Public Finance
Chapter15 Taxation and
Efficiency
CHENG Beinan PH.D
Contents in this chapter
 Excess Burden Defined
 Excess Burden Measurement with
Demand
 Differential Taxation of Inputs
 Does Efficient Taxation Matter
§1. Excess Burden Defined
 Mini Case 1
 Consider Breyer Dazs, a citizen who
typically consumes 10 ice cream cones
each week, at a price of $1 per cone. The
government levies a 25 percent tax on his
consumption of ice cream cones, so now
Dazs faces a price of $1.25. In response to
the price hike, Dazs reduces his ice cream
cone consumption to zero, and he spends
the $10 per week on other goods and
services. Is Dazs unaffected by the tax?
 Excess Burden: A loss of welfare
above and beyond taxes collected.
Also called welfare cost or deadweight
loss.
 Mini Case 2
 Ruth has a fixed income of I dollars, and consumes
barley and corn. The price of barley is Pb and that
of com is Pc. There are no taxes or "distortions"
such as externalities or monopoly in the economy,
so the prices of the goods reflect their social
marginal costs. For convenience, these social
marginal costs are assumed to be constant with
respect to output. Now suppose the government
levies a tax at a percentage rate of tb on barley.
Analyze the tax's effect on budget constraint,
consumption bundle, and consumers' welfare.
 Mini Case 3
 Ruth has a fixed income of I dollars, and
consumes barley and corn. The price of barley
is Pb and that of com is Pc. There are no taxes
or "distortions" such as externalities or
monopoly in the economy, so the prices of the
goods reflect their social marginal costs. For
convenience, these social marginal costs are
assumed to be constant with respect to output.
Now suppose the government levies a tax at a
percentage rate of tb on barley. Is there any
excess burden in this condition?
 Equivalent Variation: A change in
income that has the same effect on
utility as a change in the price of a
commodity.
1.1 Questions and Answers
 Does every tax entail an excess
burden?
 Basic Conclusion: A lump sum tax has
no excess burden. It is more efficient
than the taxes which change the relative
price. A tax that changes relative prices
is inefficient in the sense that it lowers
individual utility more than is necessary
to raise a given amount of revenue.
Leaves the taxpayer on
the same indifference
curve.
Raise
revenue.
the
Conclusion
same
Lump Sum Tax
Taxes that change
the relative price
Generates more
revenue.
Generates more
revenue.
Leaves the
taxpayer on higher
indifference curve.
More efficient
Leaves the taxpayer
on lower indifference
curve.
Less efficient
 Lump Sum Tax: A tax whose value
is independent of the individual's
behavior.
 The problem of Lump Sum Tax
 It is technically impossible to make Lump
Sum Tax equitable.
 The practical lump sum tax is unfair.
 Any feasible way to modify the lump sum
tax to produce more equitable results,
actually is not a lump sum tax.
 The Welfare Economics explanations
on the Excess Burdens
 The necessary condition of efficient
allocation: MRS  MRT
 Tax effect: MRS  (1  t ) P 
bc
bc
b
bc
MRTbc 
Pc
Pb
Pc
b

  MRSbc  MRTbc


 The utility loss arises because the barley
tax creates a wedge between what the
consumer pays and what the producer
receives.
 The Welfare Economics explanations
on the Excess Burdens on income tax
 Basic Conclusion: Generally speaking,
Income Tax entail an Excess Burden. ①
If income were fixed, an income tax
would be a lump sum tax. ②However,
when people's choices affect their
incomes, an income tax is not generally
equivalent to a lump sum tax.
 Mini Case 4
 Ruth is consuming three commodities,
barley, corn, and leisure time, l. Ruth
gives up leisure (supplies labor) to earn
income that she spends on barley and
corn. The government levies an income
tax on the wage at the rate of t. Will this
policy introduce excess burden? Why?
 Leisure is the substitution of barley and
corn. Leisure is an input to produce of
barley and corn.
 MRSlb  MRTlb

