chapter 2 consumption tax - keio university

Chapter 2 Consumption Tax

2.1 Consumption Tax in Practice1 One often hears that a consumption tax would be unjust, since the rich consume less (as a proportion of income) than the poor. We will see that by using judiciously the equivalences recalled above, one may conceive a consumption tax that is as progressive as one likes. The frequent assimilation of the consumption tax to a renunciation to progressivity is a confusion that partly results from the fact that many proponents of the consumption tax indeed favor a proportional income tax: the flat tax. A proportional (income or consumption) tax would have obvious administrative advantages. First, it would simplify (marginally) the tax returns2. It would also eliminate one of the anomalies of progressive taxes: with such schedules a taxpayer pays more tax when his income varies over time than when it is constant. Finally, it would make pay-as-you-earn withholding systems much simpler when the taxpayer has several sources of income. Despite these advantages most voters estimate that taxes should be progressive. Thus the tax acts proposed usually comprise a personal exemption that takes the poorer families off the tax rolls; this clearly detracts from the advantage of strict proportionality3. There are many ways to make a consumption tax progressive. In general, a consumption tax is the combination of a corporate tax and a personal tax4. The corporate tax often is a proportional tax on noninvested value added. Since investment is deducted from the taxable basis, this amounts to allowing for immediate depreciation of all capital investment, which is a simple if radical way of equating fiscal depreciation and economic depreciation. It also restores the neutrality toward all forms of investment, which is a radical change on current income taxes. In the best-known blueprint, due to Hall and Rabuschka (1995), wages paid by firms are deducted from noninvested value added before computing the corporate tax; the personal tax is a tax on all wage income received by families. Changing the schedule of this personal wage tax allows the government to achieve any degree of progressivity. Opponents of the consumption tax justly remark that such a wage tax would exempt people who have had 1 This section draws from Salanié (2003, Chap. 9, pp.190-2). 2 Several presidential candidates in the United States have taken to waving a postcard as the promise of a much

simpler tax return. 3 This type of tax schedule was already the favorite of classical authors, from Smith to Mill. 4 Some proponents of the consumption tax seek to abolish all personal taxes by relying on a tax on (noninvested)

value added, which is the same as a consumption tax as we know. The disadvantage of this method is that it makes it hard to make the tax progressive.

Lectures on Public Finance Part2_Chap2, 2011 version P.1 of 50

the good fortune of a large bequest and live off it without working. Most people find this immoral, so the wage tax should be complemented with a progressive tax on bequests. Another possibility (the Unlimited Savings Allowance or USA Tax; see Seidman (1997)) consists in taxing families in a progressive manner on the difference between the money flows they receive (whether it is labor income or capital income) and their savings, since this difference by definition equals their consumption. The USA Tax was inspired by the writings of Irving Fisher; it supposes that families keep proper accounts of their money flows (in and out) that are not linked to consumption. To make it equivalent to a tax on wages and bequests received, the USA Tax should also tax the bequests left by taxpayers. Proponents of the consumption tax predict a large positive effect on savings and, since the economy is assumed to have too little capital, on welfare. There have been many quantitative studies on this topic. They usually do obtain a positive effect on welfare, but with very variable figures. One of the most serious problems of such a reform arises when moving from an income tax to a consumption tax. The unfortunate taxpayers who have saved while paying the income tax, hoping to live off the income from their savings without paying any more tax, now have to pay the consumption tax. This could represent a large welfare loss for them. The proposed reforms thus all contain more or less satisfactory clauses to account for this so-called old wealth problem.

2.2 An Example of Consumption Tax Assume that the individuals’ income is fixed, and he can choose between purchasing two commodities, soda and beer. Suppose now that the government imposes a tax on beer. What will be the effect?

Figure 1

BEER

SODA

•

• PS/PB

S

B’

B

E

E*

After-tax budget constraint

Before-tax budget constraint Y=PBXB+PSXS

After-tax indifference curve

Before-tax indifference curve U(XB, XS)


Initially, the individual allocated his income by choosing point E on his budget constraint. This is the point of tangency between the budget constraint and the before-tax indifference curve. After the imposition of the tax, there is a new equilibrium, at point E*. We can decompose the effects of the tax into two parts. The income effect reduces the demand for beer. In addition however, the tax has increased the price of beer relative to the price of soda, so the substitution effect will discourage the purchase of beer. Now, both the income and the substitution effects reinforce each other: they both lead to a reduction in the demand for beer. But the distortionary effect of the tax is only associated with the substitution effect. To see this, we contrast the effect of the beer tax with that of a lump sum tax. A lump sum tax represents a reduction in the amount of income the individual can spend on either commodity. The relative price of the two commodities remains unchanged. If we measure the tax in terms of beer, the tax revenue is represented by the vertical distance between the before-tax and after-tax budget constraints. In Figure below, we can compare the revenues raised by a beer tax with those raised by a lump sum tax, with equal effect on the level of utility.

Figure 2

BEER

SODA

•

•

E**

E*Budget constraint after beer tax

Before-tax budget constraint

After-tax indifference curve

•

•

Deadweight Loss

Lump sum tax revenue

Beer tax revenue

It is clear from the figure that the lump sum tax raises more revenue (and leads to a higher level of consumption of beer) than does the beer tax. The difference between the two is a measure of the inefficiency resulting from the tax --- the deadweight loss associated with the tax. If it is very difficult to substitute soda for beer, i.e. if the indifference curves are very curved --- the distortion associated with the tax is very small. The magnitude of the distortion can vary from commodity to commodity.


2.3 Equivalences between Taxes5

We focus here on ideal taxes that are both proportional and comprehensive (with no special provisions). Then a first equivalence links a uniform tax on incomes of all factors and a uniform VAT on all goods. A uniform VAT indeed has exactly the same economic effects as a uniform factor tax of the same rate. This result must be slightly modified in the many countries whose VAT allows firms to deduct investment from value added (just as they do with intermediate consumptions). Then VAT bears on noninvested value added, and it is equivalent to a tax on that part of income that is not invested, or again to a consumption tax.

In a world where financial markets are perfect, we can write the intertemporal budget constraint of a consumer-worker who lives T periods, receives a bequest and leaves a bequest as

1H

TS

11

11

1 )1()1()1(H

rLw

rS

rC T

tt

ttT

TT

tt

t ++

=+

++ ∑∑

=−

=−

his equality shows that if there are no bequests, then a consumption tax is exactly equivalent to

equivalences only hold for uniform, comprehensive, and proportional taxes,

he Comprehensive Income Tax

The income tax as we know it is a rather hybrid construction: it taxes income from various

end-of-period wealth then is

Ta wage tax – which is not an income tax since it does not tax income from savings. More generally, a tax on both consumption and bequests left is equivalent to a tax on both wages and bequests received. Recall that these whereas actual taxes are neither of these three. Still, they throw some light on the debate on the consumption tax.

T forms of savings in a very unequal way and relies on a concept of income that satisfies few economists. Since the work of Haig and Simons in the 1930s, economists indeed have leaned toward a definition of comprehensive income as the total amount that can be allocated to consumption or savings in a given period. To understand this, consider the equation that sums up the changes in an agent’s wealth. During a period t, the agent receives wage income, consumes, and gets a rate of return tr on its beginning-of-period wealth tA . His

1+t

CLwrAA −A

tttttt ++=+ )1(1

5 This and the next sections draws from Salanié (2003, Chap. 9, pp.187-90).


This equality allows us to define comprehensive income as

Thus comprehensive income is the sum of the agent’s consumption and the increase in his wealth. To put it differently, it is the amount the agent may consume without reducing his wealth (for , we get

tY

tttttttt A=+ )( 1 rLwAACY +−+=

tt+1 ttAA = YC = ). The equality above shows that comprehensive . If the

return on wealth is entirely accounted y interest and dividends, then it is included in the usual definition of income and thus comprehensive income coincides with national accounts

Comprehensive income accounts

ce of accounting for inflation properly.

tt Arincome can also be defined as the sum of wage income and return on wealth

for b

income. On the other hand, national accounts income only accounts for capital gains (the appreciation of stocks, housing, ets.) when they are realized, that is, just before the underlying asset is sold. for these capital gains even when they are latent, that is, before the agent even considers selling the asset. Take a bullish period on the stockmarket; then consumers who own shares will probably boost their consumption since they perceive a higher wealth. Comprehensive income explains this, while national accounts income does not even register the latent capital gains. Several economists start from this more satisfactory definition of income to argue that the income tax should be a comprehensive income tax. This amounts to saying that the income tax should also tax latent capital gains. This is not a trivial change ,as many families own stocks and even more own their house. Beyond the argument above, the proponents of a comprehensive income tax note that the current income tax creates a lock-in effect: since it only taxes capital gains when they are realized (and not at all when the owner of the asset dies), it provides incentives for owners to keep the asset for longer than they would in a world without taxes. These economists also insist on the importanRecall that comprehensive income is the sum of consumption and the real increase in wealth, so that a comprehensive income tax would only tax real income from savings. On the other hand, the current income tax taxes the nominal income from savings. In inflationary periods it also taxes pseudo-income that contributes nothing to consumption or increases in wealth. Thus a 50 percent tax rate on income from savings in fact confiscates the whole real return from savings when inflation is 2 percent and the nominal interest rate is 4 percent. The creation of a comprehensive income tax would imply a notable extension of the taxable basis, since this would include latent capital gains and all the income from various sources of savings that are currently tax-favored6. Advocates of a consumption tax go to the polar opposite, since they would exempt all income from savings, whether it consists of interests,

6 The most spectacular exemption in may – but not all – current income tax systems concerns fictitious rents, that is,

the rental value of an owner-occupied house. These rents are implicitly received by the owner and in fact constitute income from the savings materialized in the house.


dividends, or capital gains (latent or realized).

Annual versus Lifetime Equity Events that influence a person’s economic position for only a very short time do not provide an adequate basis for determining ability to pay. Some have argued that ideally tax liabilities hould be related to lifetime income. Proponents of consumption taxation point out that an

s that can differ quite substantially even for people who ave the same lifetime wealth.

wealth later in life, because she wants a lavish retirement.

l tax

Grasshopper, her lifetime tax burden is greater than Grasshopper’s. sumption tax, lifetim

tastes for saving, other things being the same7. To prove this, all we need to do is write down the equation for each taxpayer’s budget constraint. Because all of Ant’s noncapital income

consumption must equal the present value of lifetime income. Hence, Ant’s consumption

sannual income tax leads to tax burdenh Borrowing an example from Rosen (1999), consider Mr. Grasshopper and Ms. Ant, both of whom live for two periods. In the present, they have identical fixed labor incomes of Y0 and in the future, they both have labor incomes of zero (for convenience). Grasshopper chooses to consume heavily early in life because he is not very concerned about his retirement years. Ant chooses to consume most of her Define Ant’s present consumption in the presence of a proportional income tax as Co

A and Grasshopper’s as Co

G. By assumption, CoG > Co

A. Ant’s future income before tax is the

interest she earns on her savings: )( 00ACYr − . Grasshopper’s future income before tax is

)( 00GCYr − .

