THE ROLE OF THE SERVICE SECTOR IN THE
PROCESS OF INDUSTRIALIZATION
by
Mukesh Eswaran and Ashok Kotwal
University of British Columbia
1st June, 2000
INTRODUCTION
² Is high agricultural output (per capita) a help ora hindrance to industrialization?
{ The historical evidence is mixed: the Industrial
Revolution in Britain; Canadian development andthe Staple Theory of Growth.
{ Matsuyama (1992) gives examples of agricul-turally deprived countries that became leading in-
dustrial nations
² Trade-o®: high per capita agricultural output im-plies high wages but it also means high domestic
demand for industrial goods.
{ high wages work against the emergence of an in-
dustrial sector that could withstand internationalcompetition.
{ high domestic demand is conducive to the emer-gence of an industrial sector in a closed economy
² The land-surplus countries of North America de-veloped through growth ¯nanced by primary ex-
ports
{ Staple Theory of Growth argues that primary
exports spearhead growth of industrialization
² Matsuyama (1992) provides model capturing thetrade-o® stemming from high agricultural produc-
tivity.
{ in a closed economy, high agricultural output
aids industrialization through the creation of in-
dustrial demand and, once an industrial sector
is created, industrial productivity grows through
learning-by-doing.
{ in an open economy, on the other hand, a coun-
try with comparative advantage in agricultural
goods may never industrialize unless government
protects its nascent industry
² Matsuyama's model does not explain how indus-trialization occured in some countries despite fee-
ble attempts at protecting its nascent industry
(e.g., Canada); his model embodies the linkages
from the demand side but not those on the supply
side
² We build a model that explicitly takes into ac-count the supply side linkages that the Staple
Theory deems important
{ speci¯cally, we focus on the role of the service
sector in the process of industrialization.
{ we focus on non-traded services (e.g., construc-
tion, transportation, distribution, credit and in-
surance)
{ many of these are both consumer and producer
services; `construction' includes the construction
of both homes and factories, `transportation' moves
both passengers and cargo
² Expansion of the service sector bene¯ts the in-dustrial sector by (i) enabling greater specializa-tion and division of labour [Jones and Kierzowski(1988 ), Francois(1990)], and (ii) by lowering thee®ective costs of service inputs to industrial pro-duction; we focus on the latter.
{ the greater the variety of competing services,the lower are the e®ective costs. This is becausegreater variety a®ords greater °exibility to pro-ducers in minimizing the cost of producing a givenlevel of output.
{ income growth, whether as a result of primaryexport growth or some other exogenous reason,will lead to a larger service sector and hence to anindustrial sector that is better able to withstandinternational competition.
² Thus a primary exporting economy can industri-alize without having to resort to protection.
{ this part of our paper can be viewed as a modelof the Staple Theory.
² We show that the three-sector model yields inter-esting results:
(a) growth in the primary sector productivity of
a small open economy (SOE) may lead to the
emergence of a domestic industrial sector
(b) a decline in its terms of trade may lead to the
emergence of a domestic industrial sector even
when comparative advantage remains with agri-
culture
(c) industrialization will be accompanied by a sharp
increase in the welfare of the representative con-
sumer (RC)
(d) between two SOEs, the one with the smaller
land-to-labour ratio could achieve a higher welfare
for its RC.
THE MODEL
² It is assumed that services are non-tradeable, whilethe outputs of agriculture and manufacturing are
tradeable.
² Factor endowments of the LDC: land and labour.Let L0 denote the labour force ( population) and
H0 its stock of land.
{ land distribution is egalitarian: agent owns an
amount (H0=L0).
Consumption Side
² Preferences are non-homothetic
{ consumers spend all of their income on food
(grain) until they have had a su±cient amount,
G, and at higher levels of income they spend all of
their additional income on manufactures (M)and
an aggregate of services (S).
² The preferences over M and S of a consumer
who has had G units of grain to consume is rep-
resented by the utility function:
U(M;S) =M1¡®S®; 0 < ® < 1: (1)
The aggregate S comprises a bundle of n ser-
vices, Si; i = 1;2; :::; n, (such as transportation,
refrigeration, etc.).
² We assume that the aggregator S is given by theconstant elasticity form:
S =
24nX
i=1
(Si)®
351=®
: (2)
{ hereafter, this aggregate input is referred to as
`Service'.
