Increasing returns and the shift from customs union to common market

Reglonal

Science and Urban

Economics

23 (1993) 315-335

North-Holland

Increasing returns and the shift from customs union to common market Earl L Grmols Department of Economics, Unrverszty oflllmozs, 483 Commerce West, 1206 South 6th Street, Champagn, IL 61820, USA Received

February

1992

This paper analyzes the welfare effects of presence of mcreasmg returns to scale, condition for gains 1s derived m terms increasing returns industries The theory countries As a percent of GDP, potential m the move to full common market are 07%

the shift from customs umon to common market m the either internal or external to the firm A sufficient of a weighted average of the output changes m the 1s applied to data from European common market gams from mcreasmg returns related cost reductions almost surely less than 2% and more hkely less than

1. Introduction The European Commission’s June 1985 White Paper sets out over 300 leglslatlve proposals as part of its timetable for creating by 1992 condltlons for an integrated internal market for the European Economic Community Unlike a customs union which allows free movement of goods between member states, the obJective of the Commission 1s comprehensive, covering free movement of goods, people, capital, and services - m short it IS a mandate for the creation of a true common market Benefits from the move are expected to come from better resource allocation between member states and better dlvlslon of labor, as well as gains from mcreasmg returns to scale m production and the associated benefits of larger integrated markets These are the same benefits which Canadians and Americans hope to receive from the ten-year implementation of the US-Canadian Free Trade Agreement begun m 1989, which also has provlslons for freer flow of factor services, people, and capital Both mltlatlves are only the most recent evidence of a longstanding desire to reap the full benefits of mcreased trade The interest m the economics of customs unions traces back at least 40 years to Jacob Vmer’s 1950 volume The Customs Unzon Issue After the 1958 Treaty of Rome established the Correspondence to Earl L Grmols, Department Commerce West, 1206 South 6th Street, Champaign, 016&0462/93/$06

00 0

1993-Elsevler

of Economics, IL 61820, USA

Science Publishers

University

B V All rights reserved

of Ilhnols,

483

316

EL

Grrnols,

Increaswg

returns

and the shaft from

customs unron to common market

European Economic Community, interest grew m the economics of all forms of preferential trading - customs unions, free trade areas, and common markets Moreover, the research devoted to preferential trading arrangements continued through the 1970s and 1980s as more countries have been added to the European original SIX ’ It now appears that free trade areas, customs unions, and common markets will continue to be a slgmficant, perhaps even the most significant, feature governing international trade m the coming decade and the first part of the next century With the above m view, the purpose of this paper 1s to fill two significant gaps m the literature First, m spite of the importance accorded m recent years to the role of increasing returns to scale m international trade there 1s no available theory that provides a sufficient condltlon for welfare gains from customs union expansion or ehmmatlon of barriers to factor movements within a customs union when increasing returns to scale (IRS) are present Kemp and Wan (1976) and Grmols (1981), for example, show that union expansion coupled with an appropriate external tariff and distribution of tariff revenues insures welfare gains for all union members under condltlons of perfect competltlon and convex production technology However, their results do not apply when production is subject to increasing returns to scale because technologies are non-convex dnd also because some forms of increasing returns to scale are mcompatlble with perfect competltlon Second, m cases where increasing returns ure taken mto account m the gains from trade literature the sufficient condltlons for gains relative to autarky that ‘The literature on customs union 1s too ldrge to review m this paper, prlmarlly focusmg on the welfare effects of union formation and muon enlargement, but a brief hlstory and a number of references which themselves summdrlze and contrlbute to earher work can be given Other questions Include how the union chooses its common external tariff m dn optimal manner [see Grmols (1986)], the role of capital flows m the umon formation proLess, and the Impact of Internal tariff adjustments on the external trade flows of umon countries Wmters (1986) surveys a number of quantltatlve studies relatmg to Bntam’s role m the European Economic Commumty Vanek (1962, 1965) and Kemp (1964, 1969) were apparently the first to note that the common external tariff may be chosen to hold the terms of trade with the non-umon rest of the world constant If this IS done, union formatlon IS non-harmful to the rest of the world and transfers internal to the union can be used to Insure that each union member gams Grmols (1981) used a revealed preference argument to cdkulate the needed transfers dnd showed that the sum of transfers equalled the tariff revenues collected by the umon as a whole A number of papers, mcludmg Berglds (1979), Collier (1979), Rlezman (1979), McMdlan and McCann (1981), Lloyd (1982), and Wooton (1986, 1988), exdmme how Issues such as country slmllarlty or dlsslmllanty, initial trade patterns, and relative size affect country benelits from umon formation Much of this actlvlty was devoted to explammg a multitude of different results dependmg on what assumptions were made about trade patterns Ethler and Horn (1984) consider the welfare effects of margmal preferential tdrlff reductions dnd margmdl tariff mod1ficdtion from an inltiai customs umon posItion They suggest the r-ed for dn extension of theory to Loses of scale economies and product differentldtion One of the assumptions made by a number of earlier papers including Berglas, McMdlan and McCann, Rlezman, Wooton and others, that will be relaxed m the present discussIon of shift from customs umon to common market in the presence of mcreasmg returns to scale, IS that trade hberahzatlon may change the volume but not the pattern of trade and that countries consume all goods though they need not trade m all goods

