Competitive tax theory in open economies

Journal

of Pubhc Economics

Competitive economies Constrained

48 (1992)

361-375.

North-Holland

tax theory inefficiency

in open

and a Pigovian

remedy

R. Krelove*

Received February

19XY. revised version received hlarch

IYY I

In an economy wth multiple governments. each is constrained to raise revenue for public expenditures ustnp dastortwnary tares on a directly mobile tax base. A povcrnment is said to bc competitive if the IOLII CO~I of IIS decisions, including the excess hurden. is perceived to be mternalired. The competitive euullibrium allocations are not constrained eflicient in wncral: there is another ce~ ,;f dlxtortickry t;lnes and associated public expenditures for which alI individuals in the wrnomy are better OIT. II is shown that the source of the Llilure can be intcrpretcd as a m~s~np market. and the l’orm of the hesl decentralwcd remedy is derived.

1. Introduction In

this

paper

economics straincd t3xcs *

arc to

on

intcrtanporal firms

within

costs to

(and

bc

I invcstigatc linkd

raise

rcvcnuc

;I directly moclcl its

bcnclits) that

an economy

trade for

mohilc whcrc

borders.

intcrnalizcd.

conditions,

by

in public tax

govcrnmcnts

arc

taxes

is said

govcrnmcnts whcrc

employing

Specifically

including

compctitivc

goods,

cxpcnditurcs

base.

A govcrnmcnt

multiple

and

each jurisdiction

of its decisions. The

with

factors

net-of-tax

price

;I

simple by

if the total

the cxccss burden, rcquircs,

con-

cmploycd

to bc competitive

assumption

is

distortionary

I consider the capital

whose

each

is pcrccivcd among

tukcrs

for

other traded

C‘r~rrespo~nlo~~,~, IO: R. Krelove. Smlon Fraser University, Burnahy. I&C. VSA IS6. Canxlx *I am grateful to two anonymous referees , ~1s well as seminar participants ;II the University of Toronto and Quwn’s University at Kingston for helpful comments and suggestions. An e:Irlicr version ws presented ;II the North American Summer Meetings of the Econometrw Society and appeared as University of Toronto Discussion Pap no. 881X. Wildasin (IYXY) has independently investigated the Jcs~gn of mterventions in a related model; he amrlyses the ekes of 3 subsidy tu 13x rate incrs;tses (abstracting from the issue of tin;mcing the subsidy program). Such il subsidy is not the bcs~ intervention in the tarpang sense. The views in this paper are mine. They do not neccswrily reflect the ofliwl position\ of the Intsrncltwnal Monetary Fund. 0047 -2727,YZ SM.00

I’

IYYZ --lilscvier

Science Publishers I$.V. All rights reserved

commodities.’ In this context 1 mean to show two things. After the model and the equilibrium in section 2. I show first in section competitive

equilibria

counter-intuitive

are not constrained

ellicient

in general.’ This

describing 3 that the result

is

to some extent, since there is no obvious marginal incentive

problem. Analogizing to the fundamental theorem of welfare economics. the assumption that the burden of a tax, including the excess burden. is internalized

by a jurisdiction

taking

world

prices as fixed

appears to be

exactly what is needed to provide the correct marginal incentive to each government to make the appropriate second-best tradeoffs. This intuition breaks down. however, because governments’ decisions together affect world prices, and these prices, through alter the possibilities government

budgets.

their effect on private maximizing

for transferring Competitive

behavior.

resources between private budgets and communities

ignore

these

additional

transfer possibilities in their decisions. One way to intcrprct the failure is that traded goods prices do not provide :I sufficient competitive

set of signals to coordinate the decisions of independent govcrnmcnts. and the second thing I do is ask what would constitute ;I just-sufkicnt set of signals. This question is taken up in section 4. where it is shown that at ~1constrained eflkicnt allocntion :L tcrm cmcrgcs that

can

be intcrprctcd as the shadow value of (traded) capital ;IS tax base to

the economy.