If the proportional income tax rate is t, in the present Ant and Grasshopper have identica

liabilities of 0tY . However, in the future, Ant’s tax liability is )( 00ACYtr − . Because of Co

G > Co

A, Ant’s future tax liability is higher. Solely because Ant has a greater taste for saving than

In contrast, under a proportional con e tax burdens are independent of

( oI ) comes in present, its present value is simply oI . Now, the present value of lifetime

pattern must satisfy the relation

rcI oo +

+=1

(1)

Similarly, Grasshopper is constrained by

c AoA

7 However, when marginal tax rates depend on the level of consumption, this may not be the case.


rc

cIG

Goo ++=

11 (2)

Equations (1) and (2) say simply that the lifetime value of income must equal the lifetime value of consumption.

If the proportional conser tax liability in the second period is ; and the present value of her lifetime consum

umption tax rate is , Ant’s tax liability in the first period is Act occt ;

ption Acct 1h

tax liability, AcR , is

rct

ctRA

cAoc

Ac +

+=1

1 (3)

Similarly, Grasshopper’s lifetime tax liability is

rct

ctR cGoc

Gc +

+=1

1 (4)

By comparing Equations (3) and (1), see that Ant’s lifetime tax liability is equal to It .

is also It We

G

we

Similar comparison of Equations (2) and (4) indicates that Grasshopper’s lifetime tax liability conclude that under a proportional consumption tax, two pe

entical lifetime incomes always pay identical lifetime taxes (where lifetime is interpreted in the present value sense). pattern of lifetime consu

A related argument in favor of the consumption tax centers on the fact that income tends to en income is unusually low, individuals may

raw on their savings or borrow to smooth out fluctuations in their consumption levels. Annual consumption is likelyincome.

Opponents of consumption taxation would question whether a lifetime point of view is really ent

tation for most households (see

oc

ople withoc .

id This stands in stark contrast to a proportional income tax, where the

mption influences lifetime tax burdens. fluctuate more than consumption. In years whd

to be a better reflection of lifetime circumstances than is annual

appropriate. There is too much uncertainty in both the political and economic environm s for a lifetime perspective to be very realistic. Moreover, the consumption smoothing described in the lifetime arguments requires that individuals be able to save and borrow freely at the going rate of interest. Given that individuals often face constraints on the amounts they can borrow, it is not clear how relevant the lifetime arguments are. Although a considerable body of empirical work suggests the life-cycle model is a good represenKing (1993)), this arguments still deserves some consideration.


2.4 The General Model8 Now consider the general equilibrium of a simple production economy. The economy

consists of I consumer-workers with utility functions ),( iii LXU , where iX represents

consumptions of the n goods and iL is the supply of labor. For a start, we assume that production has constant returns of the simplest variety: each good is produced from labor alone. Production of a unit of good j requires

ja units of labor so that the production price can only be wap jj = in equilibrium. We choose to normalize 1

=w ; moreover we choose the units of goods so that each ja equals one, so that all production prices satisfy 1=jp .

Since this is a general equilibrium model, we must specify how the government intervenes in the economy. The government may want to pay civil servants, finance the production of ublic goods, or purchase private goods. To simplify, we assume here that it just buys T units

alized to one, the government must collect revenue T. We consider the following taxes:

pof labor. Since the wage is norm

・ linear taxes on goods, which raise consumer prices to )1( jt+

・ a linear tax on wages, so that the after-tax wage is )1( τ− .

It

The budget constraint of consumer i, who only owns his labor force, then is

in

j

ijj LXt )1() τ−=

1(1

+∑=

is easy to see that in this setting (with no nonlabor income, and no bequests), the tax on wages is equivalent to a uniform tax on goods. Indeed define

ττ−

+=

1' jj

tt

Since )1)(1(1 ' τ−+=+ tt , we can rewrite the budget constraint of consujj mer i as

in

j

ijj LXt∑

=

=+1

' )1(

8 Section 2.4 and 2.5 draw from Salanié (2003, pp.64-73).


The tax system then is equivalent for all consumers to the tax system , which

the former tax system

he consumer i’s bud

is tax revenue can also be written

which is exactly what the government collects from consumer i in the latter tax system. Thus a tax on wages is absolutely equivalent to a uniform tax on goods.

As a consequence only of the

)),(( τjt )0),(( 'jt

does not tax wages. Replacing the former with the latter leaves consumer choices unchanged. Moreover the government collects from consumer i with

in

j

ijj Xt∑

=

+1

τ L

But using t get constraint

∑=

+=n

j

iji XtL

1

' )1( j

th

∑∑==

=++n

j

ijj

n

j

ijjj XtXtt

1

'

1

' ))1(( τ

n )1( +n

for instance, fix arw

rates are determined at the optimum,

hatever that is. We may the rate of the tax on wages. This taxes are differentiated across goods, and

notation, which fixes

)),(( τjt

bitrarilyw ,hardly matters, since we focus here on ho '

jt

0=τ . We will work on the indirect utility of consumers, which can be written , where

is the vector of consumption prices:

under

We are in a second-best situation, since we do not allow for the lump-sum transfers that would implement any Pareto optimum. To model the redistributive objectives of government, we assume that it maximizes a Bergson-Samuelson functional

)(qVi

'1 tq +=

ii LXq =⋅ ),(max)( iii LXUqV =

),( LXi ii

))(,),(()( 1 qVqVWq IK=W


To fulfill its needs in the most efficient way, the government must maximize )(qW in q under its budget constraint (remember that '1 tq += , so choosing the tax rates is equivalent to

choosing the consumption prices):

TqXq ij

I n

j =−∑∑i j= =

)()1(1 1

Where the are the dem ous consumers9.

Let

)(qX ij ands of the vari

λ differentiating in

denote the Lagrange multiplier of the budget constraint of government. We have, by , kq

∑ ∑∑ ⎟⎟⎞

⎜⎜⎛

∂

∂+−=

∂∂

∂∂ I n i

jj

ik

iI

qX

tXqV

V'λW

= == ⎠⎝i j kki i 1 11

B s identity,

y Roy’

iki

k

i XqV

α−=∂∂

where iα is the marginal utility of income of . We define

i

ii

i Vαβ

∂∂

=W

T ewsocial welfare function;

his n parameter weights the marginal utility of income of consumer i by his weight in the

iβ is called the social marginal utility of in , since it is the

muelson functional when is given one more unit of

income. We have, by substituting these definitions,

come of ii increase in the value of the Bergson-Sa

9 We should note here that the indirect utilities are quasi-convex, so that even though is concave, the

program we shall solve may not be concave. Diamond-Mirrlees (1971b) prove that the calculations that follow can nevertheless be rigourously justified.

)( qV i W


∑ ∑∑= ==

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂+=

II

i

n

j k

ij

jik

i

iki q

XtXX

1 1

'

1λβ

We will now use Slutsky’s equation

i

ijii

ij X

XX ∂

−∂

kjkk R

Sq ∂

=∂

where we defined

iUk

iji

jk qS ⎟

⎟⎜⎜∂

=

We get, by rearranging,

X

⎠

⎞

⎝

⎛ ∂

∑ ∑∑∑∑===

=

== ∂

∂+−=

n

j i

ij

ji

ik

i

ik

kii

i

ijk

jj R

XtXX

XSt

1

'

11

1

11

'

λ

which contains the new parameter

∑ IIiIIn β

∑= ∂

∂+=

n iXβ

j i

jj

ii R

t1

'

λ

The first term of is the social marginal utility of income of , divided by

b

ib i λ , which is the

ost of budg for the government; the second term is the increase in tax revenue n his income increases by one unit. The parameter us measures

what is called the net social marginal utility of income of consumer . It accounts not only for the direct term

c et resources e

collected on i wh i thbi

λβ /i of social utility (measured in monet ry ts) but or the fact that the increase in taxes paid by allows to reduce tax rates. endogenous, just like

a

uniOf course,

also f

i is i b

iβ .


Let us denote the aggregate demand for good by . Rearranging and using

the symmetry of the Slutsky matrix, we finally get

k ik

Iik XX 1=∑=

⎟⎟⎠

⎞⎜⎜⎝ === kiij 111

⎛−−= ∑∑∑

ik

I

ik

Iikj

n

j XXbXSt ' 1

By definition,

11=i k

Denote

=∑I i

k

XX

b as the average of the s'ib and define the empirical covariance (across consumers) as

⎟⎟⎜⎜= kik X

IXbb

,covθ

We can now write

⎠

⎞

⎝

⎛

k

i

kk

ikj

Iij

nj bb

XSt

θ−−=∑∑

− == 11'

1

s, first obtained in this form by Diamond

(1975).

The left-hand side of this equation is called the discouragement index of good . Let indeed the be small (which must hold if the government collects a low tax

which is Rasey’s formula with several consumer

k revenue '

jt T ). hen the ta on good x t '

jj

e

T reduces the consumption of good by consumer by

el. The l ft-hand side is, to a first-order approximation, minu

f decreas of the consumption of good summed across consumers. Th reduction in the co ensated demand for good induced by

system. As for the right-hand side, it depends negatively on the term

k i jt '

s the percentage

us it can be t

ikj at

e tax

S

h

a fixed utility lev

o e interpreted as the relative

kmp k

kθ , that is, on the covariance

between the net social marginal utility of income and the share of consumer in the total consumption good . With only one consumer,

i k kθ obviousl is zero. It onl differs from y y


zero in that consumption structures and the i factors differ across agents. For this reason it

kR

b

is called the distributive factor of good . amsey’s formula therefore indicates that the government should discourage less the

onsumption of these goods that have a positive kθc , that is, of goods that are heavily consumed

by agents with a high net social of income. But who are these agents? Coming back to the definition of the , it is clear that ceteris paribus, the agents with a high

marginal u

ib ’stility

iV∂∂W also have a high ese agents, who are privileged by the government in

n, are y This suggests that the tax system should discourage less the consum e poor buy more, since these goods have a positive distributive factor

ib .

probabl

But

also

th

ption of the goods thatits objective functio the poorest.

th

kθ .

To obtain this formula, we assume oduction exhibited constant returns and moreover ad a very simple structure – each good being produced independently from labor alone. It is

g, then firms make profits that (possibly after taxation) are paid to their shareholders. C

d that prheasy to show that the formula remains valid for any constant returns technology. If returns are decreasin

onsumer demands then depend both on consumption prices q and production prices p ,

which makes the analysis much more complicated (see Munk 1978). Note, however, that th

are taxed at a 0% rate, then Ramsey’s formula again remains valid.

2.5 Some Special Cases First note that if all consumers have the same consumption structure, then all

ese profits are actually rents, and that it is efficient for the government to tax them; if profits in fact

10

kik XX terms

are equal I1 to and the cova d side is zero, so the discouragement index

is the sam and Sam

er. m

riance of the right-han

e for all goods at the optimum. But the most interesting special case is that studied by Ramsey uelson, where all b

are identical and equal to same b . This obviously holds if the population can be represented by a single consum We will focus this subsection on the study of Ramsey’s formula with a representative consu er.