E L Grrnols, InLreasmg returns and the shft from customs umon to common market

317

have been derived depend on the assumption that the aggregate production set 1s convex or that factor usage 1s fixed between equlhbrla ’ Neither assumption 1s appropriate for expansions of the Europe 1992 type because European factor usage 1s not likely to be fixed after the changes are Instituted and because it 1s not known If the European production frontier IS convex As it turns out, both of the above problems can be addressed Elsewhere I have analyzed the condltlons for single-country gams from trade relative to autarky m the absence of the convexity assumption and the assumption of fixed factor use between equlhbrla 3 The present paper analyzes the condltlons for welfare gam m the move from customs union to common market for arbitrary equlllbrla with mcreasmg returns to scale present Both increasing returns to scale mternal to the firm and increasing returns to scale external to the firm are considered The mam conclusion of this paper 1s that if a partlculdr weighted average of the output of increasing returns to scale mdustrles expands m the move to common market, and an appropriate external tariff pohcy 1s followed, gams are guaranteed No assumptions or hmltatlons need be made concerning production convexity, factor usage, or trade patterns An apphcatlon of the rule m the last part of the paper using historical estimates of the degree of increasing returns observed over long time spans suggests that gains m the case of Europe from better utlhzatlon of increasing returns to scale alone are under 1 9% of gross domestic product (GDP) and probably less than 0 7% of GDP The paper proceeds as follows Section 2 presents the notation and the elements of the model Section 3 then provides a one-line proof of gams from the shift from customs union to common market m the neoclassical case where production exhibits non-increasing returns to scale The shortness of the proof 1s due to the particular formulation of the necessary and sufficient condltlon for welfare improvement using a selection of dual functions to frame the elements of the discussion The new framework also facilitates extending the analysis to deal with increasing returns to scale Section 4 considers the shift from customs union to a common market when there are increasing returns to scale present The mam result 1s proved m two steps First, it 1s shown that gams are guaranteed from the move to a common market d those mdustrles that exhibit increasing returns are enlarged by the umficatlon of the market and operate at positive profits Second, m the more likely case that some Increasing returns mdustrles decline and some expand, it is shown that an appropriately chosen weighted increase m outputs 1s sufflclent for welfare gams In essence, if the creation of a common market shifts resources out of the constant and decreasing returns ‘See Kemp and Neglshl Krugman (1985) Yirinols (1991)

(1970), Helpmdn

(1984), Markusen

and Melvin (1984), Helpman

and

EL

318

Grmols, Increasmg returns and the sh$ from customs umon to common market

to scale sectors, ratlonahzatlon m the increasing returns to scale sector guarantees welfare gains to union countries If resources are shifted out of increasing returns mdustnes, gams are still possible, but they are not guaranteed m all cases In the last part of section 4, as discussed above, the weighted average formula 1s applied to data from the Common Market for 1987 to gauge the size of gains that can be expected from greater exploltatlon of European economies of scale Section 5 ends the paper with some concludmg remarks 2. The model 2 1