is then argued that the best remedy that prcsorvcs the involves pricing govcrnmcnts net ‘consumption’ of the tas base. With lhis remedy thcrc arises ;I corrcspondcncc ~C~WL'CII antI not (ncccssarconipctitivc equilibria ;IIKI constrained cfkicnt :Illoc;itions. dc~cntrali/ation

It

of decisions

ily) with full efficiency: there remains the cfficicncy loss that is ;I consequence of the fact that revenue must be raised with distortionary

taxes. hvc been conccrncd with Many rcscarchcrs’ in local public finance characterizing oulc0nics in environments where jurisdictions tax mobile commodities. The prcscnt paper represents a11 improvement over these results clearly

in several respects. k’irst. the compctitivc case has not itlwitys been where distinguished from various noncompetitive environments

governments

have opportunities

to mulct

lhs

foreigner,

with the result

that

‘An alloca[ion arwciatcd with ;L WI of (di\rortion;lry) I:II ralrs is non constrainsd eflicien~ if thcrc cxisrs anolher WI of pax r;Iks and aswciakd ullocrwn under which all individuals arc hctrcr off. ‘For cxxmplc. Gordon ( 19X.1). 0a1cs and Schwab ( IYX)o. Srarrell (19X0). WildaGn (IYXY). Wilson ( IYM). and %drow and M~csAowsk~ ( I9Xb).

sources

of failure

common

in

leading

to

failure.5,b

an

been confounded.’

literature

obscure

incomplete

Third,

environments

2. The

have

the

the

understanding

problem

There

are

J

I~j(_u,j..~2j.,~j).

j.

Each

nature

assumptions

of

and

of interventions

the

problem,

extent

of

for

the

competitive

systematically.

are

1,

in

first

price of savings,

amount

kj in

marginal

product Assume

Communities good to

in

that

I in cxh producer

comtnunity

provide

Then

the consumer mcjhility produced

from

I and

function

xii.

or

lend

in community

l;(kj)

in

that

the

the

it

at

second

period.

and diminishing.

marginal

an

j borrow

product

an The

J’;
costless

mobility

the

of

capital

producer

price

and

of

of

the

the

private

lirm hohitvior in j is charoctsrizctl by the l,/;(k) --q/i!. cxh j. whcrc q, is the known, in j. I.ot n,(q,) = IllilXk (/i(k)

tlcnotc

-q,ki

in ,j. is ;I govcrnmcnt

public

good.

in period producer

price of capital

assumption. 1 when

labeled

utility

Then

there the

the

economy,

jrcro.

the

price of capital

can commit

community.

periods.

firms

,/‘;. is positive, and

NorIn;Ilix

value of prolit

community to

by

period.

pilraIllclriC

cxh

the

oj; for simplicity

intertemporal

consumption

output

approaches

period.

k 10 maririiix

rcvcnuc

for

denoted

link4

each

the

r. Private

j;(O) =0

input

choice of

the Inxsiniizcd

period

denoted

of capital.

;Irc

good and two

by

I to produce

also

Iarpc as the capital private

is one private

in

population,

in its arguments. The resident of j can either use his

the

period

communities)

has a fixed

representable

after-tax

each j.

(equivalently.

community

increasing

endowment

period

aspects

the

of the design

jurisdictions

indexed

Preferences

In

of

has not yet been addressed

assume II~= I. all j. There

good

simplifying

important

model and the competitive tas equilibrium

usually _. 7

Second,

some

It

that

I to ;I unit

price

Icvics

is ilSSllIllCd

in j is given

across

communities

If f, is the t:Ix rate, the community

the capital

input

of domestic

the private

consumplion

good

taxes

and

simplicity

tax, I,. on capital

of capital

is cclu;Ili/.cd

for

firms

raises

is k,. The

in period

uses

the

that

the

input

in the

by q, = r + tj.

as

because of the rcvcnuc public

r,k,

in

good

is

2 at a constant.

unit,

364

marginal

rate of transformation;

community

j’s

budget constraint

given by the inequality gjsr,kj+ ~~~ where T, is a lump-sum community j (which equals zero at the equilibrium). Each

community

is

assumed

to

be competitive.

in

is then

transfer

the sense that

perceives that the total costs and benefits of its decisions are internalized.

