Session 6
Taxation and income distribution
Introduction
• Is the tax burden distributed fairly?
• Statutory Incidence : indicates who is legally
responsible for a tax.
• Normally the statutory incidence is on the
seller.
• But the situation differ with respect to who
really bears the burden..
• Prices may change in response to the tax.
14-2
Economic Incidence
• It is the change in distribution of real income
induced by a tax.
• The main focus in this session is on tax
shifting.
• Tax shifting is the difference between statutory
incidence and economic incidence
14-3
Tax Incidence: General Remarks
• Only people can bear taxes
– Functional distribution of income: People’s role in
production used to classify tax incidence. E.g.
capitalists, labourers and landlords classification
according to the inputs they supply to the
production process (this is considered oldfashioned)
– Size distribution of income: Looks at how taxes
affect the way that total income is distributed
across income classes.
14-4
Tax Incidence: General Remarks
• Both sources and uses of income should be
considered
• For instance if a tax reduces the demand for
cigarettes, the factors employed in cigarettes
production may suffer income losses.
• Incidence depends on how prices are determined:
different models of price determination may give
different answers to the question of who really bears
the burden.
• The SR and LR incidence of a tax may differ.
14-5
Tax Incidence: General Remarks
Incidence depends on the disposition of tax revenues:
• Balanced-Budget tax incidence: computes the combined
effects of levying taxes and govt spending financed by those
taxes
• The idea is to determine how incidence differs when one tax
is replaced with another, holding the govt budget constant
(differential tax incidence). A lump-sum tax is often used as
the basis of comparison.
• Lump sum tax: is a tax whose value is independent of the
individual’s behaviour.
• Absolute tax incidence: examines the effects of a tax when
there is no change in either other taxes or govt expenditure14-6
Tax Progressiveness Can Be
Measured in Several Ways
• Average tax rate: Ratio of taxes paid to income
• Marginal tax rate: the proportion of the last dollar
of income taxed by the govt.
• Proportional tax system(flat-rate income tax): A
tax system under which an individual’s average
tax rate is the same at each level of income.
• Progressive tax system: an individual’s average
tax rate increases with income.
• Regressive tax system: an indiv’s avg tax rate
decreases with income.
14-7
Tax Progressiveness Can Be Measured
in Several Ways
Tax Liabilities under a hypothetical tax system
Income
Tax Liability
Average Tax Rate
Marginal 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
14-8
Measuring How Progressive a Tax
System Is
v1 
T1
I1

T0
I0
I1  I 0
14-9
Tax Progressiveness Can Be
Measured in Several Ways
• The greater the increase in avg tax rates as income
increases the more progressive is the system. v1 is the
formula for measurement of progressiveness
• T0 and T1 are the true tax liabilities at income I0 and I1
respectively. I1 >I0.
• The tax system with the highest v1 is more
progressive.
• The second measure of progressiveness is to say that
for a more progressive tax system, its elasticity of tax
revenue with respect to income is higher. V2 is the
elasticity formula.
14-10
Tax Progressiveness Can Be Measured
in Several Ways
v2 
T1  T0
T0
I1  I 0
I0
14-11
Tax Progressiveness Can Be Measured
in Several Ways
• Assume that T0 = 200 and T1 = 300 and also
assume that I0 = 800 and I1= 1000
respectively.
• Now consider the following proposal:
Everyone’s tax liability is to be increased by
20% of the amount of tax he or she currently
pays. The new tax liabilities are T0 = 240 and
T1 = 360 and also assume that I0 = 800 and
I1= 1000 respectively.
14-12
Measuring How Progressive a Tax System
is – A Numerical Example
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
14-13
Tax Progressiveness Can Be Measured
in Several Ways
• V1 increases by 20% meaning the proposal
increases progressiveness.
• V2 is unchanged.
• This implies that measures of progressiveness
can give different answers
14-14
Partial Equilibrium Models
• Models that study only one market and ignore
possible spill over effects in other markets.
• The main question is how taxes affect income
distribution.
• The main tool of analysis is the ss and dd
model.
14-15
Unit taxes on commodities
• Unit tax: is a tax levied as a fixed amount per unit of the
commodity purchased.
