Efficiency and Equalization Payments in a Federal System of Government: A Synthesis and
Extension of Recent Results
Author(s): Robin Boadway and Frank Flatters
Source: The Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 15, No. 4
(Nov., 1982), pp. 613-633
Published by: Wiley on behalf of the Canadian Economics Association
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Efficiency and equalizationpaymentsin
a federalsystem of government:a synthesisand
extension of recent results
ROBIN BOADWAY
Queen's University
and FRANK
FLATTERS
/
Abstract.This paperinvestigatesthe rationalefor a system of equalizationtransfersin a federal
system of government. The existing sources of inefficiency of resource allocation in
economies with more than one level of governmentare synthesized in the frameworkof a
simple decentralizedmultiprovincemodel with mobile factors of production.The sources of
inefficiency arise, first because migrantsrespondat the marginto incorrectsignals, owing to
the phenomenaof rent sharingand fiscal exterality, and second because of global ratherthan
local inefficiencies. The model is then extendedto considerthe role of the federalgovernment
in providing intergovernmentaltransfers in the face of such inefficiencies. In addition to
synthesizingthe sources of inefficiency in federalmodels, the equity argumentsfor equalization are briefly recounted.
Efficaciteet paiements de perequationdans un systemefederal de gouvernement:syntheseet
extensions de certains resultats recents. Ce memoire examine la logique qui soustend un
systeme de paiementsde perequationdans un systeme fdderalde gouverement. Les auteurs
utilisent un modele simple d'un systeme multi-provincialdecentraliseavec des facteurs de
productionmobiles pourdefinirles sourcesd'inefficacitedans l'allocationdes ressourcesdans
les dconomiesqui possedentplus d'un niveau de gouvernement.Ces inefficacitesproviennent
de ce que, d'abord, ceux qui se deplacent le font en reponse, a la marge, a des signaux
incorrectsengendresparle partagede la rente surla base de la residenceet parles phenomenes
d'exteralites fiscales; elles sont aussi le resultatd'inefficacites globales plutot que locales.
Dans le cadre de ce modele, les auteursanalysentle role du gouvernementfederaleffectuant
des transfertsinter-gouverementaux pour corrigerces inefficacites. En plus de presenterune
synthesedes sourcesd'inefficacitedansles regimesfederaux,les auteursfont un brefrappelen
passant a l'ensemble des argumentsfondes sur l'equite qu'on utilise pour rationaliserles
paiementsde perequation.
of twopaperspresentedat theMay1982meetingsof the
Thispaperis a linearcombination
EconomicsAssociationin Halifaxentitled'Thecaseforequalization
Canadian
payments'(bythe
in thetheoryof regionaleconomicpolicyin Canada'(by
authors)and'Recentdevelopments
JimJohnsonandBaxter
Boadway).Theauthorsaregratefulforcommentsby thediscussants
and
andby JackMintz,BrianScarfe,GerardBelanger,DavidSewell,TomCourchene,
MacDonald
thereferees.
commentsandsuggestions
Weareespeciallyheavilyindebtedto DanUsherformanystimulating
whiletheworkwasin progress.Someof theabovepersonswill undoubtedly
disagreewiththe
emphasiswe havechosento puton variousaspectsof theanalysisforpolicypurposes.Supportfor
someof thisworkhasbeenprovidedby theEconomicCouncilof Canadaandis gratefully
acknowledged.
CanadianJournalof Economics / Revue Canadienned'Economique, XV, no. 4
November/ novembre 1982. Printedin Canada/ Imprimdau Canada.
0008-4085 / 82 / 0000-0613 $01.50 ? 1982 CanadianEconomics Association
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614 / Robin Boadway and FrankFlatters
INTRODUCTION
Federal-provincialtransfersaimed at redistributingincome among provinces have
been a long-standingfact of life and source of controversyin Canada.The main such
programis the federal-provincialscheme of equalizationpayments, but there are
othertypes of transfersbetween levels of governmentthathave an implicitequalizing
component (e.g., Established Programs Financing Grants).1The question of the
appropriateamountof equalization,if any, and the formulato be used have become
mattersof urgency for several reasons. The currentequalizationscheme falls due in
1982 and the renegotiation is controversialfor many reasons, including the close
relationshipbetween equalizationpaymentsandthe disposalof the benefitsof oil and
naturalgas rewards.2In addition,equalizationhas become a constitutionalissue since
the constitutionalreformpackageembeds (albeit somewhatvaguely) the principleof
equalizationinto the constitution.3
There is now a sizable literatureon the economics of federal states, much of it
directed rather abstractly to the issue of optimal resource allocation in federal
economies. We would like to extend that literatureby investigatingthe economic
rationale for intergovernmentalequalizing transfers in a federal economy. More
specifically, this paperattemptsto do threethings. First, we presenta synthesisof the
existing resultson fiscal federalism,showing in the frameworkof a simple model the
sourcesof inefficiency of resource allocationstressedin a literature.Next, using the
same model we extend the analysis to consider the role for intergovernmental
transfersin the face of such inefficiencies. Finally, we briefly comparethese policy
implications with those derived from considerations of equity. Since the equity
resultshave been discussed at considerablelength elsewhere,4thereis no need to go
into their derivationin this paper.
Our analysis begins with the sorts of identical-personeconomies which have
dominated the literatureto date. Out of this will come a survey of the sorts of
inefficienciesof resourceallocationthatcan occur in economies with multiplelevels
of government. These models will form a basis for a discussion of the role of
equalizing transfers on efficiency grounds. Subsequently, the discussion will be
extended to economies of heterogeneous individuals in which equity as well as
efficiency become relevant for policy issues. The analysis will be based upon
simple abstractmodels designed to capturethe basic forces at work. We believe that
the general results are applicable in more complicated situations. Finally, we are
1 The EPFgrantsprovide equal per capita grantsto the provinces financedout of federal general
revenues and involve equalizationto the extent that the base for federal tax collections is unevenly
distributedover provinces. For a survey of existing federal-provincialtransferprogramssee
Boadway (1980).
2 This relationshipis discussed in Courchene(1980) and Helliwell (1980).
3 Also, see the Task Force on CanadianUnity (1979), the so-called Beige Paperof the Quebec Liberal
Party(1980) and the Trudeaugovernment'sCharterof Rights (1981). There is a question as to
whether,even if equalizationturnsout to be justifiedon economic grounds,it is an appropriateobligation to include the constitution(contraryviews appearin Boadway and Norrie, 1980 and Usher,
1981). We shall ignore that question.