to it To

make this operational, I make three assumptions. First, each community takes the global consumer price of capital, r, as fixed. independent of its own actions. Thus elastic supply

the community believes that private firms face a perfectly of capital at the prevailing net-of-tax return. Second. the

community government is benevolent in this its objective is the maximization of the level of utility of its residents. Third, since it is supposed that the government takes account of the effect of its decisions on n,(.), it is assumed that this surplus accrues entirely to the domestic residents. There are several equivalent

institutional

structures

to rationalize

this

last

assumption;

for

example, it can be assumed that the domestic firms are owned internally. Equivalently. it can be assumed that there is some fixed factor in each community.

owned by the resident. that is the recipient of the surplus.’

Private consumer private consumption

behavior in j is dcscribcd by the choice of lcvcls of in the bud@ sot to maximize utility, given prices and

govcrnmcnt choices.’ Dcnotc the maximized

lcvcl of utility

by v,(I,.,~,: r. HI,);

that is. (ir,(.\.,,sL,,~,):r.~,

r~,(lj,g,;r,rti,)~rll;Ix

+.~,~r!‘j+rr,(r+f,)+ttl,).

(1)

I I.I 1 whcrc ni, rcprcscnts period-_7 lunlp-SUIII out

the analysis).

Let

period- I consumption function. With thcsc equilibrium

s,,(r,

incomc (which equals zero throughfunction for rcproscnt the demand Ict s,(.) -r’j-.\:,,( .) rcprcscnt j’s saving

.qi, I,, m,)

in j, and assumptions

wc arc

in

a position

Ik/i’riifioti.

A

rcprcscnling

cottfpditii~c

an allocation

C,SIj+Cjkj=Cj).‘j;

and, for each j, (b) (r,,,

dsfinc

the

rus c*c/lri/ihriirrtl (CTli) is a list (.u, j, x2, kj. s,), for the cconoiny, a list of capital tax rates (r,),,

and a price r, such that (a)

to

concept, called a campctitivc tax equilibrium.

.x2,) solves max,,~,x, ( ~c,(.u,,.u,;~,):r.u,+s~$r?.,+n,(r+r,)+rri~);

365

(c) (rj.gj) solves max t.p rj( t. g; r, mj) subject (i) gstkj+sj

to

and

(ii) kj solves max, (f,(k)-(r+t)ki. Capital market equilibrium is imposed implicitly through condition (a) of the definition. It is an implication of the conditions (b) and (c) that material balance in (produced) second-period consumption is satisfied. and so does not need to be entered explicitly. Note that each community takes r as parametric in its program given by condition (c).~ Consider the choice problem for some community j. Associate the multiplier ~~20 with constraint (i) above. Assuming enough differentiability and that the community’s conditions

problem is sufficiently

are given by the constraints

tj=$/‘;

well behaved, the first-order

and by”

( 1 “ri_i’j

,

i'j

whcrc urj rcprcscrits the maryinal utility of second-period consumption (irzj= I’,~ and tfUj= 11~~). The term i.J14~, is j’s pcrccivcd social marginal utility of govcrnmcnt rcvcnuc. norm:l~iizcd by the social marginal utility of private incomc. Obviously 7j/~~tjg I always at the CTE. From (3). ;),/u2,> I for positive tax rates. [Then from (2) the marginal rate of substitution bctwccn the public pooJ and period-2 consumption is greater than the marginal rate of tr;lnsk)rmatiorl (which cclu;~ls I).] A ncccssary and suflicicnt condition for ~hc constrained

incff&ncy

result

of the next section

is that

this

strict

incqu;tlity holds for some j at the CTE, i.c. that the pcrceivcd marginal dcadwcight loss of the capital tax, (yj- uzj)/uzj as usually dctincd, is positive. That this is ;I gcncral characteristic of the equilibrium follows from the rcstrictcd possibilities in the model for transferring resources bctwccn the private

budget constraint

and

the govsrnmcnt

bud@”

