Ec426 Public Economics
I
Who pays taxes?
General equilibrium tax incidence
A B Atkinson Room R515
Office hour: email tony.atkinson@nuffield.ox.ac.uk for
appointment.
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My background
• Teaching economics since 1967 at Cambridge, Essex, MIT, UCL, LSE,
Oxford, and Harvard.
• Engagement with public policy:
- Member, Royal Commission on Distribution of Income and Wealth, 1978;
- Chairman, Taxation Review Committee, Fabian Society, 1989;
- Member, Pension Law Review Committee, 1992;
- Report on Social Indicators for the EU, formed basis for Laeken indicators
(Structural Indicators) 2001;
- Member, Conseil d’Analyse Economique, advising French Prime Minister,
1997-2001;
- Report on new methods of development financing for UN General
Assembly, 2004;
- Member, High-Level Group on the future of social policy in an enlarged
European Union, 2004;
- “Atkinson Review” for UK Government of the measurement of
government output, 2004-5;
- Member of the European Statistics Governance Advisory Board
established by Council of Ministers and European Parliament, 2009-12.
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Tax Incidence
1.
2.
3.
4.
Why does tax incidence matter?
Incidence in a single market
Two sector general equilibrium model
Incidence of corporate profits tax
5.
What is missing from the model?
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1. Why does tax incidence matter?
A government imposes a tax, with a legal obligation for a person
(or legal entity) to pay the tax, but who really pays the tax?
Incidence depends on the market reactions. A tax may be
shifted on to others. Indeed, it is assumed in discussions of UK
VAT increase that it led to faster inflation.
The degree of shifting affects how we think about the
distributional impact of tax changes. What is the distributional
effect of a switch from direct to indirect taxation? What is the
effect of increasing employer payroll taxes?
“The theory of tax incidence has a number of practical results. For example, United
States Social Security payroll taxes are paid half by the employee and half by the
employer. However, economists think that the worker is bearing almost the entire
burden of the tax because the employer passes the tax on in the form of lower wages.
The tax incidence falls on the employee.”
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Distributional effect of taxation
“across the entire period [1977 to 2007], the tax system as a
whole (including indirect taxes) has had virtually no impact on
the shares of each fifth of the income distribution [in the UK]”
Report of the National Equality Panel, January 2010, page 50,
from ONS annual Redistribution of Income (ROI) analysis.
On what is this based?
Comparing for household h
Gross income Yh with Yh – Th - ∑ti Xhi
where Th denotes income tax paid and ti is rate of indirect tax
on good I, and Xhi is the consumption of good I by household h.
The calculation assumes that Yh and Xhi are unchanged. Income
tax fully borne by income recipient and indirect taxes fully
passed on to consumers. No account is taken of employer social
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security tax or of corporation tax.
2. Incidence in a single market
Price to
producer
Demand
curve after
tax
introduced
Demand curve
before tax
introduced
Tax
●
Supply
curve
Effect of
indirect tax
In the constant
elasticity case, the
consumer price =
●
(1+t) to the power
of
εs/(εs+εd)
Quantity
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Price to
producer
Assumption
underlying
official ROI
analysis
Demand curve
before tax
introduced
Tax
●
Totally
elastic
supply
curve
●
Demand
curve after
tax
introduced
Quantity
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Labour market
and cut in
payroll tax
Wage
received by
worker
Demand
curve after
tax reduced
Supply curve
Demand
curve by
employers
●
In constant
elasticity case, tax
at rate t reduces
net wage by factor
●
(1+t) to the power
of εd/(εs+εd)
Quantity of
labour
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Wage
received by
worker
Demand
curve by
employers
•
•
E1
•
Tax cut can reduce
employment if
economy moves
from E3
Supply curve
Demand
curve after
tax reduced
E2
•
E3
Market
reactions and
complications
Backward-bending
labour supply
curve and nonunique market
equilibria
Number of worker hours
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What is missing from Partial
Equilibrium Analysis?
•
•
•
•
What lies behind supply (demand) curves?
Effect on factors of production and incomes
Inter-relation between markets
Input-output effects
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3. Two sector general equilibrium analysis
Two sector/two factor model allows for a variety of
taxes AND models the whole economy
Capital
Sector X
tKX
Labour
Value
added
tLX
tX
VAT
Sector Y
tKY
tLY
tY
Corporation tax
Both
tK
tL
Payroll tax
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Demand side
Assume consumer demands are
homothetic and that government
spends revenue in same way as
consumers. Relative demands are
then function only of the relative
prices: e.g. X/Y = (pX/pY)-ε
X/Y
Closed
economy
pX/pY
w/r
Atkinson
Stiglitz
Lecture 6
45o
w/r
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Production side: assume
constant returns to scale,
perfectly competitive pricing,
and full mobility of factors.