Notation

Let P=(P,, Pf) be the domestic price vector (Pe R”B+“~), where ng 1s the number of goods that are freely traded across national borders m the orlgmal customs union equlhbrmm and n, 1s the number of factors (and/or goods) that are not tradable across national borders m the original customs union equlhbrlum but will become freely tradable between member countries m the common market equlhbrmm P, and P,, respectively, refer to the price subvectors correspondmg to the two sets of goods Because the n, goods are not traded m the customs union equihbrmm, we note that their prices across countries k, Pi, m general will differ m the customs union equlhbrmm Let t be the vector of specific common external tariffs and subsldles (TV R”g+“,) which relates domestic prices to world prices Q=(Qe, Qf), (QE Rng+“‘) For the nf goods that are not traded m the orlgmal equlhbrlum the correspondmg components of t can be arbitrarily set to zero For the ng goods that are traded, domestic prices are given by P, = Q, + t,, where subscript g refers to the subvector of traded goods Let X, Z Z and s2 (X, E: Z, 526 R”sfnf), respectively, be the consumption, production, trade, and endowment vectors A positive element of X represents consumption, while a negative element, say supply of labor, represents a commodity supplied to the market by consumers Z 1s a vector of excess demands, Z=X - Y-Sz For each variable, a superscript k will be used when the variable refers to a particular country k m the customs unions We sometimes will write Z=(Z,, Z,) where the partition corresponds to the partition m prices above Using the above notation, balanced trade for country k at world prices implies QZk = 0, and balanced

(1)

trade at domestic

prices implies

PZk = Tk,

where

Tk 1s

country

(2)

k’s share

of union

tariff revenues

Eqs

(1) and (2) also

EL

Grrnols, lncreasmg

returns and the shrf from customs utuon to common market

319

apply to the customs union as a whole, where umon trade Z replaces country trade Zk m the formulae For the union as a whole, Z = (Z,, Z,) = (Z,,O), and tariff revenues are given by T = t,Z,

(3)

Country welfare 1s measured by a strictly quasi-concave social utility function U= U(X) The income equals expenditure identity 1s given by e(P,U)=P(Y+Q)+7; where e(P, U) 1s the country income 4

22

mmlmum

(4) expenditure

function

and

P( Y +a) + T is

Welfare

For a fixed set of prices, P, the expenditure function e(P, ) 1s a monotonic transformation of utility W(X) = e(P, U(X)) 1s therefore an exact measure of social welfare for fixed P If Pm IS the set of prices prevailing the common market eqmhbrmm, the change m welfare 1s d W = e( Pm, Urn) - e( Pm, U”),

(5)

where U” and U” are utility levels m the common market and customs union eqmhbna, respectively Using the fact that e(Pm, U”‘) equals income m the common market equlhbrmm, and substltutmg from the above equations and ldentltles, (5) becomes AW=Ll+T+

T”-P”Z”,

(6)

where superscripts u and m refer to the value of variables union and common market eqmhbna, respectively, and production and consumption-related terms given by

Eq several change welfare utility,

m the customs L’ and r are

n = P”( Y” - Y”),

(7)

r = P”X” - e( Pm, Vu) ’

(8)

(6) is m the form that we will use Before turning to the analysis, remarks are m order First, expression (6) 1s an exact measure of the m welfare Thus A W >O 1s a necessary and sufficient condltlon for increase Second, by using the expenditure function to transform A W measures changes m dollar units If a dollar of welfare to member

