes.
14-17
Inelastic supply (agricultural production,
land property activities)

The aim or result – to punish producers

We can sum up: there is a minimum pressure
of producers to consumers. Tax is shifted on
producers. T1 and T2 are equivalent taxes.
14-18
Elastic supply

The aim or result – discourage the activity,
production…

We can sum up: there is a maximum pressure
of producers to consumers. Tax is shifted on
consumers. T1 and T2 are equivalent taxes
14-19
Price per Pound of food
Ad Valorem Taxes
Sf
Pr
P0
Pm
Df
Df’
Qr
Q0
Qm
Pounds of food
per year
14-20
Taxes on Factors

The Payroll Tax (see ad valorem tax above)

Capital Taxation in

OPEN Economy (Large X small)

CLOSED Economy (Large X small)
14-21
Commodity Taxation without Competition

Monopoly

Oligopoly (a few sellers)

they are able to obtain cartel solution (similar to
monopol)

or not because of cheating (similar to perfect
competition)
Monopoly maximizing profit (MR=MC)
X0 to X1
Economic
Profits
$
Economic
Profits
after unit
tax
MXX
Pg c
P0
Pn
i
dh
a
f
g
ATCX
b
ATC0
DX
MRX’
MRX
X1 X0
DX’
X per year
X01
X00 (MRx=0)
14-23
ALTERNATIVE - Unit tax on MONOPOLY
(supply side, linear demand)
½ T on
producer, ½ T
on consumer
MC before
and after the
tax
ATC before
and after the
tax
Profit
(decrese of ½
tax)
unit tax
14-24
Monopoly maximizing sales (MR=0)
UNIT TAX
before tax
$
MXX
after tax
c
P0
Pn
i
dh
a
f
g
ATCX
b
ATC0
DX
MRX’
MRX
X1 X0
DX’
X per year
X01
X00 (MRx=0)
14-25
Monopoly maximizing sales (MR=0)
AD VALOREM TAX
MR= 0
X00 = X01
$
MXX
c
P0
Pn
i
dh
a
f
g
ATCX
b
ATC0
DX
MRX’
X1 X0
MRX
DX’
X00 = X01 (MRx=0) X per year
14-26
Profits Taxes (Tax baze)

Economic profit (Long X short period)

Perfect competition

Monopoly

Measuring economic profit (as rate of return , BUT
original costs OR costs of replacing shoud be used?)

Taxation of profit:

long period (perfect competion and Profit = 0 so T = 0)

short period (perfect competion and Profit > 0 so T > 0)

long period + monopoly (Profit > 0 so T > 0)
14-27
ad valorem tax
Q0 max sales (no change)
Q1 max sales under minimal
profit constr.
Q3 max profit (Q is before tax)
(TRgross, TRnet)
profit tax
Q0r max sales
Q1r max sales under
minimal profit constr.
Qpi max profit
Q0r>Q1r>Qπ
Q3
Q
14-28
Profits Taxes (Incidence)

Profit Tax and firm maximizing profit


No change, tax is borne by producer
Profit Tax and firm maximizing sales

No change, if non binding profit constraints
(profit after tax is still higher then minimal
demanded profit by owner)

Possible change, if profit constraints becomes
operative (profit is less then minimal demanded
by owner), it is not sustainable to maximize sales
14-29
Tax Incidence and Capitalization
PR = $R0 + $R1/(1 + r) + $R2/(1 + r)2 + … + $RT/(1 + r)T
PR’ = $(R0 – u0) + $(R1 – u1)/(1 + r) + $(R2 – u2)/(1 + r)2 + … +
$(RT – uT)/(1 + r)
u0 + u1/(1 + r) + u2/(1 + r)2 + … + uT/(1 + r)T
Capitalization
PR ’ = PR minus all future tax liabilities
The today‘s owner bears the all future taxes
14-30
Incidence of Social security (SOC)
(COPY)

Who bears the burden? Is SOC direct or
indirect tax?