² Grain is the numeraire. Denote the income of
a RC by y. If y � G, the consumer's demand
for the goods, denoted, respectively, by Gd,Md,and SCdi = 0; i = 1;2; :::; n; are
Gd = y; Md = 0; SCdi = 0; i = 1;2; :::; n: (3)
If y > G, the consumer's demand function forgrain is given by Gd = G; those for manufacturesand the various services are given by the solutionto:
maxM;fSig
U(M;S) s:t: y¡G ¸ PmM+nX
j=1
pjSj ;
(4)where Pm is the price of manufactures and pj ; j =1; 2; :::n; is the price of the jth service. Sincemanufactures are tradeable but services are not,Pm is given by the world market while the pj areendogenously determined.
² The consumer's demand functions, SCdi andMd,respectively, can be shown to be:
SCdi =(pi)
¡µPnj=1(pj)
1¡µ®(y ¡G); i = 1; 2; :::; n;
Md = (1¡ ®)(y ¡G)=Pm; (5)
where µ ´ (1¡ ®)¡1.
{ the consumer spends a fraction ® of her incomein excess of G on services and the rest on manu-factures.
Production Side
² Grain production requires land (Hg) and labour(Lg), and the production function is Cobb-Douglas:
Gs = A(Lg)°(Hg)
1¡°; 0 < ° < 1; (6)
where A denotes the total factor productivity inagriculture.
² Manufacturing uses labour (Lm) and Service (Sm)in ¯xed proportions:
Ms = BminfLm; Sm=¹g; (7)
where B is the total factor productivity in man-ufacturing and ¹ (> 0) is the Service-to-labourratio.
² The agricultural and manufacturing sectors areperfectly competitive.
² If w denotes the wage rate of labour, v the land
rental rate, and pS the price of the aggregate
service, the cost function for grain is:
CG(w;v;G) = KGw°v1¡°G; (8)
where KG ´ °¡°(1¡ °)¡(1¡°)=A, and that formanufactures is
CM(w;pS ;M) = (1=B)(w+ ¹pS)M: (9)
² The price, pS, of Service in terms of those of theindividual services is:
pS =
0@nX
i=1
(pi)¡®µ
1A¡1=(®µ)
: (10)
{ we can interpret pS as the price index of all
services.
² If the manufacturing sector produces an outputMs, the conditional demand for Service is ¹Ms=B,
and the conditional demand, SMdi , for service i;
i = 1; 2; :::; n; can be derived as:
SMdi = ¹
Ms
B
(pi)¡µ
³Pnj=1(pj)
¡®µ´1=®: (11)
² Each service is produced by a single producer, andthe service sectors are monopolistically competi-
tive.
{ services are produced using only labour and pro-
duction requires the incurrence of a ¯xed cost, F
(in units of labour), and ¾ units of labour to pro-
duce one unit of any service.
{ the price of each service will not equal MC
because the service industry is monopolistically
competitive.
² If the aggregate income of the economy is Y ,the aggregate demand, SAdi , for service i; i =
1; 2; :::; n; from consumers and manufacturing is
given by
SAdi =
2664®(Y ¡GL0)Pnj=1(pj)
1¡µ +(¹=B)Ms
³Pnj=1(pj)
¡®µ´1=®
3775 (pi)
¡µ:
(12)
² Themonopolistic producer of service i; i = 1;2; :::; n;solves
maxpi
(pi ¡ ¾w)SAdi ¡wF: (13)
{ as is standard in models of monopolistic com-
petition [Dixit and Stiglitz (1977)], each producer
is assumed to take the expression in the square
bracket of (12) as parametric.
{ the optimal price for service i; i = 1; 2; :::; n; is
pi = ¾w=®; (14)
a standard result which says that each producer
marks up the price over MC by the factor (1=®¡1).
{ if LDC does not produce manufactures, the sec-
ond term in (12) will be absent, but the optimal
price of service stays the same.
² The price of the aggregate service, pS, given by(10) reduces to
pS =¾w
®n1=(®µ): (15)
{ the larger the number of services available, the
lower is the price of Service
THE GENERAL EQUILIBRIUM
Specialization in Agriculture
² Suppose LDC specializes in agriculture
- consumption of manufactures are ¯nanced by
grain exports, and services are produced only for
consumption.
² Must determine the allocation of labour betweenthe agricultural and service sectors, the factor
prices, the number of services produced, and the
consumption levels of grain, services, and manu-
factures.
² Since only agriculture uses land, we will haveHg =H0 in equilibrium.
{ the remunerations of labour and land, respec-
tively, are given by their marginal products in the
grain sector, which depend on Lg:
w(Lg) = A°(H0=Lg)1¡°; v(Lg) = A(1¡°)(Lg=H0)°
(16)
For a given Lg, the aggregate income in the econ-
omy given by
Y (Lg) = L0w(Lg) +H0v(Lg): (17)
At this income level, the aggregate demand for
labour from the service sector, LdS(Lg; n), is given
by
LdS(Lg; n) = nF +®2
w(Lg)[Y (Lg)¡GL0]: (18)
² The labour market clearing condition may thenbe written as:
Lg +LdS(Lg; n) = L0: (19)
{ the solution to (19) determines the labour em-
ployed in agriculture, Lg(n), as a function of the
number of services being produced.