4As 1x1eq (4) the use of country superscript k has been suppressed confusion 51t IS understood that U(X”) = U” and U(Xm) = U”

where this will not cause

320

E L Grmols, Increasmg returns and the shift from customs umon to common market

countries 1s considered equally socially valuable, then summing d W over member countries gives the correspondmg change m welfare for the customs union as a whole Finally, the terms m (6) place the mformatlon from convexity of preferences and perfect competltlon m discrete terms This slmphties comparative statics comparisons which depend heavily on the signs of n and r In particular, we recognize n as the increase m firm profits at common market prices over profits from choosmg original production levels r, m turn, 1s the cost saving from consumption substltutablhty Consumption bundle X” gives utlhty U” Since e(Pm, U”) 1s the least cost of attammg utility U” at prices P”, it 1s smaller than P”X”, the cost of buying bundle X” We state the followmg facts Lemma 1 If consumers straznt, then rz0, Lerrzma 2 17Z06

If firms

maxzmzze

maxzmzze

utzlzty subject

the value

oj

only

productzon

to the budget

at price\

3. Customs union to common market: The case of non-increasing

con-

P”, then

returns

We know from section 2 that countries moving from customs union to a common market experience welfare gains d and only if A W > 0, where A W IS taken to mean the sum of member country welfare changes If markets are competltlve, It can be shown that there exists an equlhbrlum with the total trade of union countries with non-members unchanged ’ Then AW-(II+r)=T”-P”Z”=T”-P$Z;=T”-P;Z;=O Apphcatlon of Lemmas 1 and 2 then proves that A W 2 0 becduse (fl + r) 1s non-negative If the union distributes tariff revenues after the shift to common market so that each member country k receives tariff revenues Tkm= PmZku, where Zk” IS country k’s trade m the original customs union equlhbrmm, then by the same argument each member country gains as well 8 We summarize this as Proposltlon 1 Proposztzon

1

Let the unzon countrzes

zn an znztzal customs

unzon equzlzbrzum

6Thls follows trlvlally from the fact that If P”Y” has mdxlmal value, It 1s no less than Pm Y” P”Y”, for example, has maxlmdl vdlue If markets are competltlve and firms have constdnt returns to scale ‘External trade 1s fixed by choosmg the common external tariff Existence of eqmhbrla with unchanged external trade can be proved usmg conventIona general equlhbrmm existence proofs as m Grmols (1981) Becduse II+rhO, sAt the country level, d W-(IZ+ F)= TX” -PmZk”=PmZku-PmZku=O country welfare rises The umon duthorlty has enough money to pay for the transfers because their sum over countries equals P”Z” = P”Z” = T”, the avallable tariff revenues

EL

Gnnols, Increasrng returns and the sh$t from customs umon to common market

321

move to a common market equlhbrlum where all n,+n,

goods are freely traded between the member countries and P” IS the n,+nf dlmenslonal vector of internal equdlbrlum prices in the common market equlllbrlum If (1) firms maxlmlze the value of production at market pnces, (2) aggregate external trade of the union is held constant by adjustment of the common external tar& and (3) revenues are dlstrlbuted to each member k accordmg to the formula PrnZkU, then the werfare of each country rises m the common market equlllbrlum Moreover, the sum of payments to members equals the tariff revenues collected by the union It 1s significant that the above result 1s able to compare two second-best trading equlhbrla It 1s doubly interesting because it can be proved m a single line and the dollar amount of gain, n+ r, depends on potentially knowable components The feature that the proposltlon falls to address, however, 1s the effect of increasing returns to scale m the move from customs union to common market Since increasing returns are not compatible with perfect competltlon, the assumption that the value of production 1s maxlmlzed at equlhbrmm prices must be replaced by another assumption for mdustrles and sectors that exhibit increasing returns Fortunately, if the effect of the shift to common market 1s to increase the scale of those firms that exhibit increasing returns, the assumption of value maxlmlzatlon can be replaced by the assumption of non-negative profits

4. The case of increasing returns

We now consider the posslblhty that some firms exhibit increasing returns to scale Because Lemma 2 does not apply to firms exhlbltmg increasing returns, it 1s necessary to find other condltlons that allow us to sign ZZ We prove below that two condltlons are suficlent the requirement that mcreasmg returns to scale firms operate at non-negative profit levels, and that m the new common market equlhbrmm production of increasing returns to scale firms rises