Determinants of incidence (pure PAYGO x
FF systems), backward shaped S

Incidence in general equil. models (GEM)
14-31
General Equilibrium Models

Partial equilibrium (One Market, One
Product, tax remains on this market)

General equilibrium (tax can escape its
market to other market/s)

2 Markets, 2 Producers (sectors)

2 Products (food X, manufactures Y)

2 production factors – L and K
14-32
Tax Equivalence Relations
tKF = a tax on capital used in the production of food
tKM = a tax on capital used in the production of manufactures
tLF = a tax on labor used in the production of food
tLM = a tax on labor used in the production of manufactures
tF = a tax on the consumption of food
tM = a tax on consumption of manufactures
tK = a tax on capital in both sectors
tL = a tax on labor in both sectors
t
= a general income tax
14-33
Tax Equivalence Relations

Partial factor taxes (C = I, I = TC = Wages + Interest)
tKF
And
and
tKM
tLF
are equivalent
to (TC =
W+Int)
and
and
tLM
tF
and
are equivalent
to
tM
are
are
are
equivalent (it can
move between
sectors)
equivalent (it can
move between
sectors)
Equivalent
( budget constr.
down)
To
to
to
tK
and
tL
are equivalent
to (I =
W+Interest)
t
14-34
The Harberger Model (F + M sectors)

Assumptions





Behavior of factor suppliers (perfect mobility,
wf=wm)
Market structure (competitive markets,
MR=P=MC, full employment)
Total factor supplies (Kf+Km = K, is const.)
Consumer preferences (we focus only on source
(I) side (capitalists x labourer), the uses side is
same for all subjects)
Tax incidence framework (differential tax
incidence, I is const.)
14-35
Assumptions II

Technology (Cobb-Douglas prod. f.)

Elasticity of substitution K for L

Capital / Labor intensive sector

aFL = number of person-hours needed to produce one
piece of food)

aFK = amount of capital needed to …

Line of constant profit, see graph later…
Pf=aFL*w + aFK*r, do same for M

if aFL/aFK > aML/aMK so F is labour intensive
industry
14-36
r
r = (px/axk) – (axl/axk) * w
(křivka nulového zisku na trhu zboží X)
E1
r = (py/ayk) – (ayl/ayk) * w
(křivka nulového zisku na trhu
zboží Y)
E0
E2
w
14-37
Analysis of Various Taxes

General tax on labor (tL) (no escape to other, non
taxed sector, no shift)

Income tax (t) (equivalent to tfk+tfl and all is
employed, so again no escape, no shift)

Commodity tax (tF) ?escape?

Pf increase, Subst. Effect, Q of F decrease (how big? - )

factors move to other sector

if F is K intensive, too many K and too less L (how much)
for M industry, r must go down, W goes up, capitalists are
worst off

if F is L intensive, … laborer are worst off
14-38
Commodity tax (tF) or some tax exclusively
introduced in only one sector… ?escape?

Pf increase, Subst. Effect, Q of F decrease (how big? –
Part. Eq.)

factors move to other sector due to decrese of production

if F is K intensive, there will be too many K and too less
L (how much?) asking for utilitization in M industry,

SO

r must go down, W must goes up, capitalists are worst off

BUT

if F is L intensive, … laborer are worst off
14-39
Partial factor tax (tKM)


Output effect (similar Commodity tax) –
ambiguous with respect to who is worst off
Factor substitution effect


r*gross goes up – SE, less K and more L is
demanded
Total effect = OE + SE


clear
ambiguous (for tkm if m is L intensive, OE
decreases w, increases r, SE decreases r and
increases w)
14-40
Some Qualifications (releasing of
assumption)

Differences in individuals’ tastes (impact on
uses side)


Immobile factors


PIT – first impact on capitalist (progressive tax),
but later through the increase of Px also on
consumers (regressive impact)
all burden on L or K, can not excape)
Variable factor supplies

tk in long run decrease Q K, but it mieans also
decrese of productivity of L)
14-41
An Applied Incidence Study
Table 14.3
Average federal tax rates and share of federal taxes
by income quintile (2006)
Income Category
Average Federal
Tax Rate
T/BAZE
Share of
Federal Taxes
T/SUMT
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.
14-42
Wage rate per hour
The Payroll Tax
SL
Pr
wg = w0
wn
DL
DL’
L0 = L1
Hours per year
14-43