It

is assumed

“It is being assumrd that the community has good knowltxlg:e of prefercnccs to bc used for some decisions but not fur othrrs; in parlicular the knowledge of prcfcrenccs is nol used IO levy (oprimal) lump-sum I;WS. This is 3 standard assumption in optimal IU theory. often juslilicd by the clssumption rh;:! Ihe govcrnmcnt may hare god information concerning the distribution of IASICS and endowments but cannot dcnrify the characteristics of a particular individual’. “‘NOW that the j tirms’ upid demand function has slope tX,/Cr,= I//;. ’ 'l'osi~ivc public goods provision (positive 13x rates) will bc ;L characwristic of the CTII for il larpc SCI of prrferences. One contrary cast arise when period-2 consumption and the public good arc perfec! substiiutcs for all individu:lls [so utility in j is given by, say. u,( ‘) =h,( t,,J + rz, +,g,. with /I,(.) mucasing and coruve].

throughout

that a CTE

exists, that the equilibrium

ized by (2) and (3). and that the equilibrium

choices can be character-

world price of capital is positive

and locally unique and varies smoothly (with not all derivatives zero) in government decisions in a neighborhood of the CTE.” It is said that the tax structure is incomplrtr if yji tlZi > I for some j at the equilibrium.

3. Strictly improving perturbations In this section

I examine the effect on utilities

changes in communities’

resulting

from

marginal

decisions around a competitive tax equilibrium.

feasible changes are constrained

The

by private sector budgets and behavior, in

particular by the maximizing behavior of firms and households, and material balance. The goal is to identify the circumstances under which there exists a perturbation that results in a strict Pareto improvement. It is shown that such an improvcmont

exists

in general; thus

the CTE

is not constrained

efficient. Consider a differential change (dt,. d,~,)~ in communities’ decisions around a conipctitivc tax equilibrium, along with changes (drj)j in community govcrnmcnts’ lump-sum incumc. Through private behavior the change inducts a change in the allocation pivcn by (d.~, i, d_~~,.dk,),, and a change in the net-of-tax intcrcst rate. dr. The perturbation is called fcasihlc when it povcrnnicnt budget balance for all j. satisfies 1, T, SO. and maintains allowing for private sector responses. LA !I’(‘, r,, IN,) dcnotc the equilibrium lcvcl of lhc ohjcclivc (utility) in community j. Since the change in taxes and public cxpcnditurc lcvcls is along the budgets starting from the CTli. and the chnngc in private hchavior is along private hudgcts starting

from a consumer

optimum, it follows from the cnvclopc thcorcm that the marginal change has no direct first-order cffccts on utility. so the lirst-order change in utility is given solely by the indirect cffccts, through dr. and through the rcvcnue cffcct from dr,. That

dlij=

is to say. the change in utility

(7/I’ t'r

dr +

in j. JII,, is given by

(‘ddTj. ?Tj

The goal is to find fcasiblc changes that satisfy &cj>O for all j. From the regularity assumption there exists a fcasihlc change yielding dr #O. Then. the lemma below follows directly from cq. (1). using cj risOO, and using (71~j/?s,=;,j (from the envelope thcorcm):

There

LOWFla.

exists

du, > 0, all j. if‘und

7 ;‘, y

only

u />asible

marginal

chungr

from

the

CTE

satisflving

if

f @

(5)

Using the envelope theorem and eqs. (3). the form of a typical elemen ,t in the sum in eq. (5) is given by

(6) at the equilibrium. and where fact that ~I,,,~=II~~ evaluated is saving in j. The first term on the RHS of (6) is the wealth erect of the change in the consumer price of capital. the difference between the change in value of savings and the change in profit income (from the using the sj=(_rj-.~,j)

envelope theorem, c’nj/?r = -k,).