 MRSlc  MRTlc
 MRS  MRT
bc
bc

MRSbc  Pb / Pc 
  MRSbc  MRTbc
MRTbc  Pb / Pc 
MRSlb  (1  t ) w / Pb 
  MRSlb  MRTlb
MRTlb  w / P

MRSlc  (1  t ) w / Pc 
  MRSlc  MRTlc
MRTlc  w / P

 If the demand for a commodity does
not change when it is taxed, does this
mean that there is no excess burden?
 Mini Case 5
 Naomi's initial budget constraint is AD,
and after the barley tax, it is AF. She
does not change her barley consumption
after the barley tax; that is, B1 = B2. The
barley tax revenues are E1E2. Is there an
excess burden?
 Basic Conclusion: Naomi purchases
the same amount of barley after the
tax as before the tax. Nonetheless,
the tax still yields an excess burden
of E2S.
 (1) Analysis with the figure: Although
B1 = B2, the barley tax E1E2 <
equivalence variation RE3, the excess
burden isE2S.
 It is the
substitution
effect that
breaks the
Pareto
efficiency
condition.
 Income Effect: The effect of a price change
on the quantity demanded due exclusively to
the fact that the consumer’s income has
changed.
 Substitution Effect: The tendency of an
individual to consume more of one good and
less of another because of a decrease in the
price of the former relative to the latter.
 Compensated Demand Curve: A demand
curve that shows how quantity demanded
varies with price, holding utility constant.
Contents in this chapter
 Excess Burden Defined
 Excess Burden Measurement
with Demand
 Differential Taxation of Inputs
 Does Efficient Taxation Matter
§2. Excess Burden
Measurement with Demand
 △CS =gfih, among which tax revenue
= gfdh, excess burden = fid .
 The math expression of Excess
Burden EB  1  P qt
2
b
2
b
1


EB   di  fd 

2


1
di  Pb  tb  Pb   EB  tb Pb q

2


fd  q
1
1

2


EB

t


t
P
q


P
qt

b
b b
b b

2
2

qPb 



Pb q   qPb  Pb q   tb Pb q 



Pb  tb  Pb 
 Implications of equation
1
2
EB


P
qt
b b
:
2
 ① η (compensated price elasticity of
demand)↑→ EB↑;
 ② Pb q ↑(the initial total commodity
expenditure)→ EB↑;
 ③ A broader tax has less excess burden
than a narrow tax.
 Empirical evidence in U.S.
 Oum(1992) shows that the airline ticket
tax imposes an annual excess burden of
$430 million, and collect $86 billion
revenue annually. (Tax rate 10%, price
elasticity of demand 1.0)
2.1 Preexisting Distortions
 Basic conclusion:
 In the presence of existing distortions, policies
that in isolation would increase efficiency can
decrease it and vice versa.
 Mini Case 6
 Suppose that consumers regard gin and rum
as substitutes. Suppose further that rum is
currently being taxed, creating an excess
burden "triangle". Now the government
decides to impose a tax on gin. What is the
excess burden of the gin tax?
 Theory of The Second Best: In the presence
of existing distortions, policies that in isolation
would increase efficiency can decrease it and
vice versa.
 Double-Dividend Effect: Using the proceeds
from a Pigouvian tax to reduce inefficient tax
rates.
 Tax-Interaction Effect: The increase in
excess burden in the labor market stemming
from the reduction in real wages caused by a
Pigouvian tax.
 Double-Dividend theory and policy
 Basic conclusion: The environment tax
increases efficiency both in the market
with the polluter and in the markets that
are distorted by the income tax.
However, the consequences of DoubleDividend hypothesis for efficiency
depend on the extent to which existing
taxes already distort the labor market.
2.2 The Excess Burden of a
Subsidy
 Basic conclusion: A subsidy is just a
negative tax, and like a tax, it is associated
with an excess burden.
 Before tax：Demand curve: Dh; Supply curve:
Sh = Ph; Equilibrium quantity: h1, CS = mno;
 After tax：Demand curve: Dh; Supply curve:
S’h= (1- s )Ph; Equilibrium quantity: h2, CS =
mqu;
 Subsidy effect: Benefit of subsidy is △CS
=nouq; cost of subsidy is nvuq. Because Cost of
subsidy > Benefit of subsidy, EB =ovu.
 Deeper thoughts and implications on
Excess Burden of a Subsidy
 Whey subsidy is inefficient?
 The tax wedge makes consumer price ≠
producer price, thus MRS ≠ MRT .
 Policy implication: Commodity subsidy
vs. Grant
 Grant is better than Commodity
subsidy.Less money could make them
as well off if it were given to them as a
direct grant.
2.3 The Excess Burden of
Income Taxation
 Basic conclusion: The theory of excess
burden applies just as well to factors of
production as it does to commodities.
 Before tax：Supply curve: SL; Wage: w;
Working hour: L1; Labor Surplus(LS) = adf;
 After tax：Supply curve: SL; After-tax Wage:
(1-t)w; Working hour: L2; After-tax LS =
agh;
 Income Tax effect: △LS =fdhg; tax revenue
is fihg, EB = idh.
 The math expression of income tax
1
Excess Burden 2  L t
2
1
1