4 Boadway and Flatters(1982).
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Efficiencyand equalizationpayments/ 615
ignoringthe sortof inefficiency in federaleconomies arisingout of interjurisdictional
spillovers of benefits and costs. The literatureon this topic is well established,
non-controversialand of no essential relevance for the issue of equalization.5
OF FEDERAL
MODELS
INDIVIDUALS
ECONOMIES
WITH
IDENTICAL
Thoughoften formulatedin simplisticterms, models of federaleconomies or systems
of local governmenthave proven to be powerful tools for elucidating some of the
inherentinefficiencies inducedby interjurisdictionalfactormobilityon the one hand,
anddecentralizedpublic sectordecision-makingon the other.We shallbegin with the
simplest of models in orderto concentrateon the firstof these issues, especially the
inefficiencyof individuallabourmigrationdecisions in models of local government.
Local governments (hereafterreferredto as provinces) will be assumed to behave
myopically with respect to the size of their populations. This turns out to be an
innocuousassumption,since, as shown in Boadway (1982) and Lange (1982), local
governmentscannot improve themselves by behaving otherwise in these models.
Thatis, provinces are assumedto behave as if theirpopulationswere given, despite
the fact that they are not.
Ideally, we would like our model to incorporateseveralfeaturesof the real world,
including interregional trade and factor mobility, differences in local resource
endowments,differences in industrialstructure,heterogeneityof tastes, income and
labourforce quality, complicatedfederalandprovincialtax/tariff/subsidystructures,
unemployment,and the provision of public services at several levels with possibly
some spilloversof benefits. However, to begin with it is useful to abstractfrommany
of these featuresof regional economies in orderto concentrateupon the interaction
between labour mobility, decentralizedpublic sector decision-makingand differences in regional productivity or resource endowments. The tendencies to inefficiency in these simple models will continue to hold in more complex economies.
Subsequentanalysis will involve a gradualrelaxationof some of these assumptions.
Federalism models with myopicprovincial governments
Let us begin with a simple federationconsisting of two provinces. The federationhas
a given aggregate population N, which also represents the labour supply. It is
assumedto be costlessly mobile between provinces. In equilibriumL1 will locate in
province 1 while L2 will locate in 2. Each province has a Ricardian-typeaggregate
production function of the form fi (Li), where fi' (Li) > 0 and fi" (Li) < 0 (at least
beyond some level of Li). The output thus producedcan be allocated to use in the
privatesector or in the public sector within the province. Thus, the marginalrate of
transformation(MRT)between private goods and public sector goods is unity. This
assumptionis not essential. It is easy to generalizethe model to allow MRTto vary.
All individualsareendowed with one unitof labourandhave identicalpreferences
5 Surveys of this topic may be found in Oates (1972) and Boadway (1979).
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616 / Robin Boadway and FrankFlatters
represented by the utility function u(Xi, Gi/Li) where Xi is the per capita
consumptionof privategoods, Gi is the quantityof public sector goods providedin
province i, and GiLia is the services of the latter. The parametera is an index of the
1. This
a
'publicness' of provincial public services and can take values 0
formulationallows us to span the spectrumfrom pure public goods to pure private
goods since these correspondto a = 0 and a = 1 respectively.6The public service
would be 'impure' or 'partially rivalrous' to use Musgrave's (1969) term if a is
between zero and unity. Assuming initially that the value of output of a province
accruesentirelyto its own residents,per capitaprivategoods consumptionXi is given
by [fi(Li) GiLi]. Notice that we are ignoringany activityby the centralor federal
government.7
Provincialgovernmentbehaviouris easy to characterizein this simplemodel. Each
one is assumedto behave myopically in the sense that it ignores the influenceof its
actions on migration. This assumption has been used almost universally in the
literatureon local public goods,8 and as we have mentioned, it does not affect the
results of the model. Under this assumption, a provincial governmentthat aims at
maximizingthe welfare of its citizens will solve the following problem:
Max u[f(L) - GIL, GILa],
(1)
G
where we shall follow the convention of droppingthe provincial subscriptswhen
analysingthe behaviourof a representativeprovince.
The first-ordercondition for this unconstrainedmaximizationproblemyields:
L(-a)
UG/UX = 1,
(2)
where UGand ux are the marginalutilities of GILaandX respectively. If a = 0, this
correspondsto the familiarSamuelsonconditionthatthe sum of the marginalratesof
substitution(MRS)equals the MRT(here unity). Similarly, if a = 1 it reduces to the
optimalityconditionfor pureprivategoods. The solutionto (2) for G determineshow
provincial output is divided between private and public sectors. To characterizea
migrationequilibrium,we must examine how per capitautility in a province varies
with populationsize.
6 This is similarto the techniqueused by Borcherdingand Deacon (1972) and Bergstromand
Goodman(1973) in their empirical studies of local public expendituresin the U.S.A. Both papers
found a close to unity. An alternativeway to introduceimpurityinto public goods is to explicitly
include congestion costs. See Buchananand Goetz (1972), Flatters,Henderson,and Mieszkowski
(1974), and Oakland(1972) for examples of this approach.The formermethod is more convenient for our purposesbut both yield qualitativelysimilarresults.
7 The structureof this model is similar to that found in much of the theoreticalliteratureon the
subject, except for our generalizationto allow for impurepublic goods. See, for example, Flatters,
Henderson,and Mieszkowski (1974), Stiglitz (1977), and the survey in Atkinson and Stiglitz
(1980). Othermodels have used slightly differentdevices from the diminishingmarginalproductof
labourwhen applied to fixed land to generatediseconomies of populationincrease. Buchananand
Goetz (1972) use club goods (see also Henderson, 1974). Starrett(1980) used spatialconsiderations.
In these alternativemodels the qualitativeresults derived in this section continueto hold.
8 Exceptions to this are Boskin (1973), Pauly (1973), and the recent paperby Starrett(1980).
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Efficiencyand equalizationpayments/ 617
Migrationequilibrium
The maximumu attainedin problem(1) is contingentupon L, which is exogenously
determined for each province. The relationship between per capita utility and
provincialpopulationsize is definedby the maximumvaluefunction V(L)associated
with problem(1):
V(L) = Max
ulf(L) - GIL, GIL"].