Case I

Expansion of all IRS mdustrles

It 1s convenient definitions Definztions

(I) Let

to work with the cost function,

Yl,=(y,

-v,,)

be the

so we make the followmg

production

vector

of firm

J

in

322

E L Grmols, lncreasmg

returns and the shift from customs unum to common market

industry I, where y,, IS the level of output of the good m question and -o,, 1s a vector of factor inputs Let the prices faced by the firm be given by P =(p, w), where p 1s the price of the output and w 1s a vector of factor prices, and let the firm’s cost function be given by C,,(w, y,,) Then a firm 1s said to exhibit increasing returns to scale d C*Xw, AYJ < Z,XW> Y,,) for any scalar i greater than one (n) If the firm’s costs depend on industry output, CJw, y,,, y,), where y, 1s industry 1’s output, then a firm 1s said to experience external mcreasmg returns to scale if costs decline with larger industry output, X,,(w, y,,, y,)/ aY,,0 Proof

Rewrite

n as a sum over all sectors

and firms

z7=P”(Y”-Y”) =c

1,

PF(y;-

y:])

= 1 PPYZ - C,Awrn, YZ>YP) - P:Y; ‘1 + cwmv:: - C,Awrn, Y;>

Y31

+ CAwrn, Y$ YP)

EL

Grmols, Increastng returns and the sh$t from customs umon to common market

c

=

c

P?%xY:- Yl) +

323

Pi%JlY:: - YY,)

1,

1,

summed all r,such

summed over all rJsuch that

over that

Yfy#Y?,

Yfy#YE

091

[Term (a)1

+ c Cw”G,- qwm> Yyl,Y31 1,

[Term (41 where w = 11

qwm,Y$

I_

YP)- CljtWrn~ YYJ,Y3 P3Yt

-

YP)

’

E = C~jtWrn~ YY,,Y3 - CIAWrn~ YYJ? Y3 1, PrYYiy- YYJ) First, consider term (a) w,, equals zero for constant returns to scale firms, ~~,{y;-y;,) 20 for firms that maxlmlze the value of production at price py, and O O~pp~~~- CIJ(wm,y$ y;) by the asumptlon that profits are positive for operatw

firms

If YE = 0, then pi”yt - C,,(wm, YE, YP) 2 pryi’, - C,,(wm,

YY,, yr”)

smce y; # y: and zero production 1s revealed by the firm to achieve the best profits at prices (pr, wm) Next, consider term (b) It 1s immediate that E,, 1s posltlve for firms m expanding mdustrles with external Increasing returns to scale present Thus, term (a) m Eq (9) 1s positive if yr;’2 yyj for all firms ZJand y: > y: for at least one firm y Term (b) 1s non-negative, and term (c) 1s non-negative because C,,{w”, y;, yp) 1s the least cost of producing output, yt at prices wm Thus, as 0 the sum of a positive and non-negative term, n 1s positive Combmmg following

Lemma

3 with the methodology

of Proposltlon

1 leads to the

Proposztzon 2 Let the union countries zn an znztzalcustoms union equzlzbrzum move to a common market equzlzbrzum where all ng + n, goods are freely traded between the member countrzes and Pm IS the n,+nf dzmenszonal vector of internal equzlzbrzumprices zn the common market equzlzbrzum If (1) firms exhzbztzng internal increasing returns to scale operate at posztzve profits and have equal or larger output zn the customs union equzlzbrzum, wzth at least one firm havzng larger output, (2) firms not exhzbztzng internal IRS maxzmzze the value of productzon at market przces P”,