EB   id  ih 

2


1
ih  w  tw   EB  twL 
2


id  L
1
1

2

EB

t


twL


wL
t

1
1

2
2

Lw 



wL1   Lw  wL1   twL1 



w  t  w 
 Excess Burden of Income tax in US
 In the US, the excess burden of Income
tax is approximately 4% of tax revenues.
For American male, εL ≈ 0.2, w = $20/h,
L = 2,000, t=40%, so the EB =640.
 Jorgenson & Yun [2001] estimated the
excess burden of labor income taxation
in the United States is about 27 percent
of the revenues raised.
 Noteworthy aspects to estimate
Excess Burden of Income tax
 Wage rates, tax rates , elasticities, and
tax rates on other factors should be
considered.
Contents in this chapter
 Excess Burden Defined
 Excess Burden Measurement with
Demand
 Differential Taxation of Inputs
 Does Efficient Taxation Matter
§3. Differential Taxation of
Inputs
 Model discription
 OO': total labor available in society.
Labor used at home and in the market.
 VMPhome: the value of the marginal
product of household work.
 VMPmkt : the value of the marginal
product of hours worked in the market
sector.
 Before tax
 Equilibrium: H*; Labor used at home:
OH*; Labor used in the market: O’H*.
 After tax：
 Procedure: Tax on market labor (t) →
Real wage↓(tw)→VMPmkt becomes (1-t)
VMPmkt
 Equilibrium: Ht; Labor used at home:
OHt; Labor used in the market: O’Ht.
 Excess Burden: abe.
 Result:
 Too much labor is devoted to the
housework; and too little labor is devoted
to the market work.
 Analysis:
 At the new equilibrium, the value of
Marginal Product is (1-t)w2. The tax
wedge prevent efficiency improvement
from Ht to H*.
 Conclusion:
 The tax leads to an inefficient allocation
of resources, because it distorts
incentives to employ inputs in their most
productive uses.
Contents in this chapter
 Excess Burden Defined
 Excess Burden Measurement with
Demand
 Differential Taxation of Inputs
 Does Efficient Taxation Matter
§4. Does Efficient Taxation
Matter
 Excess burden is conceptually a
rather subtle notion and is not trivial
to calculate.
 Although the efficiency considerations
alone are never enough to determine
policy, ignoring efficiency is also
incorrect.
 It will be used to obtain something
beneficial for society either in terms
of enhanced efficiency or fairness.
 Intelligent policy requires that excess
burden be included in the calculation
as a social cost.
 Excess burden is extremely useful in
comparing alternative tax systems.