G
(3)
This gives the per capitautility attainedundervariousvalues of L when the province
is maximizingmyopically. Fromthe envelope theorem9we know thatdVIdL= duldL
(evaluatedat the optimum);therefore, using (2)
V'(L) = ux(f'(L) - X - aGIL)/L
(4)
V"(L) = [uxx(f'(L)
- X)IL - uGxaG/LL l]V'(L)/ux
+ ux(f(L) + aG/L2)L - V'(L)/L. (5)
From(4) we observe thatthe optimalpopulationis thatat which the marginalproduct
of labour equals per capita consumptionof the private good plus aG/L.?1 This is
intuitively plausible, since the contributionof a marginalperson to productionis
f'(L), while his additionalclaim on resourcesis per capitaprivateconsumptionX and
his congestion cost imposed on others is aG/L. 1 From (5), when G is a purepublic
good (a = 0) andprovided V'(L) > 0 at L = 0, we can deducethatsince the firsttwo
terms on the right-handside are negative the graph of V(L) is single-peakedwith
V"(L) eventually becoming positive as in figure 1.12 This diagram reflects the
contervailingeffects of diminishingreturnsto labourand economies of scale in the
consumption of the public good. Inspection of (5) indicates that this singlepeakednessof V(L)is also plausiblewhen a < 1, althoughone could contrivecases in
which there are more than one peak. For simplicity we shall assume singlepeakedness, althoughour analysis remainsintactundermore complicatedshapes of
V(L).
Free migrationensures that labourallocates itself among provinces until V(L) is
equalized. This is shown in figures 1 and 2, where subscripts 1 and 2 refer to
provinces 1 and 2. Figure 1 shows the case in which there is a unique stable
equilibrium.On the other hand, in figure 2 there are three possible equilibriawith
9 A convenient summaryof the use of maximumvalue functions and the envelope theoremmay be
found in Dixit (1976).
10 This characterizationassumes that the optimal populationis positive and finite. In additionone
requiresthat V(L) be strictly concave as discussed below. This condition on optimalpopulationis
similarto that obtainedby Flatters, Henderson, and Mieszkowski (1974), generalizedhere to
include congestion costs.
11 The interpretationof aGIL as the marginalcongestion costs comes from noting that the change in
the utility benefit from public services as L increases is -auGG/La+l. Convertingthis to private
goods units using (2) and multiplying by L to aggregateover the entire populationyields -aGIL.
12 V"(L) may be positive initially if f"(L) > 0 at low levels of labour supply. Eventually, however,
diminishingmarginalproductof labourwill occur and V"(L) < 0.
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618 / Robin Boadway and FrankFl
V2(L2)
V,(L,)
->L
FIGURE 1
L
L2=N-L,-
A unique equilibrium
V (L2)
V, (L,)
Le
Lm
L?
L2=N-L,4FIGURE 2
Multiple equilibria
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Efficiencyand equalizationpayments/ 619
only the corer ones being stable. The internalequilibriumLeis unstablesince any
departuresfrom it would result in the complete depopulationof one or other of the
provinces. The ultimateconsequenceof this could be a level of V which is lower than
thatattainedat Le. This resultis reminiscentof Mydral's(1957) cumulativecausation
model of regional disparities, but here it is generatedfrom neo-classical postulates
alone.13
One way of distinguishingcase 1 from case 2 is the size of the federation'stotal
populationrelative to the optimal amount. If each region had its optimalpopulation
(i.e., that which maximized its V), the aggregateN would be less than that which
actually exists in 1 and more than that which exists in 2.14 In that sense it is
overpopulatedfederations which would tend to have a unique stable equilibrium
(althougheven it could be unstable). In an underpopulatedfederationan internal
equilibrium,if it existed, would tend to be unstable.15 Since it is hard to imagine
Canadaas being anythingbut underpopulated,this seems to bode ill for the stability
of the migrationprocess.
We do not observe the complete depopulationof provincesor regions, however,
and that is presumably because there is not free migration as we have so far
postulated.It is instructiveto illustratethe role of migrationcosts in lending stability
to the model. In the free migrationmodel the condition for stability of the internal
equilibriumcan be written:
dVI(L1)
dL1
dV2(N-L1)<
dL1
or
(V,' + V2') < 0.
(6)
Let us now introducemigrationcosts. If the initial distributionof populationis such
thatmigrationwill go from 2 to 1, the migrationequilibriumconditioncan be written:
Vl(L) = V2(L2) +m(L2),
(7)
where m(') is the migrationcost function and is assumed to depend upon L2 (and
hence uponthe numberof migrants).A stableinternalequilibriumnow requiresthat:
(V1' + V2' + m') < 0.
(8)
13 See Kaldor(1970) for anotherview of regional disparitiesstressingcumulativecausation.
14 Actually, the definitionof optimal populationfor a federationis an ambiguousconcept. An
equilibriumin which each region had its optimal pupulationwould generally be unsustainablesince
the maximum V(L) would be higher in one region than another.This is incompatiblewith free
migration.The optimal populationunderfree migration(with Vs equated)might make more sense,
and the text could be interpretedin that way. Even this is not totally satisfactory,since, as we
shall see, migrationis generally not efficient.
15 There are other patternsthan those we have drawn. For example, cases of multipleinternal
equilibriaare depicted in Atkinson and Stiglitz (1980). Such multiple equilibriacan occur in both
under-and overpopulatedcases. In addition, an underpopulatedfederationcan have a stable free
migrationequilibriumthat is unique if the optimal Vs are different. We have benefittedfrom discussions with Sam Wilson and some of his unpublishedwork on the stabilityof free migration
equilibria.
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620 / Robin Boadway and FrankFlatters
Even if (V1' + V2') > 0 at the equilibrium,this conditionmight still hold if m'(L2)<
0; thatis, if per capita migrationcosts rise with the numberof migrants(sufficiently
rapidly). This is a reasonableassumption, since it is consistent with the notion that
migrants have differing degrees of attachmentto their home province. Figure 2
illustratesthis case. The allocation L? is the historically-giveninitial allocation of
labourover provinces while Lmis the after-migrationequilibrium(which is stable).
The introductionof migrationcosts has precludedcomplete depopulation.However,
it is also importantto observe that Lmis not in any sense an efficient allocation of
labour.On the contrary,as the diagramindicates, the residentsof both regions may
well be ultimatelyworse off as a result of migration.
More complicated analyses would look at the development over time of the
federationas the total populationgrows. We shall not pursuethattopic here. Rather,
we shall indicate another source of inefficiency that has been prominent in the
literature.Let us revertto the stable internalsolutioncase with free migration.In this
case an equilibriumsuch as Lein figure 1 is achieved where equal per capitautilities
are obtained in the two provinces. Even in this stable case it is unlikely that the
distributionLeis optimal. The most importantreasonfor this non-optimalityhas to do
with the inefficiency of the migrationprocess itself. Owing to a type of migration
externality, the private signals that potential migrants are getting differ from the
social signals they should be receiving.16
Inefficiencyof migration
Considerthe migrationequilibriumLein figure 1. We can obtainan expresssionfor
the net benefitto the existing residentsof a provincefrom having one moreresident.