324

E L Grmol~, Increasmg returns and the shft from custom9 unron to commonmarket

(3) zndustrzes with external increasing returns have equal or larger output zn the common market equzhhrzum, (4) aggregate external trade oj the umon zr held constant by cholte of the common external tariff; and (5) revenues are dlstrzhuted to each member k accordrng to the formula PrnZk”. then the welfare

of each

country 1s higher m the common market equlllbrlum

Proof AW-(I7++)=T”-P”Z”=T”-P;Z;=T”-PFZF=O

Since H + r 1s posltlve

from Lemmas

1 and 3, A W >O

0

It 1s reasonable to expect m many circumstances that the effect of a move to common market, m fact, will be to increase the size of increasing returns to scale firms and industries If some increasing returns to scale firms and mdustrles decline m size after the move to common market, however, welfare gains are still possible Inspection of Eq (9) reveals that terms (a) and (b) may become negative if the size of the increasing returns to scale firms decline, but term (c) remains non-negative Moreover, other components making up A W contribute non-negative terms o,jyzyy,) 1s non-negative for non-increasing returns to scale firms, and substltutlon m consumption If the posltlve terms outweigh the guarantees that r 1s non-negative negative, gains occur, even though the size of increasing returns to scale firms has declined Caye 2

Some IRS mdustriey contract

The followmg proposltlon provides a general sufficient condltlon welfare gains when some mcreasmg returns to scale industries decline

for

Proposltlon 3 If the output of some firms and/or industries exhzbltrng mcreasmg returns to scale declines after the move to common market, then conditions (1) and (3) m Propopltzon 2 may be replaced by the requirement that the weighted change m output,

c PYt(Yf”

- YPL

(10)

IS positive, where 1 IS summed over all rndustrles with mcreasmg returns to scale present either internal to the firm or external to the firm for which yp # yp, and

EL

Proof

Grmols, Increasq

Direct computation

returns and the shaft from customs umon to common market

325

shows that

We have that Q,(yF - y,“) 20 for mdustrles wlthout IRS present which maxlmlze the value of output at price py (m fact, Q, = 0 for constant returns to scale industries) If (10) 1s posltlve as a sum over the firms and mdustrles with IRS present it follows that the sum of terms (a) and (b) m Eq (9) 1s posltlve, and Zl>O f IS non-negative from Lemma 1 Therefore, from the proof of Proposltlon 1 we have

Proposltlon 3 1s a significant advance m our ability to analyze the effects of increasing returns to scale In particular, Proposltlon 3 accomplishes three things (1) it expresses the condltlon for welfare gains m terms of zndustry output rather than m terms of the mdlvldual firm, (2) it depends only on the effect of the move to common market on those mdustrles m which mcreasmg returns to scale are present (either internal to the firm or external to the firm), and (3) it does not depend on any assumption about fixed factor usage between equlhbna, convexity of production, or the nature of competltlon It 1s therefore a stronger proposltlon m ways that are important to practical applications The next subsection Illustrates Proposltlon 3 with a computable general equlhbrlum example In subsection 4 4 we make use of it to calculate an upper bound on the extent of gains that can be expected due to better use of increasing returns to scale m the European 1992 mltlatlve

43

A computable

general equzhbrzum example

In view of the fact that gains are still possible when the scale of operations of the increasing returns to scale sector as a whole moves m the ‘wrong’ direction, it would be nice to find a rule for predlctmg gains that 1s not based on measuring a weighted average of the output of the mcreasmg returns sector The following counterexample shows, however, that such a proposttlon cannot exist, m general, apart from knowledge of specific functional forms The case that we have illustrated m fig 1 gives a circumstance where increasing the scale of the increasing returns sector is necessary and sufficient

326

EL

Grmols,

Fig

Increasmg

returns

1 Increasmg

and the shift from customs umon to common market

Y, 1s necessary

and suffbent

for welfare gam

for welfare gains In this sense, Proposltlons 1 and 2 are the most general results possible without measuring output m terms of a weighted average or lmposmg more restrlctlons on the nature of technology, imperfect competition, and preferences Fig 1 plots the production posslblhty frontier T,T,T, for a two-country customs union 9 Good 1 1s produced competltlvely m country 1 using a constant returns to scale technology, and good 2 1s produced by a monopolist m country 2 using an increasing returns to scale technology with constant marginal cost Labor IS the only factor of production Trade between the union and the rest of the world 1s given by the difference between production Y” and the consumption X” The union exports 819 units of good 2 m return for imports of 9 units of good 1 A tariff on imports of good 1 1s indicated by the fact that domestic prices, Id, are flatter than world prices, I” In the customs union equlhbrlum labor markets are separated so that production 1s fixed at Y” with different wage rates prevadmg m the two union countries The union now moves to a common market, adlusting the common external tariff to leave world prices unchanged The effect of labor market unification 1s to decrease employment m monopohstlc industry 2 as labor moves to country 1 m search of higher wages This increases the marginal ‘The detads