In this case too, all discouragement indexes are equal. This prescription is very different in general from the popular notion that “to avoid distortions”, all goods should be taxed at the same rate. Our formula now is

i

bX

St

k

kjjnj −=

∑− = 1

'1


Note that if we move to the right-hand side and sum the equalities across goods, weighted

by , we get

for the semidefinite positive matrix and and side is the product of tax revenue

k

'

= kkk

n

kjkkjj

1,

The left-hand side is the semi-norm of therefore it is nonnegative. The right-h

X

t

∑∑ −=− XtbtSt ''' )1(

't )( S−T with 1( )b− .

Thus 1≤b if the tax is to collect any revenue. In return, we conclude that the discouragement indexes are all nonnegative: the optimal tax system does not encourage the consumption of any good10.

At this stage Ramsey’s formula still is rather opaque. It nevertheless yields some

conclusions. Consider, for instance, the two-good case, 2=n . By solving the Rams y formulas associated with these two goods, and denoting 02

122211 >−= SSSD as the

determinant of the Slutsky submatrix for the two consumption goods, we find

e

⎪⎩ 2111212 D

Now the expenditure function is homogeneous o

⎪

⎪⎪⎨

−= )( 122212'1 XSXS

Dt

⎧

−−

=

−

)(1

1

' XSXSbt

b

f degree one in prices and the Slutsky matrix is its second derivative.

ies as

Denoting 0 for the good “leisure”, Euler’s theorem implies that

02210 =++ iiii SqSqS for 2,1=

We rewrite these equalit

i

⎪⎪⎨

⎩−−=

1

112

1

2021 q

SqqSS

Define as usual the compensated elasticities as

⎪⎪⎧ −−=

2

111

2

1012 q

SqqSS

ijijij XqS=ε , whence

10 This observation no longer holds in the several-consumer model, where the optimal tax system may in fact

encourage the consumptions of some goods.


⎪⎪⎩

⎪⎪⎨

D⎧

−−=

−−=

)(1

)(1

2211201

21'2

2211102

21'1

εεε

εεε

qXX

Dbt

qXXbt

It follows that

)(1'' εε −−

−=− XXbqtqt

Since 't , the left-hand side is just '

2'1 tt − . Thus this equation implies that '

2'1 tt > if

and only if 2010

2010211221 D

1q +=

εε < , that is, if and only if good 1 is more complementary to leisure than good

2. To interpret this result, recall that by definition,

U

ii w

X⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

=loglog

0ε

2010 εε < Therefore if an increase in wages induces a larger increase in the consumption of

good 2 than in the consumption of good 1 for a fixed utility level. But for a fixed utility level only substitution effects come into play, and a wage increase leads to an increase in labor supply. Thus good 1 must be taxed at a higher rate than good 2 if when the consumer works more, he increases his consumption of good 2 more than that of good 1.

taxing m re heavily the goods that are complementary to leisure (e.g., skis) than the goods that are complementary to labor . The intuition can be seen by recalling that a uniform taxation is equivalent to a tax on wages, which discourages labor supply. One way to courage the consumption of leisure by taxing more heavily the goods that are complementary to leisure.

Let us now make even more restrictive assumptions: we assume that all compensated cross-elasticities of good with other goods are zero. Define

This result was obtained by Corlett-Hague (1953): when preferences are not separable between goods and leisure, the government should deviate from uniform taxation by

o (e.g., urban transportation)

counter this distortion is to dis

k kkkkk XqS−=ε as the

direct compensated elasticity of good . Then we get the inverse elasticities rule:

k


kk

k bt

tε−

=+

11 '

'

If these assumptions hold for all goods, then tax rates should be (to a first-order approximation) inversely proportional to demand elasticities11; this is the formula from the beginning of this

tant, ∞=Sε . This hassection, except that since returns here are cons been used as a way to

justify the so-called sin taxes on tobacco and alcohol, but it is not clear that their demands in fact are price-inelastic.

One may wonder when Ram ’s formula for a representative consumer yields uniform taxation of goods. Deaton (1981) shows that a necessary and sufficient condition is that the utility function be quasi-separable12, that is, that the marginal rates of substitution between goods on a given indifference curve be independent of the consumption of leisure. It can be pr -separability holds if and only if the expenditure function can be written.

is easy to see that then a wage increase does not change the relative compensated demands

gene e n-go

hen the consumers are heterogeneous, then the analysis of the practical consequences of R in particular impossible to find reasonable conditions for uniform taxation to be optimal.

Note, however, that there may be reasons outside this model that plead for uniform taxation. For instance, uniform ion can lower administration costs, and limit the lobbying by interest groups, since each group attempts to bend the tax system in its favor.

sey

oved that quasi

)),(,,(),,( * qubwuewque =

Itof the various goods. Thus Deaton’s result ralizes that of Corlett and Hague to th od case. This condition clearly is very restrictive.

Wamsey’s formula becomes very complex. It is

taxat

11 Conrary to appearances, this formula is perfectly consistent with the Corlett-Hague result. The compensated

cross-elasticities indeed are zero if the utility function can be written

∑=

−n

kkk BLXu

1

)(

But then minimizing expenditure yields

k∀ , Bw

Xuq

kk

k =)('

It follows that for any good k ,

w

BqXu k

kk =)('

so that kk εε =0 : the goods that are more complementary to leisure are also those with the less elastic demands. 12 Sometimes the term “implicitly separable” is used. This property should be distinguished from weak separability.


Finally, recall that Ramsey’s formula only holds in a world where income is taxed linearly. Setting this assumption aside has spectac

ular consequences on the structure of optimal indirect

ta

2.6 Extension of the Ramsey Model to Many Households

start considering many persons/households in an economy, we need to define how to formulate social welfare as a representative of individual utilities, i.e. social welfare function. 1. The minimal state [Nozick (1974) Anarchy, State and Utopia], limited to the narrow

functions of protection against force, theft, fraud, enforcement of contract and so on is

e of nature or anarchy

y, because of free-rider problems has to adopt coercive taxation to

The minimal state is to allow the government to carry out unanimously approved activities. No violation of individual ghts is involved.

3. Pareto efficiency

4. Individualistic Social Welfare Functions

elfare function This function is Paretian in the sense of respecting individual valuations. 1 2 3 H h y of individual/household h.

Two classes of social welfare functions are most well known. ec of maximizing the sum of individual utilities, i.e. any positive

linear transformation of

xation.

Once we

justified. Any more extensive state will violate person’s right not to be forced to do certain things is unjustified. The initial position taken by Nozick is a stat . In this anarchy situation, there is a limited recognition of the rights of others, in sufficient to allow peaceful co-existence and Nozick argues that a dominant agency supplying protective services will emerge. This agencfinance the operation. Hence the minimal or ‘night watchman’ justification for the state. The minimal state offers only one public good – protection against violence, theft, and fraud – and the enforcement of contracts. Redistributive activity is limited to the financing of this minimal collective outlay.

2. Unanimity

ri

The minimal state can approve Pareto improvements, i.e., to make at least one person better off and no one worse off. A Pareto efficient allocation is one where no Pareto improving move can be made.

The standard procedure for arriving at a complete ordering is to postulate a Paretian social w .W(U ,U ,U , …U ) where U denotes the utilit

1) The Benthamite obj tive


W = u1+ u2 + u3 + … + uH (5) (Utilitarian social welfare functions)

2) The Rawlesian objective of maximizing the welfare of the worse-off individual

(maxi-min)

W Uh

h= min( ) (6)

These two are, in fact, special cases of the isoelastic formulation

( )[ ]∑ −− kv1

=−vhUW 11 1

(7)

is assumed to ensure that the choice of moral principles is impan a 5.

e: it equalizes utilities. h the Rawlesian objective is frequently supposed to be egalitarian in this sense,

, the social welfare function is decreasing in iate objectives may trade-off between distance and the level

tes individual utilities to social welfare. The society is concerned not with the allocation of particular goods such as civil

Where the Benthamite case is v = 0 and the Rawlesian case is v → ∞. Note that Rawls [(1971) A theory of Justice ] considers the choices made in an initial position (original position) which is defined such that people have no knowledge of their social position or preferences. This ‘veil of ignorance’

artial or just; it is asserted that the decision made by people in that hypothetical position are cceptable basis for a theory of justice.

Non-Individualistic Social Welfare Functions From 1 to 4, social welfare is supposed to respond positively to individual welfare. The first departure from this is where the social welfare function still takes individual utilities as its arguments but is no longer monotonically increasing – it is individualistic but not Paretian. 1) The egalitarian objectiv

Althougit is clearly not the case. The egalitarian objective is concerned with the distance

between individuals and where 12 UU >2U . Intermed involve some

of utilities, an example of such a social welfare function is W = U1 - θ (U2 – U1) 2) The paternalist (right based) approach.

It no longer relaonly with general inequality but also rights, the vote, essential foods, medical care, education and housing.


The

Source: Atkinson and Stiglitz (1980) Fig

hich social welfare function you choose ?

hese functions vary amongst the households.

Writing

is g

Social w

above social welfare functions can be illustrated in figure below.

Figure 4 Alternative Views of Government Objectives

U2

N’C• • •

TW

B

D

••

ure 11-1.

WLet’s extend the Ramsey model to many households case13. The economy is consist of H households. Each household h is described by an indirect utility function.

Uh = Uh (q1, …, qn, y) (8) T

hhnxxx ,...,, 21 for the consumption demands from h, the government revenue constraint

iven by

h

∑∑i= =h

ii xt1 1

(9)

elfare function is defined on the vector of indirect utilities

=n H

hR

13 This part draws from Myles (1995, pp.108-111).

U1

R

D

•

•

Egalitarian Solution

45º

•

N

2)

MinimalSocial Indifference CurveState

Benthamite SocialWelfare FunctionSocial preference

with weight ondistance U1-θ(U1- U

•

Rawlsian SocialWelfare Function


(10) The express

(11)

The first-order conditions for the choice of the tax rate on good k, is

W = W (U1, U2, …, UH)

government’s maximization problem is to maximize (39) subject to (38). It can be ed in terms of the Lagrangean

⎤⎡

−+= ∑∑n H

hh RxtUWL λ ⎥⎦

⎢⎣ = =i h

ii1 1

)(

h

H

h

h

kkh

h

H

ih

H

i

nih

k

wu

uq

x t xq= = ==

+ +⎡

⎣⎢

⎤

⎦⎥ =∑ ∑∑

1 1 11

0Σ∂∂

∂∂

λ∂∂

(12)

With Roy’s identity, the first term of (41) can be written

∂∂

∂∂

∂∂

αwu

uq

wu

xhh

H h

kh

h

Hh

kh

= =∑ ∑= −

1 1

(13)

and define

hhu∂

h w αβ ∂= (14)

come accruing to household h. αh is the marginal 1) becomes,

where β h is the social marginal utility of inutility of income for h. Employing the definition of β h , (4

β λ∂∂

hH

h khh= ==⎣ ⎦1 111kh

kh

iihH

i

nH

x x t xq=

∑ ∑∑∑= +⎡⎢

⎤⎥ (15)