Unit costs and hence prices are
X/Y
pX = cX(r,w); pY = cY(r,w)
Eg Cobb-Douglas case
pX= rα w(1-α) ; pY = r βw(1-β)
X more labour intensive if α < β
pX/pY
w/r
Assume X
more
labour
intensive
45o
w/r
Pricing
relationship
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pX/py = cX[r,w(1+tL)]/
cY[r,w(1+tL)]
X/Y
Eg Cobb-Douglas case
pX/pY = [w(1+tL)/r] β-α
Not lose sight of
purpose = model
effect of taxes: e.g.
effect of payroll tax
X more labour intensive if α < β
pX/pY
w/r
45o
Assume X
more
labour
intensive
Effect of payroll
tax, given the
assumption that
X more labour
intensive.
w/r
BUT not only
effect.
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Factor market
clearing
X/Y
Assume fixed supplies of
capital, K0 and labour, L0.
Factor market
KX + KY = cKX X + cKY Y = K0
LX + LY = cLX X + cLY Y = L0
If cij fixed, then only one X/Y (at
most) clears market. If cij variable,
then different combinations of X/Y
and w/r clear market. If w/r rises,
both sectors use less labour.
Equilibrium can only be reestablished if there is a switch of
outputs towards the labourintensive sector (X).
w/r
Assume X
more
labour
intensive
45o
w/r
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X/Y
where w/r
= K0/L0 /[β/(1-β)]
Cobb-Douglas example
The market clearing equations (where
both factors fully used) are:*
X α(r/w)-(1-α) + Y β (r/w)-(1-β) = K0
X (1-α) (r/w)α + Y (1-β) (r/w)β = L0
w/r
•
where w/r
•
Solving these equations, we obtain the
values of X and Y that ensure factor
market equilibrium for given (r/w). We
have to ensure that the values of outputs
are non-negative. This is guaranteed
where
β/(1-β) ≥ (K0/L0) /(w/r) ≥ α/(1-α)
= K0/L0 /[α/(1-α)]
* Obtained using the fact that the factor
demands are given by derivatives of the
cost function.
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X/Y
Putting it together:
Demand and “Supply”
“Supply”
•
•
•
w/r
•
•
Demand
px/py
w/r
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Supply
X/Y
Putting it together:
“Demand” and Supply
“Demand”
w/r
•
•
px/py
w/r
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4. Incidence of corporate profits tax
Harberger (Journal of Political Economy 1962) used this
model to examine incidence of the corporate income tax.
Corporation tax = tax on use of capital in the corporate
sector. It is a partial factor tax.
Effects:
• not enter the demand side;
• affects the pricing relationship;
• affects the choice of production techniques.
Outcome depends on whether corporate sector is capitalintensive or labour-intensive.
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Begin by assuming
Fixed coefficients and
X/Y
Demand
curve
Corporate sector is
capital intensive (Y).
Determined by full
employment condition
pX/pY =
pX/pY
cX[r,w]/cY[r(1+TKY),w]
Corporation tax in this case is
the same as a partial excise tax,
and reduces return to factor
used intensively in its
production.
What would happen if the
corporate sector were X?
w/r
Effect of the tax
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Effect of the tax
“Demand
curve”
X/Y
Supply
curve
Now allow variable
coefficients. Corporate
sector is capital
intensive (Y).
●●
pX/pY
w/r
Effect of the tax
45o
w/r
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“Demand
curve”
Effect of the tax
X/Y
Supply
curve
Suppose now that the
corporate sector is
labour intensive (X).
●
●
pX/pY
w/r
Effect of the tax
45o
w/r
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Algebraic version: see Atkinson and Stiglitz, pp 166-70
Three key equations of proportionate change:
dX/X – dY/Y = - σD [dpX/pX – dpY/pY] + T1
dpX/pX – dpY/pY = θ* [dw/w – dr/r] + T2
λ* [dX/X – dY/Y] = σS [dw/w – dr/r] + T3
where T1, T2 and T3 show the effects of taxes.
and
σD is the aggregate elasticity of substitution in demand
σS is the aggregate elasticity of substitution in supply
and θ* and λ* are measures of relative factor intensity.
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Solve for induced changes in w/r
(dw/w – dr/r) [σS + σD θ*λ*] = λ*T1 - σD λ*T2 - T3
The square bracket on the LHS is positive, since θ* and λ* have
the same sign (in the absence of taxes and other distortions).
Effect of corporation tax in sector X:
T1 = 0
T2 is positive, but effect depends on sign of λ*, which is positive
where X relatively labour-intensive
T3 is negative and magnitude depends on elasticity of
substitution in X sector.
w/r most likely to fall where
• Little scope for factor substitution in taxed sector
• Elasticity of substitution in demand is larger;
• Larger difference in factor intensities.
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5.What is missing from the model?
•
•
•
•
•
•
•
•
•
Open economy (tax competition);
Unemployment;
Imperfect competition;
Other market imperfections;
Other taxes and subsidies;
Input-output relationships;
Demand influences;
Variable factor supplies;
Environmental impact.
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