The second term captures the induced effect

on utility through ;I change in tax revenue (and hence public expenditures); this offccf is nonzcro when the tax structure is incomplctc. Summing cqs. (6) over j:

(7)

The sum on (he R tIS of (7) is a non-negative-wcightcd sum (with weights summing to I) of numbers, 11~~/;‘~,;III no larger lhan one and at least one of which is less than one when the tax struclurc is incomplete. Hence the sum is Ihl: expression in brackets is negative. It follows less than one, and immcdia~cly from the lcmm;l that an improvement exists; formally, it has been proved that:

An important role in the failure of the proof is played by (6). in particular by the second term in that expression, which captures how ;L government’s choices afkct utilities through their indirect effect on market-determined variables (here. the equilibrium price of capital) when the tax structure is incomplete. This second term can be interpreted as follows. The fundamental allocation problem in the model is that in each community there arc restricted possibilities for transferring resources across the two budget

constraints.

from

the resident

to the government.

What

can be called the

‘technology’ of the transfer possibilities depends on r, through its effect on private maximizing behavior. A change in r affects private behavior in a way that

alters

the marginal

possibilities

available imperfect tax instruments. equal to tj?kj/c’r,

for Using

transferring

resources

with

the

(3). the term can be seen to be

which is the induced tax revenue in j from a change in r.

evaluated at the equilibrium

tax rate. Moreover,

the direction

of the effect is

the same in all communities. so the sum does not vanish [unlike the wealth effects, captured in the first term in (6). the sign of which varies in general across j]. The failure arises because a competitive community ignores the effect of its decisions on the technology of transfer through its effect on world prices. Since the RHS follows

from

improvement. case would

of (7) is negative when the tax structure

eq. (4) The involve

that

any

change that

induces

is incomplete.. it

a fall

in

r

is

an

type of change that would accomplish this in the normal an increase in tax rates on capital.

However,

income

effects on saving and interactions bctwecn saving and the public good can produce counter-intuitive rtsults. To briefly invcstignte this, total diffcrcntiation of the capital market equilibrium

equation yields the comparative statics

of the modol:

~:urthcrmorc. the change, dgi, is constrained to maintain the j-budget. i.c. d,~,=dr~+(r,/J‘;) dr +(k,+ f,.:j’;) dfj, with ~,rj~O. For simplicity. consider the case whcrc the incomc effect on savings is zero and the public good and substitutes. Then (%/c’f,= saving eomplcments nor arc ncithcr 1/_/‘y& ( I/j‘: - t?s:jCr)] < 0, each j, where ?.s:/i7r dcnotus the (non-nugativc) compensated cfkct on saving. Under these circumstances a uniform increase. dr, in aII tax rates will lower r, resulting in an improvement. Savings and the capital stock fall; hcncc thcrc is ovcrsaving at the CTI:. It can bc shown that total tax rcvcnue rises with the uniform incrcasc in taxes, so that expcnditurc on public services c;ln rise in each community. It is important to note that the indicated change actually increases the aggregate deadweight loss associatcd with the tax system alone (since the gap between every individual’s intertemporal marginal rata of substitution and the marginal product of capital in any community widens); Proposition 1 establishes that this loss is more than offset by an efkiency gain in public good provision. In the special case, prominent in the previous literature, where the supply of savings is fixed, the first-order conditions characterizing the CTE, eqs. (2) and (3). continue to hold. because from any community’s point of view the

size of its tax base is independent of the domestic savings rate. Then eq. (6) continues

to

hold.

without

change.

Eq.

(8)

becomes drxi(

I:fy)

= -

xj(dt,/f;), so that any improvement involves raising taxes on average. Of course in this case a coordinated increase in taxes does not necessarily imply an increase in the excess burden of the tax system.

I close this section with two corollaries to Proposition I. First. an improvement exists satisfying dsj=O. all j. if any only if sj--(;‘j/rrri)kj
4. A Pigovian rrrndy l’hc demonstration of constraioncd incficicncy in the previous section is constructive in that it indicates the information that is nocdcd to idsntify an improving direction. With this information. communities may agree to some change. or in some contexts the changes may bc imposed. In this section I consider the possihilitics for improving intcrvcntions that prcscrvc the dcccntralization

of decisions:

in

particular

the goal is to find

the best

‘-‘Note th;lt since the KtiS trf (7) is nonrero. o utilit;lri:m welfare improvement without translixs alw;~ys exists when Ihe 1;1x structure is incomplete. Ilence the prohlcm arises because the price ch;mgcs have advercc wcdth elTcc~s for some j. In il model with more tradrablcs (in the present model there is onl) one r&live world price), il is more likely mu be ;~ble IO manipul;lte world prices IO engineer benelici:d wealth CITCCIS. so thal it is more likely that an improvemrnr without transfers exists. “‘This assumes th;lt. in the USC where the wealth rlTcct of the price change does not have the s;Lrnc sign for all nont;~ning communities. a trxder dr, IO nontaring community j has utility due for the resident equal tu the siLe or the transfer (IO make it possible IO OITS~I adverse wealth rll~ts. iT any). This complication does not detract from the point beins made here. “The conventional argument is that a community. when it considers raising its tax rate. ignores thal a higher lit\ T;LIC creates a re;II benefit for other communities by incrrasing the sire of their Ian bases as domestic capital migrales in response IO the higher tan rate. The demonstrations have been verb4 and intuitive; the argument can be found in. for example, Gordon (19X3.p. 5X3). Oates and Schwab ( IWX. p, 343). Wildusin (19X9. p, lY6). Wilson (IYX6. p. 303; lYX7. p. 837). and Zodrow and Mieszkowski (I986, p. 369). Starrett (19X8. pp. 187-1Xx) is a tcxlhook treatment of Ihe analogous problem for local sales taxes. whcrc individuals can choose the community of purchase.

intervention in the sense of the minimal dimension decentralize a constrained efficient allocation.

set of signals necessary to

The point of view is that the source of the failure of the CTE identified with a missing market for the mobile tax base. That constrained

eflicient allocation

can be is. at a

a number, ci. emerges which is interpreted

as

the shadow value of capital as tax base. By completing the markets (that is, in our model, by adding an extra signal corresponding to this shadow value in guiding communities’ decisions), a correspondence is established between the competitive equilibrium of this modified economy and the constrained ellicient allocations. Thus, the economist’s standard response to esternalities in competitive private ownership economies carries over to the present context. which contains two novel aspects: first the mode) has competitive governments using distortionary taxes (these distortions are not usefully thought of as standard technological externalities); and second the comparison allocations arc not fully (Pareto) efkient. but only second best. The

strategy of the approach in this section is, first.

to define the set of

constrained cflicicnt allocations prcciscly, and then to characterize those allocations by the first-order conditions for a constrained maximization problem. A modiftcd cconumy is then dclincd whcrc thcrc is a compctitivc for this modified niarkct for the tax base. and a compctitivc equilibrium economy is charactcrizcd by the first-order conditions for each community’s constrained maximk~tivn problem. A comparison of thcsc two sets of firstorder conditions cstablishcs a corrcspondcncc bctwccn the critical points. I begin with scvcral definitions. The economy is as dcfincd in section 2 above. A d~sj~~~r~ for the economy is dcfincd as an allocation (.ulj. _s~,.~~~,k,),, ;I ;I net-of-tax price of capital, r, and a set of

set of capital tax rates (tj),. transfers among community satisfies:‘” (i)

( r,)j.

A design is Jiwsihl~~ if it

Cj.\.I,‘+C,x,5;C,J’,;

(ii) illld,

govcrnmcnts

Cj

Sj~;O;

for each j:

(iii)

(.r,,, s2,) solves niax,,, ~) 1~r,(.u,,.\‘~;,~,):r.~, +~,~‘r)‘,+f[~(~+t~)+~)~~:;

(iv) g,sfjkj+r. (v)

I’ ’.tnd

kj SOIVCS max) ( J;(k)-(r+lj)k);

where n,(.) denotes the maximized value of profit in community j. A feasible design is said to bc ~~n.s~roirtc~cleJki~( if there dots not exist some other fcasiblc

design

whcrc

all

individuals

in

the

economy

arc

strictly

bcttcr

off.

Constrained ditions

efficient

for

function

designs

problem

LV[( u,Jx,

feasibility

SgO

that

will

of

be characterized

choosing

a

[the

(i)Hv).