Substituting from the Slutsky equation

∂∂

∂∂

xq

s x xy

ih

kikh

kh i

h

h

= − (16)


into (44) and rearranging gives the Ramsey rule for many households

t s

x

x

x

tx

xh hH

ihn

hH

∑∑⎡ ⎤∂

y

x

ih

H

kih

i

n

hH

kh

hH

i hi

kh

hH

== = ==∑∑

∑

∑

∑ ∑= − + ⎣

⎢⎦⎥

11 1 111 1λ

β ∂ (17)

kh

kh

kh= = =1 1 1

(46) can be expressed as

t s HxxH

hn

hkh

h

H

=∑∑∑

∑ ∑= − − −

⎡⎢⎢

⎤

1

βt x

yxi

hki

ik i

i

nih

hkh

h

H

== = =

⎡

⎣⎢

⎤

⎦⎥

⎣⎢⎢

⎥⎥⎥⎥

11 1 1λ∂∂

(18)

⎦

xx

Hk

kh= =∑

1 is the mean level of consumption of good k. where

hH

ine Def

b t x

yii h=λ ∂1

hh n

ih

= +∑β ∂ (19)

h ond’s net social marginal utili

It is net in the sense that it measures both the gain in social welfare β due to an increase in come to h and the increase in tax payments of h due to this increase in income. Thus bh

th equity and efficiency effects. sing (48), (47) can be rearranged to give

b is Diam ty of income measured in terms of government revenue.

h

ininvolves boU

t s

x

b

H xkh

h

Hkh

=

=∑ ⎣⎢

⎦⎥

1

1

xih

H

kih

i

n

hkhH

==∑∑

∑= − −⎡ ⎤11 1 (20)

s is the alternative Ramsey rule for m The Ramsey rule (49) implies that the reduction in demand is smaller: (i) the more the good is

Thi any households.


consumed by individuals with a high bh (ii) the more the good is consumed by individuals with

ds ( )x xkh

k . a high marginal propensity to consume taxed goo

mal commodity tax rule for many households illustrates aspects of In other words, the opti the efficiency/equity trade-off by the manner in which the reduction in demand for a good is related

the social importance of the major consumers of that good and their general contribution to

As is always the case with the Ramsey rule, it remains very general to obtain detailed results on the optimal tax structure, we need to make more specific assumptions about the nature of differences between individuals and the form of the utility function.

2.7 Empirical Studies of Optimal Commodity Taxation

ptimal tax rates is concerned with two issues: (1) The optimal tax les derived theoretically suggest general observations about the structure of optimal taxes but

they do not have precise implications. Empirical analysis can be seen as providing a check on the interpretations and a means of investigating them further. (2) Empirical analysis can

vide practical policy recommendations. To do this, t ing applied to data and the values of the resulting optimal taxes calculated. As Deaton (1981) notes, “present theoretical formulae do not yield clear-cut results except in pecial cases and it has recently become clear that optimal rates depend crucially on the detailed

structure of consumer preferences” (p.1245). For example, Atkinson and Stiglitz (1976) show al nonlinear inco odity taxes are only necessary

hat indivi leisure. ometricians estimating commodity demand and labor supply equations make generous

se of separability assumptions to enable estimation at all. In consequence, it is likely that pirically calculated tax rate be

determined in structure, not by the measurements actually made, but by arbitrary, untested (and ven unconscious) hypotheses chosen by the econometrician for practical convenience” (Deaton,

follows.

tothe tax revenue.

Empirical analysis of oru

pro he tax rules must be capable of be

s

that with an optim me tax, discriminatory commto the extent t dual commodities are not weakly separable from “Econuem s, based on econometric estimates of parameters, will

eibid.)14. To remedy this situation, and as a prelude to fruitful empirical work, it is necessary to have more explicit understanding of how preference structure affects optimal tax rates. The major empirical modifications are as 14 Many econometric works on consumer demand is based on the Linear Expenditure System (LES) in which

demands are additively separable and the linear Engel curve or linear (quasi-homothetic) preferences the theoretical attraction of linear preferences lies in the aggregation theorems of Gorman, while the empirical attraction is ease of interpretation and estimation of the underlying parameters.


(1) The many consumers economy. Consumption demand and and

commodity tax can be treated separately. If they are not, both taxes must be determined jointly.

(3) The relationship between consumption demand and income (known as the Engel Curve)

axes wil e uniform if (i) labor supply is completely inelastic, or (ii) consumption is weakly separable from leisure, and the consumption

one factor.

Ray (1984)], and the goods tility function is not additively separable, for less homothetically so. In the Indian context,

ommodity demand nctions with non-linear Engel curves. Further evidence of non-linear Engel curves on time

how the tax rates very

(2) labor supply are not separable. If they are, income tax

can be non-linear. Indeed, the importance of assumptions about consumer preferences for the ‘optimal’ commodity tax rates is now widely accepted in the literature [see, Deaton (1981)]. For example, it is well known that commodity t l b

indifference map is homothetic or Engel curves are linear or an optimal non-linear income tax is allowed for. One ought to emphasize here that the uniformity result is only valid within a framework where people have identical preferences and differ only in their earning power which consists of None of the above requirements for uniform commodity taxes is likely to be met in practice. There exists a large body of empirical evidence which suggests that leisure is not weakly separable from goods, the Engel curves are not linear [Blundell and uRay (1986 a,b) provides evidence of non-homothetic and non-separable cfuseries of national accounts data of some developing countries is also available.

2.8 An Econometric Case Study of India Although it is widely recognized that calculations on optimal tax rates depend quite crucially on assumptive about consumer preferences, the empirical evidence onwith utility and demand specification seem virtually non-existent. Exceptions are a series of studies in India (see Marty and Ray (1987), Ray (1986 a,b)). To calculate the optimal tax rates, the first step is to specify the social welfare function. Denote the aggregate expenditure of household h, which is assumed to be equal to income, by yh and let the social utility of income to h be given by

hU 1 1 1

≠−

=−

εε

φ εhy

(21)

1= log εφ hy= (22)


where ε ≥ 0 is required for concavity and can be interpreted as the planner’s inequality

y of

aversion with higher ε representing greater aversion.

With the additive social welfare function ∂ ∂W U h= so the social marginal utilitincome to h, βh as defined in eg. (43), is given by

β ∂∂

φ εhh

h hUy

y= = − (23)

The households are ranked according to their expenditures, with the lowest expenditure

household first in the ranking. Setting β1=1 for the lowest expenditure household in the data set, it follows that15

βε

h

h

yy

=⎡

⎣⎢

⎤

⎦⎥

1 . (24)

The social marginal utility of income for the poorest household is unity and declines monotonically with an increase in household affluence at a rate determined by ε.

ses the Linear xpenditure System (LES) to allow for non-linear Engel curves and non-separable preferences

The advantage of this method of defining the marginal social utilities is that the βhs are fixed exogenousely and can be determined by the abserved expenditure levels in the data set. In addition, the concern for equity is clearly expressed and can be varied parametrically.

Next step is to estimate the price-expenditure elasticities (including the Slutsky equation). As mentioned above, the good utility function is not additively separable and the Engel curve is non-linear. Blundel and Ray (1984) and Ray (1986a) introduce new estimation method called the Restricted Non-Linear Preference System (RNLPS) which generaliEvia an extra parameter, α .

The indirect utility function of RNLPS is given by

15 suppose β φ 1= =y , then φ = y1 . We substitute it into equation (2.49), ε1 − ε

β ε εε

hh

h

y y yy

= =⎡

⎣⎢

⎤

⎦⎥

−1

1 .


V q yy q w

hh i i h

i

n

( , ) =−

=∑α α αγ 1 2

1 q wk

k

n

kk

=∏ αβ αβ0

1

(25)

where

w hh = =k + < ≤ < < −wage for = , , , ,Σ ,1β α α α α α α1 0 1 0 0 12 1< ≤ −

12 1 2

α α . The corresponding demand system, in budget share form, is given by

S q x q w p wi

i ii

ii k

n

= = ⎛⎝⎜

⎞⎠⎟⎛⎝⎜

⎞⎠⎟⎛⎝⎜

⎞⎠⎟ + −

⎛ ⎞ ⎛ ⎞⎡⎢

⎤∑γ α

αβ γ

α α α

12 1 2

1y y y yk⎣⎢ ⎦⎥

y

i n

k

⎝⎜

⎠⎟

⎝⎜

⎠⎟ ⎥

=

=1

1 ..., ,

(26)

S wxy

py yi

i 1⎨⎩

⎬⎭ ⎝

⎜⎠⎟

⎝⎜

⎠⎟

=∑α

γ (27) wL in

0 02 0

1 2

= = +−⎧ ⎫ ⎛ ⎞ ⎛ ⎞

βα αβ

α α

x is leisure demand, x .

y expenditure:

where L i i Li=1

Equation (56) and (57) can be re-expressed as Sic, S0

c which are defined as the proportion of aggregate commodit

y p x wn

= +∑

S q xy

qy

qy

i n

ic i i

ci

ii i

i⎛⎝⎜

⎞⎠⎟ ⎝

⎜⎠⎟ + −

⎝⎜

⎠⎟⎢

⎢⎥⎥

− − ∑γ αα

δ θ βδ δ γ θα α α α α1 1 12 2

(28) c ci

= =⎛ ⎞ ⎛ ⎞⎡

⎣

⎤

⎦=

α1

1 ... , ,

Swx qc L

ii

n

0 02 0 1

1

2= = +− ⎛

⎜⎞⎟− ∑β δ

α αβα

δ γ θαα

α (29) y yci 1 ⎝ ⎠=

where y q x wy

yy Sc i i

c c

= = = =−

Σ , , θ δ 11 0

The goods parameter estimates (γi, βi, α1) for the nine commodity classification are presented in Ray (1986a). Using there estimates, and a priori assumed values for 2α and 1θ , the

optimal tax rates are calculated (with ε=2).


Table 1 Estimates of optimal commodity taxes

Item θ=0.05 θ=0.1 α2=0.0 α =0.025 α =0.05 α =0.025 α =0.05 2 2 2 21. Cereals -0.015 1.437 -0.089 0.745 -0.376 2. Milk -0.011 -0.307 0.118 3. 0.342 0.315 0.202 4. Meat, fish & eggs 0.671 -0.330 0.083 -0.122 0.090 5. Sugar & tea 0.013 -0.210 0.003 -0.044 -0.091 6. Other food 0.226 -0.153 0.231 0.061 0.200 7. Clothing 0.038 -0.431 0.082 -0.255 0.326

Fuel and light 23 Other non-food 40

and Milk Products -0.042 -0.504 Edible Oils 0.359 0.111

8. 0.038 0.072 0.014 0.131 -0.19. 0.083 -0.451 0.126 -0.239 0.3Note: β0=0,ε=2, α2≠0 implies non-separability of goods and leisure,α2=0 implies separability. Source: Murty and Ray (1987, Table 1).

lowing features emerge from Table 1. (1) The optimal widely

considered case of leisure/goods separability (i.e.α2=0). (2) More important from the viewpoint of the present study is the extreme sensitivity of the

optimal taxes not only to deviation from leisure/goods separability (α2≠0) but also, to further changes inα2. For a givenθ, the optimal commodity taxes for the principal items als, Fuel and light, on one hand, and Clothing, Other non-food, on the other, move in reverse directions asα2 varies.