² To determine the number of services produced,invoke zero pro¯t condition in each service sector.
{ setting pi = ¾w=® for all i in the objective func-
tion of (13), the zero pro¯t condition becomes:
®¾[Y (Lg(n)) ¡GL0]n¾µw(Lg(n))
¡ F = 0: (20)
{ this condition determines the number of ser-
vices, n¤, that will be provided in equilibrium.
{ the per capita income in this equilibrium is given
by y = Y (Lg(w(n¤))=L0. Each agent's con-
sumption of (imported) manufactures and domes-
tic services can now be obtained.
² The supposition that the LDC specializes in agri-culture may be incorrect.
{ if so, at the equilibrium computed above, man-
ufactures can be can pro¯tably produced, that is,
Pm will exceed the LDC's MC of producing man-
ufactures.
{ if this is so, the economy is necessarily diversi-
¯ed and the GE has to be computed anew.
Diversi¯ed Economy
² Let G(Lg) denote the amount of grain producedby LDC when Lg workers are employed in agricul-ture.
{ the di®erence between the production and con-sumption of grain, [G(Lg) ¡ L0G], is exportedand these exports will ¯nance the import of anamount, [G(Lg) ¡ L0G]=Pm, of manufactures.Consumers spend on manufactures a fraction (1¡®) of their income in excess of G, that is, theyconsume an amount (1¡ ®)[Y (Lg) ¡GL0]=Pmof manufactures.
{ the di®erence between domestic consumptionand imports of manufactures yields the amount ofmanufactures, Ms(Lg), that is domestically pro-duced:
Ms(Lg) =n(1¡ ®)[Y (Lg)¡GL0]¡ [G(Lg)¡L0G]
o
(21)where, for brevity, only Lg has been retained asan argument on the left hand side.
² For a diversi¯ed economy, the demand for serviceswill come from consumers and from the manufac-turing sector.
{ if Ms(Lg) is the output of manufactures, theservice sector demand for labour now becomes:
LdS(Lg; n) = nF+®2
w(Lg)[Y (Lg)¡GL0]+¾
Ms(Lg)
Bn1=(®µ):
(22)
² Manufacturing demands labour directly for pro-duction and also indirectly, through its use of ser-vices.
{ if Lm(Lg) is the amount of direct labour de-manded by this sector when its output isMs(Lg),from ¯xed coe±cient production function it fol-lows that Lm(Lg) =Ms(Lg)=B.
² The labour market clearing condition which re-places (19) now is given by
Lg + LdS(Lg; n) +Lm(Lg) = L0: (23)
As before, the solution to the above equation
yields the amount of labour employed in agricul-
ture in terms of the number of services, Lg(n).
² The equilibrium value of n is obtained from the
zero pro¯t condition for service producers:
1=(®µ)¾
"®2(Y (Lg(n))¡GL0)n¾w(Lg(n))
+ ¹Ms(Lg(n))
Bn1=®
#¡F =
(24)
As before, all the endogenous variables of interest
can now be obtained.
RESULTS
² We present some simulation results of the modelset out above. Intuition is robust.
² First consider the e®ects of (exogenous) agricul-tural productivity growth on the GE.
{ Figure 1 (a) depicts the e®ect on the utility
of a RC. Parameters are such that even at low
values of the agricultural TFP, A, the LDC has
comparative advantage in agriculture.
{ as A increases, the RC spends her higher in-
come on imported manufactures and nontraded
services.
{ at a su±ciently high value of A, the economy
acquires comparative advantage in manufactur-
ing.
{ the higher consumer income increases the va-
riety of services produced, as seen from Figure 1
(b).
{ this reduces manufacturing costs, as the greater
variety of services reduces the price of Service
(Fig.1 (c)).
{ cost reduction enables the manufacturing sec-
tor to come into existence, despite international
competition.
{ this contrasts with the result of Matsuyama's
(1992) learning-by-doing model, where agricul-
tural productivity growth in a SOE can only re-
duce the growth rate of industry
{ Figure 1 (d) shows extreme scenario where the
SOE reverses its comparative advantage and be-
comes an industrial exporter.
² Transition is accompanied by a discrete increasein the RC's utility.
{ when the manufacturing sector becomes viable,
its demand for services augments that from con-
sumers, leading to a discrete increase in the va-
riety of the services produced and an increase in
the RC's utility.