• E.g. if govt imposes a tax of 10 cents per litre of petrol.
• A unit tax changes the dd curve as perceived by suppliers. The
new dd curve is located below the old one by the magnitude of
the unit tax.
• The equilib is where the ss equals dd as perceived by the
suppliers
• The tax lowers the quantity sold from 4 to 3.
• There are two prices to consider: the price perceived by
producers and the price paid by consumers.
14-16
$
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
Quantity
8
14-17
Unit taxes on commodities
• The price received by producers is at the intersection
of their effective dd and ss curves (P = $1.00).
• The consumers pay $1.00 plus the unit tax.
• This is = $1.40. This is called the price gross of tax.
$1.00 is the price net of tax.
• The tax makes consumers worse off but the
consumer’s price does not increase by the full amount
of the tax.
• Producers also pay part of the tax ( in our case it’s a
50-50 situation). They are also worse off.
14-18
Unit taxes on commodities
The incidence of a Unit tax is independent of
whether it is levied on consumers or producers.
• Suppose the same unit tax is levied on suppliers of
champagne.
• The supply curve as it is perceived by consumers
must shift up by the amount of the unit tax to S1.
• The posttax equilibrium is at 3 and the price at the
intersection($1.40) is paid by consumers.
• The price received by producers is $1.00.
14-19
Unit taxes on commodities
• What matters is the size of the disparity the tax
introduces between the price paid by
consumers and the price received by suppliers
and not on which side of the market the
disparity is introduced.
• The tax induced difference between the price
paid by the consumers and the price received
by producers is called the Tax Wedge
14-20
Unit taxes on commodities
The incidence of a unit tax depends on the
elasticities of ss and dd
• A unit tax on a good that has perfectly inelastic
ss causes the price received by the producers
to fall by exactly the amount of the tax.
– Producers bear the entire burden of the tax
• A unit tax on a good that has perfectly elastic
ss causes the price paid by the consumers to
increase by exactly the amount of the tax.
– The consumers bear the tax burden.
14-21
$
2.6
SX
2.4
2.2
2
1.8
1.6
tax
1.4
1.2
DX
1
Perfectly
Inelastic
D ’
Supply X
0.8
DX1
0.6
0
1
2
3
4
5
6
7
Quantity
8
14-22
$
2.6
2.4
2.2
2
1.8
1.6
Perfectly
Elastic
Supply
1.4
tax
SX
1.2
1
DX
0.8
DX’
DX1
0.6
0
1
2
3
4
5
6
7 Quantity 8
14-23
Ad Valorem Taxes
• A tax computed as a % of the purchase value.
• For example 10% tax (VAT) on the purchase of food in
SA.
• Ad valorem taxes are often levied on luxuries.
• The analysis of an ad valorem tax is similar to that of a
unit tax.
• The basic plan is to find out how the tax changes the
effective dd curve and compute the equilibrium.
• The ad valorem tax however lowers the curve down by
the same proportion(%) which is a swivel rather than a
parallel shift.
14-24
Price per Pound of food
Ad Valorem Taxes
Sf
Pr
Pc
P0
Ps
Pm
Df
Df’
Qr
Qn
Q0
Qm
Pounds of food
per year
14-25
Ad Valorem Taxes
• An ad valorem tax on consumers shifts the dd curve
down by the same proportion at each level of output.
• Df’ is the effective dd curve faced by suppliers.
• Df is the original dd curve.
• The equilibrium is where Sf and Df’ intersect.
• The incidence will be determined by the elasticities of
supply and demand.
• Pc is the price paid by consumers and Ps is the
price received by suppliers.
14-26
Taxes on Factors: The Payroll Tax
• A similar analysis can be applied to factors of
production.
• The Payroll Tax:is paid from the employer's own
funds and that is directly related to employing a
worker, which can consist of a fixed charge or be
proportionally linked to an employee's pay.