(3) The optimal taxes are also sensitive, though less s reduced wage rate generally reduces the absolute magnitude of optimal taxes and subsidies though, unlike in the case of the non-separability parameterα2 , it does not reverse the sign.

2.10 An Econometric Case Study of Japan

ypes of consumption taxes: general and specific. An example of a general consumption tax is the general sales tax, which can be divided into single-stage or multi-stage taxes. The single-stage tax comprises three major types: manufacturers’, wholesalers’, and

ilers’ sales taxes. Each is levied on the sales of goods and services at each stage of production and distribution. Sales taxes are collected from the seller and shifted forward on to the consumers.

typical type of multi-stage sales taxes are the valu The value added tax is levied on the difference between what a firm sells and what it purchases; i.e., on the net value added by each firm. In contrast, the turnover tax is levied on the value of the

tion when one firm turns over a commodity another firm at each stage in the economy. Another form of consumption tax is the excise tax, which is selecctively levied on the sale of

The fol

commodity taxes in each item are far from uniform and this includes the

, Cere

o, to the wage rate parameterθ. A

(1) Pre-VAT indirect tax in Japan. There are two t

reta

A e added tax or the turnover tax.

transac to


a p

During the postwar period, the Japanese indirect tax system developed exclusively on the use of excise taxes on selective goods and services. In Japan, excise taxes are conventionally classified into four major groups by the Ministry of Finance, i.e. (1) excises on alcohol, tobacco and sugar, (2) selective taxes on goods and services, (3) taxes on stamp, security transactions and bourse, and (4) earmarked taxes. Table 2 Revenue Share

(%) The

Shoup Mission

1950 1955 1960 1965 1970 1975 1980 1985 1987 1990 1996

articular commodity or group of goods and services. Selective excise taxes commodity used throughout the world include those placed on alcoholic beverages, tobacco, petrol, and consumer durable goods.

National Tax

Income 58.1 55.8 45.1 43.1 42.4 46.9 45.9 47.4 45.7 46.7 47.1 38.7Consumption 16.8 17.3 23.7 23.5 21.3 18.5 15.7 14.3 13.7 12.2 15.8 15.1Wealth 0.3 2.1 2.2 2.5 1.9 2.1 2.5 2.4 3.4 4.9 3.5 2.0

Local Tax

Income 7.8 12.8 13.5 14.2 16.2 18.1 19.8 20.7 21.8 21.5 21.0 25.7Consumption 10.2 4.4 6.3 6.7 7.5 8.0 7.2 6.9 6.4 5.9 4.1 2.2Wealth 6.8 7.6 9.0 10.0 10.7 6.5 9.0 8.2 8.9 8.6 8.3 16.3

Total Income 65.9 68.6 58.6 57.3 58.6 65.0 65.7 68.1 67.5 68.2 68.1 64.4Consumption 27.0 21.7 30.0 30.2 28.8 26.5 22.9 21.2 20.1 18.1 19.9 17.2Wealth 7.1 9.7 11.2 12.5 12.6 8.6 11.5 10.6 12.3 13.5 11.8 18.3

Source: Konishi (1997), p.106, Table5-1

Estimating Excess Burden of Consumption Tax (1) Effective indirect tax rates It is an open question how much consumption taxes are ultimately transmitted to the consumers. In this exercise, we assume that all taxes are transmitted to the consumers. The results are reported in Table 3. Table 3 Major Effective Tax Rates in 1984

(%) Item Effective Rate Main Consumption Taxes

Liquor 38.4 Alcohol tax, Excise taxTobacco 64.7 Earmarked taxLeather goods 11.6 Excise taxPetroleum goods 18.7 Liquefied petroleum gas tax, Petro tax

Automobile 25.4 Petroleum tax, Local road tax, Motor vehicle tonnage tax

Light electric goods 5.2 Excise tax

Effective tax rates of Tobacco, Liquor, Automobile, and Petroleum goods, were extremely high and remained more or less the same levels after VAT was introduced in 1989.


(2) Est mating indirect tax payments per household i per month. Using National Survey of Househol Expenditur te indirect t monthly expen data. oing, vide o s in i Estimated ratio of indi x urden e low up (1st decile) w 5th decile was 5.4 at of c e was . T bu den a gressiveness. ( ction can be expressed as follows.

d Income and e (1994), we estimaax payments from diture In so d we di househ ld to tenncome groups (decile). rect ta b for th est gro as 5.84%, that of 1%, th 10 deth il 5.12% he tax r shows

moderate re

3) Specification of Demand Equations We assume individual utility fun

( )∑=

−=k

kkk dxu1

lnα (30)

m

where ∑=

=m

kk

1

1α , kd =the minimum (subsistent) consumption for good k when 0>kd ,

kk dx > and when 0≤kd , 0>kx . The budget constraint is given

m

∑=

=k

kk xqy1

(31)

where consumer price kkk ptq += , tax=kt , =kp producer price.

This demand system is known as the linear expenditure system (LES). The foremost f parameters to estimate)16. Solution

f maximization of (60) subject to (61) yields the demand system,

nsumption demands for 33 goods for each income group are estimated.

advantage of LES is easy to handle (i.e. smaller number oo

kimidqydqxqm

kkkiiiii ≠=−+= ∑

=

,,,1 )(1

Lα (32)

we estimate the m-goods linear demand system simultaneously17. In this model, savings are assumed away. Inpractice, co

16 A special characteristic of LES is that each demand is additively separable. This makes the linear expenditure

system easy to handle. At the same time, LES imposes a priori assumption of additively separability which may not be guaranteed empirically. Alternatively, Trans-log type demand system and Almost Ideal Demand System (AIDS) are sometimes used.

17 Estimation method is usually Full Information Maximum Likelihood (FIML). Because of Warlas’ law, mth good can be identified as residual. In fact, m-1 equations are estimated simultaneously.


Table 4 Estimate of Demand Equation and Social Excess Burden

Constant on Income qidi Excess Burden

Excess Burden Excess

Burden

Coefficient Social Change in Marginal Social

Cereals I (untaxed) 3,614 0.0079 4,422 3,894 113 0.080 Cereals II (taxed) 1,987 0.0044 2,417 3,901 119 0.084 Flesh food 12,585 0.0837 20,853 3,832 51 0.036 Oils, fats & condiments 1,930 0.0038 2,305 3,906 125 0.088 Cakes and candies 2,773 0.0085 3,616 3,879 98 0.069 Cooked food 1,805 0.0056 2,357 3,883 102 0.072 Beverages 1,485 0.0031 1,791 4,008 226 0.160 Alcoholic beverages 1,830 0.0057 2,395 4,014 233 0.165

-2,179 0.0410 1,781 3,771 -10 -0.007 0.0852 23,984 3,841 60 0.042

2,187 0.0178 3,946 3,872 90 0.064 2 05 3,9 2

Other fuel & ligh 01 3,9 164 ,8 0

ing 92 ,8 0

e 1, 78 ,6 5 -0ng - 48 ,7 -0ute 1,3 69 2 3,812 0.0ear 1, 98 - ,6 5 -0

2, 51 ,8 03, 50 ,6 4 -01,2 30 3,7 3 -0-910 0.0541 4,431 3,922 141 0.099

Communication 1,807 0.0148 3,271 3,831 49 0.035 Recreational durable goods -448 0.0092 457 3,780 -1 -0.001

1,392 3,776 -5 -0.003 -107 3,668 -93 -0.066

Other recreational service -1,367 0.0186 466 3,766 -15 -0.011

09 0.0293 2,383 3,755 -26 -0.018

General meals Housing 15,564Electricity Gas ,735

837 0.00.0

4 8

3,2731,010

03 72

1219

0.086 0.135 t

Water 988 0.00 1,622 3 50 69 .049 Heating & cool

ces

applian 136 0.00 1,048 3 15 33 .024

General furnitur - 075 43

0.00

-301 3 76 76

-10 .074 .0Interior furnishi 2 0.00 41 3 -5 03

Other domestic nsils 02 0.01 ,976 31 22 Clothes & footw -1 077 0.09 1,214 3 36 -14 .102 Medical care

n 382 9

0.01 3,8781,

33

40 59 .042 EducatioPublic transportation

--

80 77

0.050.02

454995

97 38

-8-4

.059

.030 Private transportation

Recreational goods -186 0.0160 Package tours -1,925 0.0184

Books & other reading materials -5

Toilet articles -121 0.0096 824 3,821 40 0.028 Persona effects -2,027 0.0122 -825 3,665 -116 -0.082 Tobacco 1,823 0.0002 1,844 3,979 197 0.139 Other living expenditure -30,284 0.3065 0 3,655 -126 -0.089

Source: Konishi (1997), p120, Table5-3

As we discussed in Chapter 1, be measu nt variation (EV) or compensating variation (CV). Accordi oncept of equivalent variation, s neral indirect tax (τ posed, t under the current comsumption taxes, excess den (EB p e general indirect ta ose u urrent consumption tax.

(4) Estimation of Excess Burden

excess burden can red either by equivaleng to the c

uppose the ge )is im keeping the utility level constan bur ) is obtained as a difference between tax

ayments under th x and th nder the c


[ ][ ]

rden. Excess burden increases as income goes up.

(5) Estimation of Social Excess Burden

Let us define social excess burden (SEB), keeping the social welfare level (use an utilitarian elfare function) constant under the current consumption tax, as a difference between tax

ts under t ge

n taxcunsumptiocurrent er theundpayment tax axindirect t general under thepayment tax

),(),(

−=

−⎟⎟⎠

⎞⎜⎜⎝

⎛+−−= ∑∑

kkk

kk

kkk

uqxtupxyy ττ (33)

),(),(),(EB −+−= ∑ uqxtupEuqE τ

Table 5 shows estimation of excess buExcess burden rate is 1.43% on average.

wpaymen he neral indirect tax rate and those under the current consumption tax.

( )

( )

[ ]n taxcunsumptiocurrent under thepayment tax

(,(,

),(,

),(,(,

,(SEB

−

⎞⎛+−+

−

⎟⎟⎞

⎜⎜⎛

+−++−

=

∑

∑∑

∑ ∑

hh

k

h k

hhhkk

h

hhk

hhh

h

hh

ppv

yqvqxt

ypxypvpE

yq

τττ

ττττ

),∑ h vqE

⎠⎝ k

( )[ ]axindirect t general under thepayment tax

)(,

=

+−∑∑h k

hhhkk

h k

yqvqxt

), ⎟⎟⎠

⎜⎜⎝

+= ∑∑ hhk

hk yxypx ττ (34)

e set the general indirect tax rate 5.22%, the so that

under the current consumption tax. Total tax revenue under the general indirect tax ggregating ten income classes) sums up to 145,418 yen. That under the current consumption

MS By means of raising a certain tax revenue (say 1% total

If w cial welfare level becomes equal to

(atax is 141,637 yen. Thus social excess burden is 3,781 yen, social excess burden rate is 2.67%.