Forexample, in province 1 this would be (using equation(4) andthe definitionof X):
L1VI'(L1) = ux(fl'(L1) - f(L1)/L1
+ (1 - a)G1/L1)
= ux((1 - a)G1/L1 - R1/L),
whereR1 = fi(L) - Llf'(L1) is the totalrentin province 1, assumingwage ratesto be
equalto marginalproducts.Dividing throughby ux we obtainthe benefitto existing
residentsof an additionalmigrantin terms of consumptionof X, denotedMBL1,
MBL1= (1 - a)G1 /L1 - R1/L.
(9)
A similar expression holds for province 2.
This may be interpretedas the total amountof X residentsof 1 would be willing to
give up to have an additionalmigrant,given thatthe migrantwere to receive his per
capita shareof rents. MBL, consists of two parts. The first, (1 - a)G1/L1, is the per
capita tax payment less congestion cost for each resident in province 1 and will be
called thefiscal externality.An additionalresidentconsumesthe public good G at an
16 Anotherreason why free migrationis non-optimalis that a social welfare optimumin a federal
model, even with identical individuals, typically requiresthat utilities be unequalfor otherwise
identical individuals. This is clearly inconsistentwith free migrationmodels. The phenomenon
was first pointed out by Mirrlees (1972), and is discussed in the context of local public goods
by Hartwick(1980).
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Efficiencyand equalizationpayments/ 621
opportunitycost equal to the congestion he imposes on others, but at the same time
contributeshis share to the financing of G1 thus reducing the tax bill of existing
residents. The newcomer's tax contributionT1 is just his per capita tax payment,
G1/LI. The second term is the per capita share of the rent generatedin province 1
assumed,at this stage, to be equally distributedamongresidents.The moreresidents
thereare, the smalleris the shareof the rentgoing to each person. A marginalresident
reducesthe rents of existing residentsby RI/L1.
Assuming, as would be true at the free migrationequilibrium,that the marginal
migrantis indifferentbetweenresidingin 1 and2, the net benefitto the nationfromhis
moving from 2 to 1 is given by:
NB = MBL - MBL2=
/(l-
a)GI
L
L1
(1- a)G2
L2
1I
L1
R2
2
L0
(10)
Thereis no reasonthatthese should sum to zero in the free migrationequilibriumLe,
except fortuitously.It is worthconsideringthe two componentsof the righthandside
of (10) in turn.
Fiscal externality/ This model has typicallybeen formulatedin the literaturefor pure
public goods (a = 0). In this case the fiscal externalityterm will vanish only if per
capita tax payments are identical in both provinces. As Flatters, Henderson, and
Mieszkowski (1974) show, this requiresthat the compensatedelasticity of demand
for public goods be exactly unity, an unlikely eventuality. As (10) indicates,
however, the force of the fiscal externalitycan be diluted if, instead of being pure
public goods, provincialpublic services are impureor congested. The closer G is to
being private, the nearer a is to unity, and the smaller the fiscal externalityis. It
disappearsaltogetherif G is purelyprivate(a = 1). We shall follow the conventionof
calling G a quasi-privategood in this case.
Rentsharing/ Provincialper capitarentsharingas a sourceof inefficiencyhas played
a prominentrole in the recent Canadianliteratureon regional policy.17 It is also
analytically similar to the phenomenon of sharing the returns to public capital
discussedby Usher (1977), althoughsharablerentscan be capturedon privatecapital
as well as on public capitalvia provincialtaxationpolicies. The point is simply thatif
workersget a shareof provincialrents solely on the basis of residency, they respond
to theiraverageproductratherthanto theirmarginalproduct(wage rate)in migration
decisions. The force of this argumentdepends upon the rents accruingpublicly and
being disbursedto individuals on the basis of residency alone. If all rents went to
personssolely on the basis of ownershipof the rent-generatingfactorthe inefficiency
would disappear,since residency and ownershipof propertywould be independently
determined.In principle, even with the collectivizationof rents and free migration,
this source of inefficiency in the allocation of labour (as well as the fiscal
externality)can be considerablylessened if thereexists anotherfixed factorrequired
for residencyinto which rentscan be capitalized(e.g., residentialland). It is hardto
17 See, for example, Courcheneand Melvin (1980), Flattersand Purvis (1980), Helliwell (1980), and
Eden (1981).
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622 / Robin Boadway and FrankFlatters
believe that this is a significant deterrentto long-term migrationin Canadawhere
residentialland is relatively abundantin the rent-richprovinces.
The upshotof this discussion of migrationin a very simple federaleconomy is that
free migration will generally lead to an inefficient allocation of labour over the
federation.This inefficiency can be eliminatedby a particularsystemof interregional
transfersof privategoods eithervoluntarilyarrangedby the provincesor imposedby
the central government. Inappropriategrants would lead to inefficiency. The
appropriategrantswould ensurethatNB = 0 at the optimum.In the simple model we
havebeen analysingso far it can be shown thatthe size of the totaltransferfrom 1 to 2,
denoted S, would satisfy the following equation:18
Gl(l - a)- R1 + S G2(1 - a)- R2- S
L1
L2
or, solving for S,
LIL2 (G2(
-
L+L2
1- a)
Gi(l - a)
L1
(RR
L1
2 ]
L2
(12)
That is, the size of the transferwould be an average of the provinces' MBs each
weighted by the other provinces' population;or, proportionalto the differences in
fiscal externalityand per capita rents. This is the equalizationformulacalled for on
efficiency groundsin this model. Equalizationformulasin more generalmodels will
be introducedas our analysis proceeds.
Even in this simple model it is worthbeing cautiousaboutthese policy results.The
formulafor S in (12) is based upon marginaloptimalityconditions which may not
correspondto a global maximum. We saw earlierthat, especially if the federationis
underpopulated,the migration equilibriummay not be near the globally efficient
point, owing to inherent instabilities. In this case much more informationally
demandingtotal analyses are required.
We chose our model to be as simple as possible in orderto illustratethe natureof
migration inefficiency. However, the basic point continues to be valid in more
complicated settings. Adding migrationcosts to the model does not affect the net
benefitexpression (10). Because of migrationcosts, however, the utility levels will
tend to differ from one region to another,being lower in the province experiencing
out-migration.These differences in utility can be used to motivate interprovincial
transferson equity grounds.