of the example

are worked

out m the appendix

EL

Grmols, lncreasmg returns and the shzftfrom customs umon to common market

327

cost of production of the monopoly good and leads to productlon at the new pomt, Y”, where output of good 1 IS higher and output of the mcreasmg returns to scale good IS lower Trade with the rest of the world IS unchanged (m this case the union has reduced its tariff on Imports of good 1 to zero) Consumption is at point X”, which gives lower utility than X” Thus the net result of market umticatlon 1s welfare loss and a decline m the output of the increasing returns to scale sector Because the union’s marginal rate of transformation IS flatter than the marginal rate of substitution at point X” (see the hne lMRTthrough X” parallel to T2T3), welfare increases or falls with the amount of good 2 produced Dropping the assumption that the production of increasing returns to scale firms rises m the move from customs union to common market 1s therefore not possible if welfare gains are to be guaranteed m general In this sense, a weaker condltlon on production than m Proposltlons 2 and 3 IS not possible Proposztzon 4 The assumptzon that the output of zncreaszng returns to scale firms rzses IS necessary zf welfare gazns are to be assured zn all moves from customs unzon to common market zn the presence of zncreaszng returns to scale Proof There exist economies for which welfare rises m the move from customs union to common market d and only if production of the mcreasmg returns to scale sector rises 0

Proposltlons 2, 3 and 4 presume that the customs union follows the pohcy of keeping external prices and trade constant with appropriate choice of common external tariff As a practical matter, this pohcy need not be the only pohcy chosen that leads to welfare gams for the union countries For example, m the case of fig 1 the union might have chosen to impose an optimal common external tariff simultaneously to optimally regulating the domestic monopoly However, such pohcles are available without the shift to common market We would not want to count gains from unrelated pohcles as part of the gains from moving to a common market Fixing external trade, m addltlon to making the change unharmful to the rest of the world, has the analytical virtue of separating exploltatlon of external trade opportumtles effects from the market efficiency effects that are the object of study

44

An empzrzcal applzcatzon to the Common Market

As the proposltlons have highlighted, the additional beneficial effects of market Integration m the presence of increasing returns to scale come from the cost reductions that accompany a larger scale of operations m increasing

328

EL

Grrnolq

Incrrawq

and the yhrft from

returns

cuytorns umon to common market

Average cost

C&. Yt* Y3 Y; Cl

.

--e-w-

a

Ct,(w.Y;v Y3 Cl

c3

_-----

.---__ I

I

I

I I

I

I I I

Fig

cl

I

I I I

I

I

Y5

Y;

owut

2 The combmed effect of mcreaslng returns Internal and external to the firm m the mcredse m output from yy, to J m ,, IS the cost reduction from c, to c 3

returns mdustrles lo Not all industries exhlblt mcreasmg returns to scale, and of those that do exhlblt mcreasmg returns, many have already been able to realize the economies of scale that come from greater integration and market size The fraction of mdustrles producing tradable goods that have unrealized potential gains from increasing returns to scale therefore form the basis for estimating remaining welfare gains to Europe from greater integration How big are these cost reductlons7 Fig 2 draws the average cost curve for a representative firm assummg that mltlal (customs union) output IS JIM,and final (common market) output 1s y: The drop m average cost from c1 to cZ represents the cost savings from mcreasmg returns to scale external to the ‘“These gams accrue to mdustrles whose goods dre traded across natlonal borders Nontradable goods mdustrles whose markets are naturally hmtted to the domesttc country have already achieved whatever cost reductions dre possible based on the size of the domestlc market