Thus.

normalized

a constrained

in

there

to

its

numbers

associated

design

the

solves.

first-order

maximize

arguments,

exist

multiplier

efficient

by

design

j, xzi. s~))~]. increasing

constraints

number such

the

along

to

8jz0.

the

with

welfare

subject

(Oj)j,

with

con-

the

the

and

a

constraint

(i)]

the constraints,

for

each j:”

“ri = oj

1 _

(j

c’sj

(9)

c’gj1 ’

l'lj

[

lj = ii -

I;,.f‘;c I - p,,.

(10)

csc 3

=c ( I -

(11)

and

j(‘r

whcro

for

each j.

the (Slutsky) marginal

of income.

than can

hc

wcightcd

marginal

the tax

m;irgin;il

rate.

l;rom ralc

The

or

cvaluatcd

as

the

on eilhcr

an adjustment the

efkct

that Oulpul of

of

the reduction

zero.

value rate

of

substiturion

to

unity)

eq. (IO)

dcpcnds tluc

to

the

concerns.

tax

iIS rates relative

[From

cq.

from

in tht: economy’s

optimal

saving

the the

and the public

good

may

of

taxes;

CC.The

this

sum

along

depart to

cffcct

other

of capital

(I I),

commodity

the

from

rate.

in j

it

to

First.

the elasticity

the savings-share-weighted

(I I) is familiar

base

difkrs

two

system tax

tax

the lax rate in community

on

income

as

rather

(saving);

reasons.

for

saving

the

( 1975)

5 appears

on capital

capital

of

social savings

to Diamond’s

is that

ralc

marginal

direct

by the extra

of

bctwccn

burden

of this

rclatcd

diffcroncc tax

c’sTI~‘r dcnotcs

I/O, is the social

by the social

gcncratcd

closely

The

at the shadow

private

distributional

is not form

los(

bcncfit

(cqi~al

side of I. From

valuation

cxprcssing The

cxccss

in each community

minus

the

/ji is the sum

marginal

or substitutability

roinforcc

(capluring

normalized

shadow

the

term

to j.

CS is the shadow

the

cq. (0)

can lit

and

lcrni

The

term

of income.

of lr;Insformaliori

conlplcmcnrnrity offset

The

as before.

whcrc,

saving.

by S; /j, is thus

utility

inlcrprctctl

economy.

income

rcvcnuc.

IO ,j plus an indirect

of incomc

net social

of r on

effect

of (period-2)

of govcrnmcnl

benefit out

/I, = [I/O, + S c’s,/?rr~~]. and

compensated

utility

wclfarc

[jj),Vj.

,

Lcrm, j cquals

demand

from the

rcvcnue,

substitution

of the /Ii is less tax theory,

the compensated

(5

in j

uniformity)

government when

is (I,,

than

where

supply

I.] now

curve

is

evaluated as if there was a common tax rate equal to d. the shadow value of saving as tax base.‘“.”

I turn

now

constrained

to a consideration

efficient

allocation.

of the possibilities

First.

define the list

for decentralizing of numbers

a

(c;i)j by

cfij=O. The numbers (h,), become part of the data of a modified economy, where hj is interpreted as community i’s endowment of ‘rights to the tax vase’. Each community in the modified economy now has an additional decision, the choice of a quantity of rights to tax base, hi. subject to the constraint that it hold rights at least equal to its capital account surplus, allowing for an adjustment equal to I;,. It is assumed that these rights can be bought and sold at a price. denoted p. An equilibrium for the modified economy differs from a CTE defined in section 2 solely by the presence of this extra ‘market’; formally: Dcjinitifm.

A compt~titirx~

(fij)j is a list (.Y ,,, .~2j.sj. such that:

t0.v

c~fptifihriw

ji)r

rllc rr&j/kf

ccortom~ rdtrfir.c lo

lij. /I~)~.a list of capital tax rates (fj)P and prices (r, p)

(a) ~j.~,j+~jkj~‘cj~*,: (b) CjjljsCjh,; and, for each j. (c) (Y,,. szj) solves max.,, _ll [ ~(,(.~,..\‘,,,~~):f_\‘, +s,~r!.j+nj(r+lj)+“~j); (d) (
.r 5 rk, t I’( I;, - It).