The introductionof heterogeneity of individuals also complicates matters, and
analysesin this areaareby no meanscomplete. The fiscal externalityandrentsharing
problems remain, but the characterizationof the free marketequilibriumdepends
critically upon the technology and upon the manner in which local governments
18 These formulasare derived from the following centralgovernmentproblem(see Hartwick(1980)):
- G1 S)/L1, Gi/L1a]
Max,u[f(L1)
subject to u' = u2.
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Efficiencyand equalizationpayments/ 623
finance public expenditures. There is a natural tendency for 'likes' to wish to
congregatetogether, as in the literatureon club goods. In the latter,if the production
side is abstractedfrom(by giving everyone exogenous incomes) andif financingis by
benefittaxation, one expects to see 'likes' congregatingtogether. 9 This tendencyis
easily countered,however, by complementaritiesamongthe sortsof laboursupplied
by variouspersons, or by general forms of taxation. For example, Wheaton(1975)
has arguedthat only underpoll taxationwill homogeneous communitiestend to be
stable. A survey of these results takes us too far afield.
It is reasonablyeasy, however, to extend our model to include other factors of
production,such as capital, and heterogeneityof individuals, so long as tastes are
similar. We shall do that below. Also, we shall allow the provincial governments
some leeway in the choice of their tax instrumentsfor financing public services.
These modificationswill have importantconsequences for the appropriateform of
interregionaltransfers.
Introductionof capital and heterogeneousindividuals
Capital I We begin by allowing for capital as well as for labourand resourcesin the
productiontechnology, by treating the economy as being a decentralizedmarket
economy with privatefactorownership, and by allowing the provincesconsiderably
more scope in choosing their tax mix. Consequently, we assume aggregate
productionfunctionsfor each provincewhich takethe formf(L, K) whereK is capital
andboth K andL areperfectlymobile over provinces.20Thereis, in addition,a fixed
factor (e.g., land, resources, etc.) which we do not include explicitly, since it is in
fixed supply to each province and immobile, but which receives the residualincome
afterlabourandcapitalhave been paid. Labourandcapitalareassumedto obtaintheir
marginalproducts,andthe residualgoing to the fixed factorwill be termedthe rent.21
The rentcould differ from one province to the next because of eitherdifferingfactor
supplies or differing technologies or productivities.We need not be too explicit in
explainingthe source of regional disparities. Provinces are taken to be price-takers
and outputsare normalizedto have unit prices as before.
We considerthe special case in which all personsareidenticalandperfectlymobile
betweenprovinces. In addition, each person is assumedto own the same proportion
of the nation's resources. In particular,each person owns one unit of labourand a
portion 3 = 1/N of the nation's capital and fixed factors, regardlessof where he
resides. We are thus assumingaway foreign ownership.Differentassumptionscould
be made, of course, but at the expense of some simplicity. Provincialgovernmenti is
assumedto provide a pure public good Gi and to financeit by proportionaltaxes on
19 See the discussion in McGuire (1974) and Berglas (1976).
20 Insteadof using an aggregateproductionfunction we could have followed the tradeliteratureand
adopted, say, a two-sector Heckscher-Ohlin-Samuelsonmodel, possibly amendedto include
resourcesas in Copithore (1979). This elaborationof the productionside is not undertaken,since it
does not affect the qualitativeresults derived here.
21 It is naturalto thinkof this rent as accruingto naturalresources,but the termis much moregeneral. It
applies to any factor fixed in supply to a province. It could also include social capital as analysed
by Usher (1977).
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624 / Robin Boadway and FrankFlatters
labourincome at the rate ti, on propertyincome at the rate mi, on locally generated
rentsat the rate xi, and on local capitalreturnsat the rate zi. Thus, ti and mi may be
thoughtof as residence-basedtaxes while xi and zi are source-basedtaxes.
Individualsobtain utility from the private good and the provincialpublic good.
The per capita consumption of the private good in province i is determinedby
after-taxincome:
Xi = fi(1
-
ti) + 1(1
mi)[Rl(1 - xl) + R2(1 - x2) +
+ fK2(1 -2)(K
fK'(1
- zl)K
- K1)],
(13)
where Ri is the rent generatedin province i and, by assumption,is given by:
(14)
KifK(Li, Ki).
Ri(Li, Ki) = f (Li, Ki)
LifLi(Li, Ki)
Note that dRidJLi=
LifLLi KifKL1and dRid/Ki =
KifKK LifKLi.These are
of ambiguoussign. We have also assumedthatthe total stock of capitalin the nationis
fixed at K and the return to capital is determinedendogenously. An alternative
approachwould have been to allow foreign capitalto come in at a given worldrateof
return.The analysis is similar in this case.
Provincial governmentexpendituresare financedentirely by taxes in this 'real'
economy. The governmentbudget constraintis given by:
Gi = tifLLi + mi[P]Li,L + xiRi + zifKiKi,
(15)
wherethe P denotestotalpropertyincome acrossprovincesandis given by the termin
square brackets in (13). Substituting(15) into (13) we obtain the expression for
privategoods expenditureswith the governmentbudget implicitly accountedfor:
Xi = fL + PP + xiRilLi + zif'Ki/Li
-
Gi/Li.
(16)
Notice that ti and mi have disappearedfrom this formulation. The reason is as
follows. First, ti and mi are essentially perfect substitutesin this model. Both are
taxes levied on the basis of residency and, other than influences on the migration
decision, thereareno disincentiveeffects associatedwith them (e.g., laboursupplyis
fixed). Next, from the point of view of (15) and (16), these residency-basedtaxes are
essentially budget-balancingitems that disappearedwhen (15) was substitutedinto
(13). In the following analysis, the amountof residency-basedtax collected is that
residuallyrequiredto balancethe budget. Whetherti, mior some combinationis used
is irrelevant.One could also interpretthe general retail sales tax as equivalentto a
uniformincome tax in this model.
Equilibriumin a two-provinceeconomy will be characterizedby the simultaneous
satisfactionof a migration equilibriumcondition and a capital marketequilibrium
condition. Under free migrationthe formeris given by:
ul[L1 + P1P+ xlR1/L1 + zlfKK/LI - G1/L1,G1] = U2V2 + -3P
+ x2R2/(N - L1) + z2fK2(K - K)/(N - L) - G2(N - L1), G2].
(17)
where L1 and K1 are the labourand capital supplies in province 1, and the residuals
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Efficiencyand equalizationpayments/ 625
N - L1 and K - K1 are factorsupplies in province2. The capitalmarketequilibrium
requiresthatthe net-of-capital-taxreturnto capitalbe the same in bothprovinces, or:
fK'(1 - Z1)= fK2(1 -
Z2).