(6) Direction of Tax Reform Now we try to estimate marginal social excess burden (MSEB) for each consumption item, EB can be defined as follows.


revenue), we estimate marginal increase in social excess burden when we impose an additional consumption tax on a specific item.

revenue) totalof (1% Increase RevenueTax Burden Excess Socialin Increase MarginalMSEB =

I , the current ptio ate is gh.

T f Excess mp x Bur

Income nsumTax Burden Rate s Burden s

Ra

(35)

f MSEB is larger consum n tax r too hi

able 5 Estimate o Consu tion Ta den Decile Income

Co ption Exces Exces Burden

te Class A B C C

150,610 8, 75 B/A /B

1 809 5.849 0.851 2 190,596 10, 116

210,287 11, 140 12, 159

244,736 13, 181 13, 199

280,318 15,000 223 1.487306,432 16, 254 347,876 18, 299 426,147 21, 387

64,408 14, 203

552 5.536 1.099 3 4 227,743

504 5.471 1.217 331 5.414 1.289

5 6 259,337

238 5.409 1.367 943 5.376 1.427

7 8

237

5.3515.299

1.564

9 196 5.2315.122

1.643 10 826 1.773

Average 2 164 5.357 1.433

S ), p.121, Tab

ource: Konishi (1997 le5-4


Appendix 1 Introduction to Value Added Tax18 In this appendix, an attempt has been made to explain the meaning and characteristics of

AT) and to indicate why it is to be preferred to Prior to embarking on this explanation, it

define value added and show how it can be measured. The gross output of goods and services produced in a country is measured in terms of the

tal value of all the commodities and services when they reach the hands of the final users,

measure of total output for a year is termed gross omestic product for the year and represents the sum of all values of goods and services

. Now typically, each commodity passes through everal stages of production and at each stage some value is created or added. The total value

erned. hat account for a year can be presented in the following way (in summary terms):

Receipts Rs Expenditure Rs

value added tax (V the sales taxes levied on the gross sale value of commodities. will be useful to

tonamely, consumers and investors (buyers of capital goods), after going through various stages of production, plus the value of exports. This dproduced in the country during the yearsof a commodity as it reaches the hands of the final user is the sum of values created at the successive stages of production. The value added at each stage of production can be worked out (quantitatively) from the production account of the enterprise or producing unit concT

Income from sale of output 10,000 Cost of bought out inputs 4,000 (=gross value of output) Wages and salaries 2,000 Rent 1,500 Interest 500 Depreciation 1,000 Surplus (Profits) 1,000 10,000 10,000

GG ght out inputs

ross value of output = Rs 10,000 ross value added = gross value of output － cost of bou

= Rs 10,000 － Rs 4,000 = Rs 6,000 (It is assumed that there is no change in inventories.)

It may be noted that gross value added is equal to the sum of wages and salaries, rent, interest,

depreciation, and profits (net value added will exclude depreciation). Under VAT, the value added at each stage of production and distribution is equal to the total

nd capital inputs at successive stages of manufacturing. As has already been indicated, this

value embodied in a commodity, the VAT on a commodity amounts to a tax on just the total value of that commodity. By contrast, a sales tax on the total value of output or turnover falls on the value of inputs at successive stages unless the tax is confined to retail sales. Even the first point sales tax levied by most state governments has a base that includes the cost of current a

18 This appendix draws from Chelliah, Aggarwal, Purohit and Rao (2005).


results in cascading of tax burden and escalation of costs. Hence the need to adopt VAT, though it is necessarily a multi-point tax.

Computation of VAT AT can be computed in one of two ways: the subtr od.

In the former the tax rate is applied to the difference between the value of output and the cost of puts. In the addition method the value added is computed by adding all the payments to eh

will be shown later, this method an be used only with the ‘income variant’ of VAT).

rm of the subtraction method. The subtraction method ing VA scri

where s the tax rate e value o t, and I is ue of inputs ow n be rewritten as

V action method and the addition meth

infactors of production, viz., wages, rent, interest, and profits (as c In implementing VAT, most countries use an amended fo

of apply T may he de bed as

I)t(OVA −= T

t i , O is th f outpu the val . N I) cat(O −

I)t(tO − . That is, V n be colle s the differ bet the tax

payable on output an paid on This me f computing collectingcalled the input tax c thod. Here, we shall discuss only the subtraction method and the

In a VAT, while the tax is levied and collected at every stage of production and distribution, it i to be ultimately borne by the final user of the good. This implies that tax inclusive price at

any stage has to include taxes collected at all earlier stages. The input tax credit method achieves this by requiring the seller to collect tax on the entire value of output and retain the amount equivalent to the tax paid on purchases. However, in the subtraction method, at any stage, the tax is to be collected only on the value added at that stage. The taxes paid at the earlier stages would have to be a part of the cost of inputs, and the final price quoted by the seller would be a tax-inclusive price. The tax due at any stage is computed by using a formula as shown in Table A1.

AT ca cted a ence ween

d the tax inputs. thod o and VAT is redit me

input tax credit method. s


Table A1 Computing VAT by Two Methods with a Uniform Tax Rate of 10 percent

Raw Materials Supplier Manufacturer Wholesaler Retailer Total

Economy The Economy Purchases --- 100 350 850 ---

Value Added 100 250 500 250 1100 Sales 100 350 850 1100 --- Input tax credit method

i. Sales 100 350 ii. Taxes collected 10 35

850 1100 2400 85 110 240

iii. Purchases 0 100 350 850 1100 iv. Taxes paid 0 10 35 85 130

VAT (ii - iv) 10 25 50 25 110 Price of the good = 100 + 10 = 350 + 35 = 850 + 85 = 1100 + 110

(i + ii) = 110 = 385 = 935 = 1210 Subtraction method

i. Sales 110 385 935 1210 ii. Purchases --- 110 385 935

Calculation of tax due )1.1(

1.)0110( ×−=

)1.1(1.)110385( ×−

=)1.1(

1.)385935( ×−=

)1.1(1.)9351210( ×−

=

Tax Due 10 25 50 25 110

Table A2 Wholesaling Stage is Subject to a 15 percent tax, and Rest to a 10 percent Tax

Raw Materials Supplier Manufacturer Wholesaler Retailer Total

Economy Ef

Ratfective e of Tax

The Economy Purchases --- 100 350 850 ---

Value Added 100 250 500 250 1100 100 350 1100 -

100 1100 2400 10 35 110 240

iii. Purchases 0 100 350 850 1100 iv. Taxes paid 0 10 127.5 130 AT (ii - iv) 10 25 -17.5 110 10% ubtraction method i. Sales 110 960 1235

--- 110 385 960 C

Sales 850 --Input tax credit method

i. Sales 350 850 ii. Taxes collected 127.5

35 VS

92.5

385 ii. Purchases alculation of tax

due )1.1(1.

= )0110( ×−)1.1(

1.)110385( ×−=

1.)385960( ×−)1.1(

1.)9351235( ×−=

)1.1(

75 25 135 12.3%

=

Tax Due 10 25

Ex

ting. Exemption usually

desirable under VAT as they break the input tax credit chain. If this commodity re-enters the problem of cascading reappears.

emptions and Zero Rating Under VAT, a distinction is made between exemption and zero rameans exemption from tax on the value added of a commodity at a particular stage of production or distribution. If full exemption is desired, there should be zero rating of the commodity concerned. That is, a rate of zero should be imposed on the commodity against which rebate should be given for input taxes. This is a particularly useful tool for exports. In order to maintain the international competitiveness of a commodity, exports out of a tax jurisdiction can be relieved of all domestic taxes through zero rating. Exemptions are not

production process as an input for a taxable commodity, the


Also exemption from tax at one point does not mean total exemption because taxes on inputs at the earlier stages will remain embedded, leading to loss of transparency. Thus, an exemption oes not imply a zero effective tax rate on the commodity. Exemptions should be kept to the

ts. A VAT on gross income would therefore treat both consumption and capital formation as final

s of the good; hence capital goods purchased by the dealer would not be treated as inputs. put tax credit will not be available on taxes paid on capital goods.

= gros

xtent attributable to depreciation of capital goods, in any given year.

f the economy. A tax on income for instance, could alter consumer ecisions in favour of present consumption, because it implies double taxation of savings19.

dminimum.

Choosing a Base for VAT There are three possible variants of VAT, depending upon what macroaggregate the government wants to tax: gross income, net income- or consumption. In terms of the macro-aggregates, Gross Product = consumption + gross capital formation = gross value of output – all current inpu useIn Net Income = consumption + gross capital formation － depreciation s income – depreciation = gross value of output – all current inputs － depreciation. A VAT on net income would therefore give credit for tax paid on current inputs and tax paid on capital goods to the eUnder the ITC method, this implies that the credit for tax on capital goods will be spread over the life of the capital good. The consumption type VAT goes a step further in that only final consumption is treated as the final use of a good; full credit, therefore, is given for taxes paid on capital goods as well, in the year of purchase. Consumption = gross value of output – current inputs － gross capital formation Table A3 illustrates the calculation of VAT with three alternative bases. A tax on production or on income potentially distorts and discourages investment decisions, affecting the growth od

19 Savings are taxed at the time of saving and again the income from savings is taxed.


Table A3 Comparison of VAT on Alternative Bases tion of V Consump AT at 10% of Out

Rs) ption

(Rs) Income Type (Rs) Gross Type (Rs

Value put Consum(

Type Product )

Intermediate inputs Output 200 20 20 20

al goods 150 15 15 15 100 -10 -10 -10

5 5 5 oods

300 30 30 30 100 -10 -10 -10

50 -15 -1 Tax 5 18 20

30 43.5 45 sumption 300

435 450

CapitOutput Input Tax Paid Consumption gOutput Input Capital 1 .5

paid .5 Tax collection Total conTotal income Total production

Note: This example takes the case of a simple economy with three producers producing consumption goods, ate inputs, and capita ods, respective Both consumption goods and c al goods ire

termediate goods for production. Further, capital goods are used for producing consumption goods. It is intermediate goods do not use any inputs.

Hence, some econom a gres consum How e i difficult to minister a progressive personal consumption tax, and indirect

n tax is pref along with income tax he consumpt ax coul ade pect to consumption but tends to become regressive with respect to income.