• If the labour ss is perfectly inelastic, a payroll tax
causes the wage received by workers to fall by the
exact amount of the tax. Workers bear the entire
burden
14-27
Wage rate per hour
The Payroll Tax
SL
Pr
wg = w0
wn
DL
DL’
L0 = L1
Hours per year
14-28
Taxes on Factors : Capital Taxation in
a Global Economy
• In a closed economy the dd is downward sloping and
the ss is upward sloping.
• Therefore the owners of capital bear some burden of
a tax on K. This depends on elasticities of dd and ss.
• In an open economy where capital is perfectly mobile
the ss of K to a country is perfectly elastic.
• The before-tax price paid by the users of K rises by
exactly the amount of the tax.
• Suppliers of K bear no burden.
• K moves abroad if it has to bear any of the tax.
14-29
Commodity Taxation without Competition:
Monopoly
• If a unit tax is levied on a product, the effective dd
curve and MR curve facing the monopolist shift down
by a vertical distance equal to the tax.
• The profit-maximising output is found at the
intersection of the new MR curve and the MC curve.
• The tax reduces the equilib quantity from X0 to X1
and increases the price paid by consumers from Po to
Pg.
• The price received by the producer decreases from Po
to Pn and decreases the monopoly profits.
14-30
Monopoly
$
Economic
Profits
Pg c
P0
Pn
i
dh
MXX
a
f
g
Economic
Profits
after unit
tax
ATCX
b
ATC0
DX
MRX
X1 X0
MRX’
DX’
X per year
14-31
Oligopoly
• If the oligopoly industry output is subject to a
tax, the firms will reduce their output.
• But the firms normally over-produce (exceed
the cartel share) so the tax will move them
closer to the cartel solution.
• Their before –tax profits actually increase.
• However, it is possible for the firms to become
worse –off.
14-32
Profits Taxes
• Economic profit: the return to the owners
above the opportunity costs of all the factors
used in pdn.
• A tax on economic profits is born by the
owners of the firm.
• Under perfect compn a proportional tax on
economic profits changes neither MC nor MR.
• No firm has the incentive to change its output
decision.
14-33
Tax Incidence and Capitalization
• Capitalisation: is the process by which a
stream of tax liabilities becomes incorporated
into the price of an asset.
• Suppose the annual rate of return of land is
$R0 this yr. The rental will be R1 next yr and
R2 after 2 yrs and so on. Under perfect compn
the price of the land is the present discounted
value of the future streams of returns. If the
interest rate is r, then the price of land PR is
•PR = $R0 + $R1/(1 + r) + $R2/(1 + r)2 + … + $RT/(1 + r)T
14-34
Tax Incidence and Capitalization
• If a tax $ui is imposed for i=0,1,2,…,T. Since
land is fixed in ss the ss curve is vertical, the
owner of the land bears the whole tax.
• The landlord’s return falls by the full amount
of the tax. The after tax value of the land will
be:
• PR’ = $(R0 – u0) + $(R1 – u1)/(1 + r) + $(R2 –
u2)/(1 + r)2 + … + $(RT – uT)/(1 + r)T
14-35
Tax Incidence and Capitalization
• The two expressions above show that the value
of the land will fall by:
• u0 + u1/(1 + r) + u2/(1 + r)2 + … + uT/(1 + r)T
• At the time of the tax the price of the land falls
by the present value of all future tax payments.
• Capitalization complicates attempts to assess
the incidence of a tax on a durable item that is
fixed in ss.
14-36
General Equilibrium Models
• Partial equilibrium:
– Are simple and uncomplicated.
– They give an incomplete picture
• E.g. a tax on cigarettes affects consumers,
farmers and the farm pdn pattern and prices of
other crops.
• General equilibrium analysis takes into
account the way in which various mkts are
interrelated.
14-37
Tax Equivalence Relations
• Thousands of different commodities and inputs
are traded, so how can we keep track of their
complicated interrelations?
• Useful results can be obtained from GE
models with 2 commodities [food, F and
manufactures,M],2 fops(K and L) and no
savings.
14-38
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
14-39
Tax Equivalence Relations
• The 1st 4 taxes are levied on a factor in only part of
its uses – partial factor taxes.
• Certain combinations of these taxes are equivalent to
other ad valorem taxes outlined above. E.g. a similar
tax rate is applied on food (tF ) and manufactures (tM)
, these are equivalent to an income tax (t), becoz they
both create a parallel inward shift of a consumer’s
budget constraint.