(18)
These two equations include two unknowns, L1 and K1. If there is a unique stable
equilibrium,and we have alreadyseen how unlikelythis is in underpopulatedregions
in the absence of migrationcosts, then we could solve (17) and (18) for L1 and K1 as
functionsof the tax and expenditurevariables.
A completecharacterizationof equilibriumalso requiresa descriptionof provincial
tax and expenditurepolicies. At the theoreticallevel there appearto be conflicting
influences at work. On the one hand, the literatureon tax competitionamong local
governmentssuggests that provinces have an incentive to undertakeinefficient tax
cuttingor the provision of subsidies in orderto attractfactorsof production.22On the
otherhand, the theoryof tax incidencesuggests thatgovernmentshave an incentiveto
overexpandsince part of the burdenof marginaltax collections will be shifted to
non-residents.23This is also at the basis of a recent argumentby Starrett(1980) that
local governmentsmay undertakegreaterthanoptimalpublicexpendituresin orderto
attractlabourinefficiently.24A complete investigationof this subjectwould lead us
somewhatastrayfromthe mainpoint of our analysis, so we shall simplypointto some
general conclusions that have emerged from the analysis of the recent literature.25
The first point is that there seems to be no general presumptionthat strategic
behaviour of provincial governments will tend to cause them to overspend or
underspendon public goods to attractlabouror capital. In a quite generalmodel of
this sort Boadway (1982) has shown that it is optimalfor provincialgovernmentsto
follow the Samuelson rule for the provision of public goods - a province can do no
better by behaving strategically than by behaving myopically in this regard. The
effects of strategicbehaviouron the choice of tax policies are more ambiguous.The
choice of taxes on rents and capitalincome (both source-basedtaxes) will dependon
the balanceof two conflicting forces. First, tending to increase such tax rates, is the
fact thatthey arepartiallyincidenton non-residents;second, workingin the opposite
direction, is the fact they will tend to induce immigrationfrom other regions, thus
dilutingthe existing residents'shareof publiclycollected rentsandincomefromtaxes
on capital. In the case of capital, thereis the additionalconsiderationthatincreasesin
capitaltaxes will cause the province to lose capital.
From a social point of view, we are interested in comparing the equilibrium
22 See Boskin (1973) and Pauly (1973). See also the discussion of source-basedtax competitionin
Helliwell (1977).
23 This would be an implicationof the theory of interjurisdictionaltax shifting as discussed, say, in
McLure(1970).
24 He argues that this will be the case if local governmentsfinanceexpendituresby directtaxationon
residents. The incentive is alleged to be the other way, however, if propertytaxationis used. The
analysis of Boadway (1982) takes issue with those results.
25 See Boadway (1982) and Lange (1982) for more complete analyses. A referee has pointed out to us
that the discussion of taxation and public goods is paralleledby the analysis of educationand
taxationin the braindrainliterature.For a treatmentof this topic see, for example, Bhagwati(1976).
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626 / Robin Boadway and FrankFlatters
interprovincialallocationof resourceswith the efficient allocationof resources.One
can show thatthe allocationof resourcesthatmaximizesper capitautility, given that
free migrationexists, will be characterizedby the following:26
LiuGi -uxi
= 0
i = 1, 2,
(19)
fK1 = fK2,
(20)
fL1 - X1 = fL - X2.
(21)
The first of these is just the Samuelson condition for public goods. We have
alreadyindicatedthatboth provinces will satisfy this if behavingoptimally. Furthermore, they will continueto behave optimallyif the public good is impurein the sense
discussed earlier.
The second condition, equalityof the marginalproductsof capital, is requiredfor
productionefficiency. From (18) we see it will be satisfiedonly if zl = Z2.However,
zl and Z2are determinedindependentlyby each province, and it would only be by
chance that provinces choose zl = 22.27 Therefore, the efficient capital allocation
conditionis unlikely to be satisfied.
Finally, condition (21) is similarto thatobtainedin our simple model for optimal
labourallocation. It statesessentially thatlabouroughtto be allocatedover provinces
in such a way thatthe social benefit of having an additionalworkerin each region is
equalized. An alternativeform of expression is to substitutefor X1 and X2 from (16)
into (21) to yield:
G1
XlR1
L1
L1
ZlK1K1l
L1
G2
x2R2
Z2fK2K2
L2
L2
L2
(22)
This optimalityexpressionhas a similarinterpretationto thatof ourearliermodel (see
the discussion following equation (10), above). The first term Gi/Li representsthe
fiscal externality.In the more generalcase of impurepublic goods it becomes Gi(1 a)lLi so thatif a = 1, the fiscal externalitydisappears.The secondtermrepresentsthe
rent-sharingterm as before, while the last term representsper capita capital tax
collections. Even if xi and zl are identicalin the two provinces, these termswill not
disappear(unless they equal zero). In general, there is no reason to believe that
equation (22) will be satisfied by provinces' independentlychoosing xl and zi. It
mightbe noted as well thatthe residence-basedtax rates ti and mido not appearin this
efficiency condition. That will turn out to be of some significance in discussing
appropriatefederal governmentpolicy.
In orderto achieve nationalefficiency in interprovincialresourceallocation, the
federal government would need two policy instrumentsto correct for the two
distortions arising from decentralized public sector decision-making. The first
26 The problemis to maximize u(Xi, G1) subjectto u(X1, G1) = u(X2, G2) and L1Xi + (N L1)X2+ G1 + G2 = f'(L, K,) + f(N - L1, K - K1).
27 Furthermore,if there were perfect mobility of capital internationally,zl and z2 would have to be
zero for efficiency.
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Efficiencyand equalizationpayments/ 627
distortionis that arising from interprovincialdifferences in taxes on capital (lack of
fulfilmentof equation(20)). This could be difficultto eliminate,except by imposinga
discriminatorytax on capitalincome in the provincewith the lower capitaltax rate, zi
so as to equalize the marginalproductsof capitalin the two provinces. An alternative
would be to impose or come to some agreement on a scheme of capital tax
harmonization.