Therefore, if there exists a direct income tax, better calibrated to the abilit pay, a V f the c type at a sin be preferable, as the general practice the world

l consumption is to be taxed in a national VAT imports and exports20, the base of ctively by estic: output + imports－－current inputs－capital goods

gross investment).

n Assessment of VAT in Comparison to a Cascading Sales Tax s overcome problems we encounter in cascading types of sales

intermedi l go ly. apit requinassumed that

ists favour personal pro sive tax on ption. ever, sinc t

is extremely adconsumptio erred an . T ion t d be mprogressive with res

y to AT oonsumption gle rate is found to

over illustrates. If tota with

the tax will effe(i.e.

dom exports

A VAT by the ITC method helptax. In addition to being a transparent tax, VAT by the ITC method has several advantages which are discussed below:

1. Deriving from the fact that VAT by the ITC method permits easy and effective targeting of tax rates, exports can be zero rated, i.e. goods being exported out of the jurisdiction can be given complete refund of taxes paid at the earlier stages. In the ITC method, this implies that only the tax paid at the penultimate stage needs to be refunded to the

20 The base for a state VAT would be similar except for direct import of consumer goods by a consumer as

according to the Indian Constitution, the state cannot levy a tax on such imports.


exporting dealer. 2. Since VAT does away with cascading, it avoids distorting business decisions; the need for

vertical integration is dictated only by the market forces or technical considerations, and not by the tax structure.

3. Since all stages of production and distribution and subject to tax, this form of taxing avoids the problem of undervaluing, without introducing cascading.

a set-off for taxes paid at the earlier stages, these are not treated as

oo, is curtailed. trail of invoices, is argued to be a

ystem th t encour seeks an invoice to get input tax

stable than income, VAT

AT and etail Sa

true retail sales tax has the same merit. Since it is a atx levied at

ities. That is why it has been argued that VAT and the retail sales tax are

rmer is preferable on

tail eller). There is correspondingly greater tendency for evasion. Under VAT, generally, only a

small part of the tax is to be collected from the dealers at the lower end of the chain. The administration needs to concentrate attention mainly on the larger dealers 21 . This is administratively easier. Further, since the tax is collected in installments under VAT, there is

4. Since the dealer getspart of costs and this is expected to reduce that component of cost as well as the associated financing requirements. Further, the problem of enhanced cascading via the mark-up rule, t

In addition, the input tax credit method, by generating a s a ages better compliance since the purchaser credit. Further, this trail of invoices supports effective audit and enforcement strategies. From the point of view of the state, another interesting feature of VAT is its stability as a source of revenue. Owing to the fact that consumption is moreprovides a very stable source of revenue.

V R les Tax: A Comparison It has been shown that VAT is a form of consumption tax which does not in any way cause changes in productive activities either in terms of allocation of resources or in terms of costs. Therefore, VAT is a method of reaching consumption without affecting productive activities. It is well acknowledged that athe end of the chain of all production transactions and is collected from the final users, it does not cause any alterations and is collected from the final users, it does not cause any alterations in productive activeconomically equivalent. While VAT and the retail sales tax are economically equivalent, the foadministrative grounds. In both cases, all dealers with turnover above the stipulated threshold will have to register and file returns (This is true of the first point tax also). However, in the case of the retail sales tax, the entire tax is to be paid by the last registered dealer (the res

21 Of course in terms of choosing a sample for checking, dealers could also be chosen on the basis of other criteria,

such as, large input tax credit.


greater possibility of crosschecking. The state governments i tates of les tax. With a moderate rate – generally a sing te of 7 – the een s s. They to do so because the most i ilers there are larg zed and are in organized sec Moreover, m sales to customers are put through cash registers and the taxes are rout collected by cash counter salespersons. In such circumstances, the eration of a retail sales tax is feasible. However, there is dissatisfaction in the USA abo e retail sales tax now in regard to both a ation and cascading (b se producers a buy from dep ental stores). India, on the other h e retail lev poor and it be advisable to try t entire tax at that le .

more complicated than a simple cascading first point tax. The taxpayer has to keep accounts

s, purchase vouchers have to be preserved for being checked, if considered

old will pay tax, in a way VAT is also a very simple tax to administer nd to comply with. It may also be noted that the number of dealers who have to register and

point tax, and VAT. The

d that the introduction of VAT would cause some inflation. This

n the United S Americle ra

a levy what may be called a retail say have b to 11 percent

uccessfully operating their sales taxe have been ablemportant reta e si the tor. ost

inely theop

ut thdministr ecau lso artm In

and, account keeping at th el is would not o collect the vel22

Some Arguments Against VAT The introduction of VAT has sometimes been opposed on the following grounds. First, VAT

isnot only of sales but also of purchases and taxes paid on those purchases. Since the tax liability will be based not merely on the value of the total turnover but also on the tax paid on the inputs, there is more administrative work involved. Thus, it is argued that for both taxpayers and administrators VAT is a more difficult tax to operate. Strictly speaking, it is not true that under first point tax purchase vouchers need not be maintained or checked. Since the tax administrators have to verify in the case of a reseller that the dealer concerned has paid tax on his purchasenecessary. However, it is true that more account keeping is needed under VAT. As against this, since there will be only a few rates at the most and very few exemptions, and because all dealers above the threshasubmit returns will be the same under the first point tax, the lastdifference, of course, is that under VAT all registered dealers except those zero rated will be paying some tax.

Second, it has been argueargument has been used particularly in countries where there was no general sales tax but only a few excises. In countries such as India, where sales taxes covering a wide range of commodities already exist, replacement of those taxes by a revenue neutral value added tax 22 We do note that three states in the country, Delhi, Punjab, and Haryana, still rely mainly on last point tax.

However, Delhi and Haryana, finding it difficult to implement, have shifted a number of goods to the first point. The implementation of last point taxes has required the use of a considerable volume of statutory forms, too, making it a tedious tax to administer or comply with.


should lead to no inflationary consequences23. In fact, with a reduction in the extent of

ces cannot be attributed to VAT.

proportional tax on

med by the richer sections of society. Also, what is

e than

cascading there should indeed be a fall in prices. Of course, if the government is deliberately using VAT as a means of raising more revenue in a rational manner, there will be some increase in prices, but then the rise in pri

Third, VAT has been criticized as a regressive tax. As pointed out earlier, a full-fledged VAT levied at a single rate with no exemptions will be equivalent to a consumption (capital goods being exempt). However, like all consumption taxes, VAT will be regressive with respect to income insofar as consumption falls as a proportion of income as income rises. This regressivity could be mitigated to some extent by having excises at higher rates on a few goods largely consuimportant is the characteristic or impact of the total tax system. As has been argued earlier, if at least a moderately progressive income tax with a reasonably high exemption level is in place, the system as a whole will be a progressive one. In any case, VAT is no more regressivany other general tax on commodities an dservices.

elhi: Gayatri Publications, 1993, pp.21-30.

23 This is supported by empirical studies, Purohit, M.C., ‘Principles and Practices of Value Added Tax: Lessonsfrom Developing Countries’, D


Appendix 2 National Consumption Tax (VAT)

at 5% on value added bases of all domestic transactions nd imports, except tax exempt items in medicare, welfare and education related expenditures.

as low as 30 million yen per annum. The primary goal in sh

As of April 1989, consumption tax at the national level (3%) was introduced. In May 1992, the consumption tax law was mended by the Diet in enlarging the scope of tax exempt items and in revision of the relief provision to small traders. In April 1997, the national consumption tax was raised to 5% (including the local consumption tax 1%, see Appendix III below) in exchange of reduction in individual income tax.

The basic Framework Consumption tax (VAT) is imposedaThe exemption level for firms is

aping the consumption tax is to make the tax base as broad as possible but with a single tax rate (one rate plus a zero rate on exports). Consumption tax is paid at each stage (see Table 2A.1 below). In order to avoid multiple taxation and to compute a firm’s VAT, total purchases are subtracted from total sales by using its book-keeping records. The balance by subtraction is then subject to the rate of VAT. The consumption tax was designed with the accounts method, without use of invoices24. Firms whose annual sales are less than 400 million yen are allowed to employ the tax credit method to enhance tax compliance. Instead of directly calculating the total value of purchases from other firms, certain fixed percentages (i.e. 10% for wholesalers and 20% for other traders) are multiplied by total sales values and the results deemed to be subject to a 5% rate. The vanishing exemption method is introduced to give the relief provision to small traders. Those whose annual sales do not exceed the maximum limit of 50 million yen above the exemption level of 30 million yen can benefit from this method in terms of tax credit. The calculation is made as follows:

Tax credit = due otherwisetax million 30

sales annual -million × 50

24 Invoices admit the use of the tax-credit method, universally preferred in all VAT countries. If invoices are

compulsory, the sum of the taxes already paid by other firms on purchases by the firm in question can be traced. Each invoice for a purchase from another firm indicates the total amount of an input tax. Firms collect all such invoices during each period (three months or one year) and aggregate the input tax shown on them. This is the amount credited against the firm’s own gross tax in order to calculate VAT payable by the firm (Ishi (1993) pp.324-5).


Table A.1 System of Consumption Tax (5%)

Raw Material Producer

Sales 20,000

VAT 1,000

Tax Paid 1,000

Final Product Producer

Sales 50,000 VAT

2,500 (2)

Input 21,000

VAT included in Input1,000 (1)

Tax Paid (2)-(1) 1,500

Wholesaler

Sales 70,000 VAT

3,500 (3)

Input 52,500


Tax Paid (3)-(2) 1,000

Retailer 100,000 VAT

5,000 (4)

Input 73,500


Tax Paid (4)-(3) 1,500

Sales

Consumer Total payment 105,000 Total Tax Paid

5,000


Appendix 3 Local Consumption Tax As of April 1, 1997, consumption tax rate is increased to 5% of which 1% of local consumption tax is included. In this lecture, I would like to explain the basic framework of local consumption tax in Japan. Framework

(1) The Base: Domestic transaction; net of consumption tax of pervious transactions. saction; tax exempt for exports, tax on imports.

(2) The Rate:

local governments, according to the amount of

umer

International tran

As the national consumption tax is 4%, the local consumption tax is 1%, in sum, total consumption tax is 5% of consumption.

(3) Domestic transaction is handled by the branches of tax administration, while inter-national transaction is handled by the custom office.

(4) Final payment is made among consumption.

(5) Prefectual government transfer a half of tax to regional (city, town, village) officies, according to the amount of consumption of that region.

Example (1)

Osaka Sales ¥50,000 Tokyo Sales

¥70,000 Kanagawa Sales ¥100,000 Kanagawa

Producers Consumption

Tax 4% Wholesalers Consumption

Tax 4% Retailers Consumption

Tax 4% C¥2,000 ¥2,800 ¥4,000

ons

¥2,000 ¥500 Local consumption tax 1% ¥500

¥800 ¥200(2800-2000) (700-500)

Local consumption tax 1% ¥700

¥1,200 ¥300 (4000-2800) (1000-700)

Local consumption tax 1% ¥1,000

Branch Office of Tax Bureau

¥2,000

Branch Office of Ta

¥800 Branch Office ¥4,000 National

x Bureau of Tax Bureau Consumption Tax

¥500 ¥200 ¥300

Osaka Prefecuture Government

Tokyo

Metro olitan Government

Kanagawa

ure Go rnment

(¥1,000) p Prefectve

¥500

¥200


Difficulties

(1) by producers, wholesalers, and retailers are made in various prefectures, consumers a in their prefectu

(cross prefectural transactions must be adjusted exactly the same way as cross border international transaction ents)

ly how? N nsumption can as clearly as in Example (1). estimate consu follow

Example (2)

A pref. ef.