(ii)

hzk,-s,.

(iii)

lij solves maxI, :./;(I,)-(r+f)k).

and

Clearly the (.Y,,, s2,,g,, k,. [,)j equilibrium for the modified p(hj-(k,-s,)).

Condition

to

and r associated with ;I competitive economy is ;I fcasiblc design, with

t;ix T,=

I‘hc term (k,-.sj) is j’s capital account surplus or deficit. (ii) requires that the community hold rights at least as large as its

capital account. Then (fij-/I,) is j’s net trade in rights to the tax base. and p(I;,-11,) is the value of this net trade. An institutional structure consistent with the equilibrium concept is as

R. Kreloce. Competitive

follows.

A central

international

clearing

context,

house (perhaps

a supranational

tax theory

373

a federal government

or, in the

agency) assigns endowments

(t;j)j of

rights to communities. It collects data on supplies and demands (the size of tax bases and savings rates) and attempts to establish an equilibrium price for rights. A community value of its capital rights.”

is then charged or receives a payment

account

surplus after allowance

equal to the

for its endowment

of

In the modified tax equilibrium concept, agents are decentralized with two signals, the prices r and p. Note that the signal p is relevant only to the decisions of the competitive governments; all private agents (households and firms) are decentralized at price r and, at equilibrium, the taxes (c~)~chosen by the communities. Consider the maximization competitive tax equilibrium. constraints

problem for community j in the modified The first-order conditions are given by the

and by: 7

!'~i=;.~ "Zj

1

_,!>j

[

'Sj

1

(12)

a nd

(13)

whcrc yj is j’s pcrccivcd normalized the modified

compctitivc

with cqs. (!I)-( I I) characterizing

What

Proposition

marginal

cquillibrium.

utility of govcrnmcnt

A comparison

constrained

rcvcnue at

of eqs. (12) and (13)

efliciency yields:

2 asserts is that the net-of-tax

price of traded capital

incorrectly reflects the social scarcity value of saving to the economy. Thus, traded goods prices, while suffkient to guide the decisions of private agents in the economy, arc not suflicicnt to coordinate the decentralized decisions of govcrnmcnts. They must in addition face the shadow value of tradeablcs as tax base. An attraction of the approach is that an indirect means, the market, may be usad to discover the shadow value of the tax base. Accompanying ‘“The

anulogy IO mclrketablc permits for. say. pollution

is immediate.

this informational

parsimony

principle,

the principle

namely

is the remedy’s consistency that

with

the best remedy for

the trageting

a failure

works directly on the relevant margin. This property is of value for the design of interventions in richer models where communities make decisions on a wider number of issues. some of them with solely domestic content.”

5. Concluding remarks The focus of this paper has been an important

class of multiple-jurisdiction

of spillover effects and of any exercise of monopoly power by governments in world markets. When each jurisdiction must pursue its goals models.

purged

using distortionary instruments. the competitive equilibrium is not constrained efficient in general, even though each perceives that the total costs of its policies are internalized. The example analyzed here strongly suggests that this is a general phcnomsnon; broadly, the result cxtcnds to any economy whcrc the sacond-best instruments in agprogatc dctorminc world prices. An implication of this is that much of normative tax theory. and more gcncrally the theory of optimal policy. dcvclopcd for closctl economics is in fact partial equilibrium theory in multi-country cnvironmcnts, cvcn when govcrnmcnts arc compctitivc. In addition, the nalurc

of the best dcccntralizcd

intervention

for

the

plcasing that this takes a economy has been analyzed. It is intuitively familiar form: the simple atlditivc structure dcrivcs from the fact that wc can assign to tradcablc commodities a shadow value as tax hasc. While thcrc arc

large

gaps, informational

tation that still

and

othcrwisc.

bctwccn concept

need to bc bridged. the analysis

points

and

implcmcn-

the way toward an

intcrvcntion policy potentially applicable to the design of intcrgovcrnmcntal grant schcmcs in fcdcral countries and to lax h~lrmoiiiz~ltioii efforts in the international

context.

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