The second policy instrumentcould be a system of transfersfrom the residentsof
one province to those of the other, so that equality (21) would be satisfied. In the
general case of impure public goods the aggregate size of the transferfrom 1 to 2
would be such as to satisfy:
+ S G2(1 - a)- x2R2 z2fK2K - S
Gl(1 - a)-x x lR-fK1Kl
(23)
L2
L1
Or, equivalently,
L1L2 G2(
1 - a)
Gl(l - c)
x
xlR1
X2R2
+ (zlfK'KL zz2f2K2)1
J
LI L
2
(24)
The latter equation is similar to (12) derived in our simpler model. The only
differences are: (1) the addition of a new term representingthe differences in per
capitacollections of capitaltaxes, and (2) the modificationof the rentdifferentialterm
to indicatethatit is only publicly collected rents (in this case throughrenttaxes) that
createdistortionin interprovincialmigration.
The 'equalization'transfercould be thoughtof as consisting of three parts. The
firstis the difference in the fiscal externalitybetween the two provinces. This is not
readily measurable since ac is not observable. Such evidence as we have would
suggest that atis close to unity, in which case this termwould disappear.Thatleaves
the lattertwo terms, the difference between provincialper capita tax collections on
rents and on capital. We shall refer to these terms together as the per capita
source-based tax collections. National efficiency considerationswould dictate that
these actualtax collections be fully equalized. Note thatit is not the tax capacitiesthat
should be equalized but actual taxes collected.
Thereare several difficulties associatedwith pursuingfull equalizationaccording
to (24), even ignoring the fiscal externalityterm. Most of them revolve aroundthe
constitutionalissue of how much independenttax raisingpower the provincesought
to have. The greateris the power of the provincesto choose theirpreferredtax mix,
the greaterwill be the efficiency cost of a federalsystem of governmentas opposedto
a unitaryone. Under full equalization, the provinces would have little incentive to
levy taxes on capital or rents at all, since these revenues would be equalized over
provincesanyway. This would indeedbe an efficient solution, especially withrespect
to capital. If our model had internationallymobile capital at given interest rates,
efficiency would dictatehaving zi = 0. The case with rents is more suspect. For one
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628 / Robin Boadway and FrankFlatters
thing, aside from the interprovincialmigrationeffects, rent taxes are efficient taxes
and we would not wish to remove all incentive to use them by the province. Also, a
constitutionthat in fact gives full ownership of resources to the provinces would
inevitablybe in conflict with a scheme of equalizingthose rentsdespitethe efficiency
costs of not equalizing. At some point the conflict between decentralizationand
efficiency must be resolved. As we have indicatedelsewhere (BoadwayandFlatters,
1982), considerationsof equity help us to find a resolutionof this issue.
So far our analysis concludes that there is no need to equalize residence-based
taxes; aside from the fiscal externality, it is only interprovincialdifferences in per
capitasource-basedtax collections thatneed be equalizedto achieve efficiency. The
reason that residence-based tax collections are not included in our equalization
scheme is simple to explain. Residence-based taxes are simply payments from
provincialresidentsto themselves. Since all persons in a provinceare assumedto be
identical,all pay the same residence-basedtaxes andall receive an equivalentamount
backin the formof provincialgovernmentservices. Therefore,residence-basedtaxes
do not affect interprovincialmigrationunderour assumptions.As soon as we allow
for a heterogeneous labour force and some redistributivebehaviourof provincial
governmentsin theirtax-expendituredecisions, however, residence-basedtaxes will
affect interprovincialmigrationand will enterinto the equalizationformula.We turn
to this analysis in the next section.
Heterogeneouslabour / We now assume thatworkersdiffer in theirincome-earning
abilitiesand thatprovincialgovernmentspursueredistributivebudgetaryactivities;it
is no longerthe case that(aside from source-basedtaxes which we assumedto finance
equalper capitaservices) taxes paid by each residentof a provinceareused to finance
publicservices of equalvalue. As we shall see, the exact natureof these redistributive
activities will determinethe ideal equalizationscheme. Therefore,it is importantto
startwith some specific assumptions.
We begin by assuming that residence-basedtaxes in each province are proportional to each individual's income, while public services, assumed to be of a
quasi-privatenature,aredistributedon an equalper capitabasis. The net effect of the
provincialfiscal structuresis thereforeprogressive.
The real income for a citizen includes both the real value of private goods
consumed and of publicly provided goods and services. Retaining our fixed price
assumption,the real income for citizen j in one of the provinces may be written:
Yi = (1 - t)PIj+ gj,
(25)
where PIjis his personal income from wages and property(fLj+ pj), gj is his public
sector benefits, and t is the proportionalincome tax rate. Under our assumptions
aboutthe provincial fiscal structure,per capita public services, g, may be written
g = tPiI+ xR/L + zfKK/L,
(26)
where PIis per capita personal income (from wages and property)in the province.
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Efficiencyand equalizationpayments/ 629
Substitutingthis into the expression for individualreal income, real income may
be written:
Yj = PIj + t(Pi PIj) + xRIL + zfKK/L.
(27)
The last threeterms representthe person's net fiscal benefits (NFBS)from provincial
fiscal activities in his province of residence. This NFB from provincialactivity now
comprisestwo parts:per capitasource-basedtax collections andthe net gain through
redistributiveincome-tax-financedservices (the term in t). For a person of below
averagePij, this latterterm is positive, and vice versa.
Now compareresidentsof provinces 1 and 2 who have identicalpersonalincomes
(PIj1 = PIl2). Their real incomes will differ owing to differences in the NFB from
provincial activity. Assuming both provinces have the type of fiscal structurejust
described,
Yj -j2
= (xlR1 + ZlfK1Kl)/L
-(X2R2
+ Z2fK2K2)/L2
+ (tiiil - t2PI2) + Pij(t2 - tl).
(28)
The firsttwo terms representthe difference in per capitasource-basedtax revenues.
We have already dealt with the appropriate(efficient) equalizationscheme to deal
with them. The next term reflects the fact that a higherper capitalevel of provincial
services can be financedat a given tax rate in a high income province. To the extent
that the high income province chooses to lower its tax rate this advantagewill be
diminished. On the other hand, the latter term shows that an individualat a given
income level will benefit through lower tax payments, if the fiscal advantage is
exploited throughlower taxes.
To consider the efficiency case for equalizationin this model, suppose now that
labouris costlessly mobile amongprovinces. The real income of personj is given by
(27) and this will be equalized over provinces by migration. Since gross property
income of a migrantis independentof province of residence, migrationequilibrium
will be given by:
PI1) + (X1R1 + ZIfK1Kl)/Ll
fL1 + tl(PIl
=fL2
+ t2(i2
- PI2)
+ (x2R2 + f2fK2K2)/L2.