• A proportional tax on both capital and labour is
equivalent to an income tax.
14-40
Tax Equivalence Relations
• Partial factor taxes
tKF
and
and
tKM
tLF
are equivalent to
and
and
tLM
tF
and
are equivalent to
tM
are
are
are
equivalent
equivalent
equivalent
to
to
to
tK
and
tL
are equivalent to
t
Source: McLure [1971].
14-41
The Harberger Model: Assumptions
Technology:
• Assume 2 factors (K and L)
• The model assumes constant returns to scale ,
although production techniques may differ across
sectors.
• They differ w.r.t
• Elasticity of substitution (the ease with which one factor
can be substituted for another)
• Capital intensive (capital –labour ratio is high)
• Labor intensive (capital –labour ratio is low)
14-42
Assumptions
Behavior of factor suppliers:
• Suppliers of K and L maximize returns.
• K and L are perfectly mobile across sectors
• Net marginal return for all factors in each sector is the
same.
Market structure:
• Firms are competitive, profit maximisers, and all
prices are perfectly flexible.
• There is full employment of factors
• Each fop is paid the value of its MP.
14-43
Assumptions
Total factor supplies:
• Amounts of K and L are fixed.
Consumer preferences:
• Consumers have identical preferences
• Focus is on taxes effect on the sources of income.
Tax incidence framework:
• The model uses differential tax incidence analysis.
The model considers the substitution of one tax by
another.
14-44
Analysis of Various Taxes
Commodity tax (tF)
• A tax on food causes the relative price to increase.
• Consumers substitute manufactures for food.
• Food pdn falls=> K and L moves to manufacturing=>
relative prices of K and L changes.
• If food is a K-intensive sector, more K should be
employed in manufacturing, if the relative price of K
falls.
• In the new position all K is relatively worse off.
14-45
Commodity tax (tF)
• A tax on the output of a certain sector induces a
decline in the relative price of the input used
intensively in that sector.
• This result will depend on the elasticity of dd for food,
difference in factor proportions and the difficulty in
factor substitution.
• On the sources side, a food tax will hurt those who
receive proportionately more income from capital.
• On the uses side those who consume proportionately
more food would bear larger burdens
• Total incidence- a capitalist who eats a lot of food is
worse off on both counts.
14-46
Income tax (t)
• Since factor supplies are already fixed , this tax cannot be
shifted. It is borne in proportion to people’s initial incomes.
• Factors bear the full burden.
General tax on labor (tL)
• It is a tax on labour in all its uses.
• There are no incentives to switch labour use between sectors.
• Labour bear the entire burden.
Partial factor tax (tKM)
• Output effect: the price of manufactures tend to rise and the
quantity demanded decreases.
• Factor substitution effect: Producers use less K and more
labour.
14-47
Partial factor tax (tKM)
• If the manufacturing sector is capital intensive, the relative
price of capital falls.
• If it is labour-intensive, the relative price of capital rises.
• The factor substitution effect leads producers to use less
capital and more labour, leading to a drop in the relative price
of capital.
• If the manufacturing sector is K intensive both effects work in
the same direction, and relative price of K falls.
• If the manufacturing sector is labour intensive, the final
outcome is ambiguous.
• More generally, as long as there is factor mobility between
uses, a tax on a given factor in one sector is ultimately affects
the return to both factors in both sectors.
14-48
Some Qualifications
Differences in individuals’ tastes:
• When consumers have different preferences
for the 2 goods, tax-induced changes in the
distribution of income change aggregate
spending decisions, relative prices and
incomes
Immobile factors:
• For technical or institutional reasons some
factors maybe immobile. If the taxed factor is
immobile the factor bears the whole burden.
14-49
Variable factor supplies
• In the LR the supplies of both factors are
variable.
• If there is a tax on K, in the SR the tax is borne
by capital owners. In the LR less K will be
supplied due to the tax.
• The K/L ratio decreases and the return to
labour falls becoz it becomes less productive.
14-50
An Applied Incidence Study
14-51