Value added while final re located re.

adjustm� PracticalWe must

ot all co be tracedm asption s in Example (2).

B pr C p D pref. ref. Total

Retail Sales 1,700 250 1, 700 3,900

250

Service Sales 800 200 6 450 50 2,100

6,000

Population 42 12 24 32 100

re-distribute 382 109 291 218 1,000

(6,000x1/6)

Workers 25 5 19 11 60

re-distribute 417 83 317 183 1,000

(6,000x1/6) Estimated Consumption

(share %)

3,299 (41.2%)

642 (8.0%)

2,508 (31.4%)

1,551 (19.4%) 8,000

What does Example (2) do? Available official statistics are “commercial statistics” (shows retail sales) and “service statistics”(shows service sales). Two statistics account 3/4 of total consumption of each prefectures. So we need to make up 1/4 of consumption. Two candidates: residence (population) and workers. 1) Retail sales plus service sales must be 3/4 of total consumption. 2) 1/8 of total consumption must be distributed according to population (or 1/6 of 1)). 3) 1/8 of total consumption must be distributed according workers (or 1/6 of 1)). 1) + 2) + 3) makes up total consumption.


(2) All prefectures employ the destination principle levies the VAT on all goods and services destined for final consumption in their prefectures.

tment is needed as shown in Example (1).

concentration of local tax revenue for selected prefectures can be avoided.

requires, a simple administration (no additional administration costs). (3)

But in each transaction, consumption (VAT) tax is levied in different prefectures, so that cross prefectural adjus

(3) As consumption activities are diversified (compared with production activities),

Merits

(1) An increase in local government autonomy. (2) A simple tax

A cost-benefit (burden-benefit) relationship becomes clearer (transparent).


Exercises

n. Indicate the conditions under whi(Ra

3. [HiFor

1. Discuss pros and cons of flat tax on consumption. 2. Discuss pros and cons of Ramsey tax rule on consumptio

ch the flat tax is Ramsey optimal and under which the simple inverse elasticity msey) rule applies. ndriks and Myles (2006) Chapter 14, Exercises 14.1] the linear demand function bpax −= calculate the deadweight loss of introducing a

com odity tax t when the marginal cost of production is constant at c. How is the ht loss affected by changes in a and b? How does a change in b affect the

elasticity of dem he equil ithout t4. [Hindriks and Myles (2006) Chapter 14, Exercises 14.2]

inear de function

mdeadweig

and at t ibrium w axation?

For the l mand bpx a −=

price. What

calculate the deadweig ss of uci

at the and functio by and uppl n by . Find the equilibrium is n the equilibrium price of the tion of a tax if

ht lo introd ng a dp ε−

the effect ox = the s y functioAssume th

s

dem n is givenpy ε=

introduc t 10/1= 2/1== sd εε ? nce of the tax is

tween consumers and suppliers. . driks and Myles (2006) Chapter 14, Exercises

y with a single consumer whose preferences are given by , where

Describe how the incide

divided be[Hin5 14.5] Consider an economU = lx −)log( x is consumption and labor supply me that the

on good oduced using labor alone w onstant-ret to-scale t gy. f measurement are chosen so that the producer prices of both the consu

ge r ual to 1.he c budget constraint be

l . Assu

consumptiUnits

is pr ith a c urns- echnolo o

and the wamption good

atonsumer’s

e are eq a. Let t lqx = , where th r price is e consume tq +=1 ,

mand function and

and is the commodity tax. By maxi ng utility, find the de

b.

c. as

t mizi

the labor supply function. Assume the revenue requirement of the government is 1/10 of a unit of labor. Draw the production possibilities for the economy and the consumer’s offer curve. By using the offer curve and the production possibilities, show that the optimal allocation with commodity taxation h and 1=l10/9=x .

6. [Hi ises 14.8] An economy has a single consumption good produced using labor and a single consumer. The production process has decreasing returns to scale. Explain the derivation of the

d. Calculate the optimal commodity tax. e. By deriving the first-best allocation, show that the commodity tax optimum is

second-best. ndriks and Myles (2006) Chapter 14, Exerc


optimal commodity tax when profit is not taxed. 7. [Hindriks and Myles (2006) Chapter 14, Exercises 14.9]

Consider the utility function lxxU −+= )log()log( 21 βα and budget constraint

2211 xqxq += . wl

a. Show that the price elasticity of demand for both commodities is equal to –1. b. Setting producer prices at 121 == pp , show that the inverse elasticity rule implies

2121 qqtt = . Letting and 100=w 1=+ βα , calculate the tax rates required to achieve revenue of c.

10=R .

8. [Hindriks and Myles (2006) Chapter 14, Exercises 14.10]

Let the consumer have the utility function lxxU pp −+= 2121 , 211 xqxqwl += 2

[ ] [ ]21/1

2

22

p

qwp

x−

⎥⎦

⎤⎢⎣

⎡= a. Show that the utility maximizing demands are

11/1

1

11

p

qwp

x−

⎥⎦

⎤⎢⎣

⎡= and

b. Letting 121 == pp , use the inverse elasticity rule to show that the optimal tax rates

are related by 12

1

2

12

2

111

11

tpp

ppp

t ⎥⎦

⎤⎢⎣

⎡−−

+⎥⎦

⎤⎢⎣

⎡−−

= .

c. Setting , and 100=w , 75.01 =p 5.02 =p , find the tax rates required to achieve

revenue of 5 and .0=R 10=R .

d. Calculate the proportional reduction in demand for the two goods comparing the no-tax position with the position after imposition of the optimal taxes for both revenue levels. Comment on the results.

9. [Hindriks and Myles (2006) Chapter 14, Exercises 14.12] Consider an economy with a single consumer whose preferences are given by

, where and are the consumption levels of goods 1 and 2

me that both goods are produced using labor alone, subject to a

constant-returns-to-scale technology. Units of measurement are chosen so that the producer prices of both goods and the wage rate are equal to 1. a. Using to denote the consumer’s endowment of time and to denote leisure,

explain the budget constraint

lxxU −+= )log()log( 21

and l is leisure. Assu1x 2x

L lwLwlxqxq =++ 2211 .

b. Show that the consumer’s demands satisfy the conditions required for the inverse elasticity rule to apply.

c. Use the inverse elasticity rule to conclude that both goods should be subject to the same level of tax.

d. Calculate the tax required to obtain a level of revenue of 1=R . e. Show that the commodity taxes are second-best.

10. [Hindriks and Myles (2006) Chapter 14, Exercises 14.15]


3,2,1=k(1 xgx

(Ramsey rule) Consider a three-good economy ( ) in which every consumer has preferences represented by the utility function )() 32 xhU ++= , where the functions

that each good is produced )(⋅g and )(⋅h are increasing and strictly concave. Suppose

with constant returns to scale from good 1, using one unit of good 1 per unit of good 1≠k . Let good 1 be the numéraire, and normalize the price of good 1 to equal 1. Let kt denote the (specific) commodit

y tax on good . k so that the consumer price is )kt1(kq +=

a. Consider two commodity tax schemes ,,( 21 ttt and )3t )',','(' 321 tttt == . Show

r that if ]1[1 'kk tt +=+ φ fo 3,2,1=k for some scalar 0>φ , then the two tax

schemes raise the same amount of tax revenue. b. Argue from part a that the government can without cost restrict tax schemes to leave

one good untaxed. Rc. Set 01 =t , and suppose that the government must raise revenue of . What are the

at minimid. Show that the optimal taxes are inversely proportional to the elasticity of the demand

e. When should both goods be taxed equally? Which good should be taxed more? 11. [Hindriks and M

tax rates on goods 2 and 3 th ze the welfare loss from taxation?

for each good. Discuss this tax rule.

yles (2006) Chapter 14, Exercises 14.16] Consider a three-good economy ( 3,2,1=k )

1x

in which every consumer has preferences represented by the utility function U , where the functions is

s produced with constan rns

)(⋅g

t retu

),( 32 xxg+=

increasing and strictly concave. Suppose that each good ito scale from good 1, using one unit of good 1 per unit of good 1≠k . Let good 1 be the

d normalize the price of good 1 to equal 1. Let kt denote the (specific) commodity tax on good k so that the consumer price is kk tq

numéraire, an+=1 . Suppose that a tax

change is restricted to only good 2 so that Δ+= 2'2 tt with 0>Δ .

a. What is the correct measure of the welfare loss arising from this tax increase if ?

ct welfare

he incidence of a commodity tax under different

household receives labor income for its labor supply and profit

03 =t

b. Show that if 03 >t , then the measure of welfare loss in part a overestimates the

welfare loss if good 3 is a substitute for good 2. What is then the correct measure of the welfare change?

c. Show that if 03 >t , then the measure of welfare loss in part a underestimates the

welfare loss if good 3 is a complement for good 2. What is the correchange?

12. [Hindriks and Myles (2006) Chapter 14, Exercises 14.17] The purpose of this exercise is to contrast tmarket structures. Consider an economy with identical households and identical firms. The representative l

income π for its ownership of the firm. The utility function of the household is


lxU −= 2 . The firm produces one unit of final consumption good x with one unit of labor input. Labor is the numéraire good: the price of labor is normalized to 1, and labor is the untaxed good. The producer price is p and the consumer price is tpq +=

nd for good

, where

timization program treatingconsumer prices in the budget constraint as fixed. Find the dema

0>t is the (specific) commodity tax.

a. Describe the household’s op profit income and the x as a

sSuppose t s act in unison like a monopolist. Find of the

price charged b he monopolist? What is ducer and the

Suppose that the firms act independentl maximizing their own pr ices as ucer price? What is th the tax

pare with the result in part d. 13. indriks and Myles (2006) Chapter 14, Exercises 14.18]

co

function of consumer price q .

b. Calculate the elasticity of the lope of the inverse demand function. hat the firmc.

d.

e.

[H

the

co

e divisio

supply

the producer price?nsumer?

ofit-taking prn of

monopoly as a function of t .

What is the equilibrium y t

yWhat is the division of the tax burden between the pro

given. What is the equilibrium prodburden between producer and consumer? Com

Consider an e nomy with two representative households ( 2,1=h ) that supply labor hl to

(with 41 =l and the one representative firm and buy a consumption good La

) and in y The utilit function is the firm

hx . production. T

produces one unit

bor supplh

y isere is no

of

inelastic disutilit22 =l

yperfectly substitutable

, and of labor. hxU = x with one unit of labor. Labor is the numéraire good with its price normalized to 1. The producer

price of x is p . The government can Ievy indivi mod ood ity tax ht on dualized com gx . Thus the consumer price facing household h is hh tpq += . There is no revenue

requirement so 02211 =+= xtxtR . a. What is the equilibrium producer price? b. What is the demand for good x as a function of the tax rate for ea

price of the consump .

ch household?

c. Use the demand function to express the utility of each household as a function of the tion good

d. how that government budget balance implies that the taxes are related by S

132 11

2 +−= ttt . e. Use the budget balance condition in part d to find the tax ra zing the tes maximi

Rawlsian social welfare function { }21 ,min UUW = . f. Why individualized commodit pry taxes are not used in actice?


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