(29)
Efficiency in the allocation of labourwill be given by fL = fL2. Equation(29) is
notcompatiblewith efficiency since the NFBS aretypicallynot equal;efficiencycan be
assured only if differences in NFB over provinces are eliminated. Even if these
interprovincialdifferencesin per capitasource-basedtax collections were eliminated,
therestill would be distortionarydifferencesin NFBS, owing to residence-basedtaxes
(the last two terms in (28) or the second term on each side of (29)). Suppose, for
instance, that both provinces levied the same personaltax rates (tl = t2). The NFB
difference due to residence-based taxes would be simply t(Pii - PI2) and would
represent the difference in per capita public sector benefits arising solely from
differences in residence-basedtax bases. Notice that the NFB difference is identical
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630 / Robin Boadway and FrankFlatters
over all income groups. Therefore the equalizationprogramthat is called for on
efficiency grounds is one that fully equalizes per capita revenues from both
source-basedtaxes and residence-basedtaxes.
This system of equalization has the following characterization.If provinces
behaveidenticallyex post, they will all providethe same level of publicservicesat the
same tax rates. Any differences in the ability to providepublic services at given tax
rates will be eliminated by the equalizationsystem. Our initial assumptionthat all
provinces levy the same rate of tax in the absence of equalization is, in fact,
unnecessary.The formulaused in actualequalizationschemes uses ex post tax rates
and so provincialbehaviourin the absenceof equalizationis irrelevant.Of course, if
provincesbehave differentlyex post, no system of equalizationcan achieve perfect
efficiency. The most that can be achieved is that equalizing both source and
residence-basedtax revenues will give provinces the potentialto provide the same
level of services at the same tax rates, thoughnot all will conform.Full equalizationin
this context would presumably use national average tax rates (like the present
system).
It should be noted, of course, that our results on equalizationof residence-based
taxes are sensitive to the way in which provincialbudgets are formulated.We have
used a special case in which provincial redistribution comes about through
proportionalresidence-basedtaxationand equal per capitabenefits, andthis may not
be far from the truth. It is reasonably straightforwardto deduce the sorts of
equalizationschemes that would be called for underdifferentpatternsof provincial
redistribution,and we shall not do so here. Suffice it to say that if provincial
governmentsare more (less) redistributivethan we have assumed, a greater(less)
degree of equalizationis called for.
CONCLUDING
REMARKS
In this paperwe have investigatedsome of the efficiency implicationsof models of
fiscal federalismfor the design of interprovincialequalizationschemes. Severalkey
points have emerged from the analysis. First, one cannot expect in general that
migrationdecisions takenby individualsin a decentralizedfederaleconomy will lead
to an efficient allocationof labourover provinces. Not only can the migrationprocess
be locally inefficient (in the sense of not satisfying the first-ordersocial efficiency
conditions), it may well also be globally inefficient. Second, self-interested
provincialgovernmentsacting on behalf of their residentshave an incentive to take
budgetaryactions that, from a national point of view, lead to inefficiencies and
inequities. Finally, the federal government faced with the inefficiencies and
inequities arising out of individual and provincial governmentbehaviour will be
justified in using a system of equalizationpayments as a policy instrumentin the
pursuitof nationwideequity and efficiency.
The specific form the equalization formula should take will depend upon the
mannerin which the economy is presumedto operate. Our analysis was carriedout
for a particularset of assumptions. Prices were assumed fixed, provinces were
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Efficiencyand equalizationpayments/ 631
assumedto provide equal per capita benefitsof a quasi-privatesort to residents, and
residence-basedtaxes were assumed to be incident on residents in proportionto
income. Furthermore,provinces were assumed to behave in similar ways. Under
these assumptions,the ideal equalizationscheme from an efficiency point of view is
one that fully equalizes all provincialtax revenues per capita.
As we have shown elsewhere (Boadway and Flatters, 1982), on equity grounds,
full equalizationwould also be desirableif the federalgovernmenttook the view that
horizontalequity demandedthatpersons in identicalpositions before provincialand
federal governmentbudgets should be so afterwards.Full equalizationeliminates
differences in NFBSover provinces and allows verticalequity to be achieved via the
progressive income tax. The other view of horizontal equity is that the federal
government should take as its starting point the post-provincial government
allocationof realincomes. If so, equalizationneed be appliedonly to a proportionr of
source-basedtax revenues, where r is the overall averagefederalmarginaltax rate.
No equalizationof income tax revenues would be called for. Notice thatthis scheme
is neitherefficient nor horizontallyequitablein the above broadersense.
The implicationsof other assumptionsaboutthe economy for equalizationcould
easily be workedout using the argumentsof this paper. The variabilityof outputand
inputpricescould be allowed. This would requirea carefulconsiderationof incidence
effects of varioustaxes. Othermethodsof getting at the rentsof provincialresources
could (andshould)be includedin the equalizationformula.These includethe passing
on of 'rents'to provincialresidentsby lower prices (as hydroutilitiesmaydo), andthe
collection of rents as profits of Crown corporations.As already mentioned, other
provincialgovernmentredistributiveassumptionscould be made. Otherprovincial
taxes could be explored more explicitly, such as indirecttaxes and propertytaxes.
It ought to be remarkedthatour analysis is of a long-runnature.Thatis to say, we
are comparingallocationsof resourcesin situationsin which the labourmarketis in
equilibrium.In practice, there may be two difficulties with this approach.First, the
allocationof labourobservedin the absenceof equalizationmay be out of equilibrium
in the sense that, say, labourin a 'have-not'region may not have had time to adjustto
the opportunitiesin the 'have' region. The process of migrationtakes time and our
analysisonly partlycapturesthatelement in ourcost of migrationtermm. If this is the
case, a scheme of equalizationwill, on the one hand, slow down the pathof migration
from the have not region, but, on the other, will ensure that the path will take the
economy to the correct long-run allocation. Second, if the labour market is in
equilibriumto begin with, albeit an inefficient one, the introductionof equalization
will cause a move to a new equilibriumonly aftera periodof adjustment.Ouranalysis
does not incorporatethe dynamics of adjustmentof the labour market from one
equilibriumto another.We would conjecture,however, basedon existing analysesof
adjustmentcosts (e.g., Mussa, 1978), that the introductionof dynamic considerations would not affect the policy prescriptionfor equalization based on long-run
analysis.
Finally, virtually all our discussion of equalization concerns the correctionof
marginal inefficiencies of migration. As discussed in the second section, the
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632 / Robin Boadway and FrankFlatters
migration process is liable to be globally inefficient as well. Future research could
fruitfully consider the implications for intergovernmental transfers of global
inefficiency in underpopulated economies.
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