{ further e®ect: the larger volume and variety of
services draw away labour from agriculture, in-
creasing its marginal product and the utility of a
consumer.
² Even while exporting manufactures, the SOE con-tinues to produce some agricultural output
{ further increases in agricultural productivity raise
the RC's utility as expected.
{ however, the higher wages shrink the size of
the manufacturing sector (consistent with Mat-
suyama's claim) and thereby reduce the industrial
demand for services. So variety of services pro-
duced declines.
² After the transition, increases in agricultural pro-ductivity increase the domestic consumption of
manufactures while domestic production declines.
So, exports of manufactures decline (Fig. 1 (d)).
{ when agricultural productivity is su±ciently high,
the economy's comparative advantage reverts back
to agriculture.
² The discrete increase in the RC's utility, as shownin Fig. 1 (a), is caused by the emergence ofthe industrial sector rather than by the reversalin comparative advantage.
{ it is very likely that the emergence of a domesticindustrial sector is not accompanied by a reversalof comparative advantage but only by a reductionin the imports of manufactures (Fig. 2(b)).
² When agricultural productivity is su±ciently high,Figure 2(a) shows, paradoxically, that there is adiscrete fall in the consumers' utility.
{ this extreme scenario occurs because the man-ufacturing sector shuts down due to very highwages and there is a discrete decline in the num-ber of (non-traded) services produced, which hurtsconsumers.
{ such an outcome is not possible in standardtrade models of SOEs, where an increase in theproductivity of a domestic sector cannot lower theRC's utility.
² The e®ect of an increase in the relative price ofmanufactures (Pm) on the well being of the RC
is shown in Fig. 3. (Economy with a comparative
advantage in agriculture.)
{ as Pm increases (i.e., the country's terms of
trade decline), the RC's utility ¯rst declines, then
discontinuously increases before continuing to de-
crease again. The discontinuous increase is caused
by the domestic industrialization. Over the entire
range of Pm depicted in the Figure, the economy
is importing manufactures.
{ in the Figure the RC's utility is lower at a point
like Z than at a point like X even though the terms
of trade at Z are less adverse than at X.
{ we cannot infer that a decline in a country's
terms of trade is necessarily to its detriment.
² In a standard trade model, an increase in Pmcould result in an increase in the well-being of
the RC only when it leads to a switch in the coun-
try's comparative advantage. At a point like Z the
country is exporting the agricultural good while at
a point like X it would be exporting manufactures.
{ in our model, by contrast, an increase in Pmcould make the RC better o® despite the fact that
the country continues to export the agricultural
good.
² Figure 4 displays the GE e®ects of increasing land-to-labour ratio.
{ these e®ects are similar to of an agricultural
productivity increase.
{ this peculiar behaviour of the utility of the RC
arises because there exists a range of intermedi-
ate values of the land-to-labour ratio for which
industrialization is viable.
{ industrialization is not possible below this range
because the per capita income is too low, and
above this range because the wage rate is too
high.
{ Sachs-Warner (1995): countries rich in natural
resources tend to grow more slowly than others.
CONCLUSIONS
² In this paper, we have examined how the servicesector impinges on the process of development of
a SOE.
{ the service sector's output is nontraded and pro-
duction exhibits scale economies
{ service sector is a link between consumption and
industrialization.
{ any increase in income leads to an increase in
the consumption demand for, and the variety of,
services; and this leads to a reduction in the cost
of manufacturing goods.
² We have demonstrated that at a high enough levelof agricultural productivity (and hence per capita
income), an industrial sector could become viable
even when the economy remains open.
{ agricultural productivity growth, therefore, can
lead to industrialization.
{ this is our formalization of the Staple Theory of
economic development [Watkins (1963)].
² Wellbeing of a RC can increase through two av-enues: through the increase in the variety (and,
hence, e®ective price) of the services available for
consumption, and the increase in income associ-
ated with a movement of labour out of agricul-
ture.
{ the emergence of an industrial sector adds a
quantum increase in the size of the service sector,
which in turn contributes to a discrete increase in
welfare.
{ the rapid increase in welfare in the East Asian
success stories may be due to causes such as
these.
² The service sector plays the same role in our ¯nd-ing that an adverse change in the terms of trade
for a primary exporting country could result in a
discrete increase in the welfare of a RC.
² We also ¯nd that, between two SOEs, the onewhich is relatively better endowed with land (that
is, with the larger land-to-labour ratio) can be
poorer in per capita terms, ceteris paribus.
² Paper makes stark assumption that industry usesservices as an input but agriculture does not.
{ but it is only essential that industry uses services
more intensively than agriculture.
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