EL

Grmols, Increavng

rettwu

and the shaft from

customs umon to common market

329

firm, If present, and the drop from c2 to cj represents the cost savings from internal mcreasmg returns to scale The combmed drop m average cost IS the distance from c1 to cj Takmg Maddlson’s (1987) figure that from the nmeteenth century to the present, a doubling of inputs leads to approxlmately 2 3 times as much output, and assuming a constant cost elasticity with respect to output over the span from point u to point c implies increasing returns to scale of the magnitude correspondmg to MC/AC = 0 83 ” In terms of fig 2, If the shift from yy, to J$ represents a 100% increase m output, It would lead to only an 83% increase m cost or, equivalently, a drop m overall average cost to (1 83/2) or 91 5% of its orlgmal level Such a drop m average costs probably overstates the degree of increasing returns available to the Common Market since much of the increase m output from increase m factor mputs that Maddlson observed occurred over a period of time m which technological progress was substantial Nevertheless, now Imagine the followmg experiment Assume that all mcreasmg returns industries m Europe are characterized by MC/AC=0 83 and assume that the effect of the European 1992 mltlatlve 1s to shift all production m tradable increasing returns to scale industries with unrealized gains remaining from increased scale to one location The cost savings from this reallocatlon forms an upper bound to the true welfare gams from integration smce (1) the degree of Increasing returns assumed probably overstates the correct number, and (2) this much reallocation of production will not, in fact, occur Since we want to measure potential gains in terms of current gross domestic output and prices, it 1s a straightforward matter to apply the formula for gams given m (10) m reverse by asking what the effect would be moving from the hypothetical efficient production allocation to the current allocation Let z be the fraction of European trade subject to increasing returns to scale and let ,0 be the fraction of trade subject to increasing returns to scale that has unexploited gains remaining from increased scale Let t, be exports of country k m the mltlal (union) equlhbrmm and set pp = 1 by choice of units Wrltmg out the cost savmgs m (10) leads to

savings=

-c

(apt, - A(c$tJ”)

+

{(k

1

’

pt k)-“(F”““)

k

“That described estimates

IS, we assume that the reductmn m cost m the move from pomt a to pomt c can be by the function Cost=Ay” where A and q are posItwe constants Maddlson’s Imply that q=O 83

330

E L Grmols, Intreasrng

returns and the Fhlft from cusfom? umon to common market Table

I

Cams from reallocatlon of productlon m the Common Market to approprlate the benefits of mcreasmg returns to scale (m percent of European gross domestlc product)

02 03 04 05 06 07 08 09

P

1

02

03

04

05

06

07

08

09

1

008

012 017

015 023 031

019 029 038 048

023 035 046 058 069

027 040 054 067 081 094

031 046 061 077 092 108 123

_

_

035 052 069 086 104 121 138 156

038 058 077 096 115 134 154 173 192

-

-

_

_ _

_

_ _

_

_

Notes Figures are based on 1987 trade volumes a=fractlon of exported goods subject to mcreasmg returns to scale /I=fractlon of exported goods subject to mcreasmg returns to scale wth unreahzed potential for further gams due to scale

Assummg that sales imphes

the average

k

k

profit

rate m mcreasmg

returns

sectors

IS T% of

k

or

Substltutmg this mto the above gives the gains from shifting existing European productlon of tradables to the largest, and therefore most efficient scale, as

savings=ccfl(l

-z)

Table 1 reports the increasing-returns-related gains as a percent of European GDP for a range of x and fl using 1987 export figures for European Community countries ’ 2 As can be seen, even if all trade is subject to increasing returns and has unexploited potential for further gains, the cost More reahstlcally, we might expect that savings are less than 27, of GDP “We assume a 2% rate of prolit on productlon m mcreasmg returns sectors, which probably understates the true figure Smaller profit r&es enlarge the benefits due to mcreasmg returns to scale because they Imply larger unexploited gams

EL

Grmols, Increasrng returns and the shift from customs umon to common market

331

figures for CIand fl below two-thirds would be closer to the truth In this case cost savings drop to less than 1% of GDP Finally, if mcreasmg returns are such that a doubling of output raises cost by, say, 90%, rather than the longrun figure from Maddlson of 0 83, the cost savings for c(=p=O 7 drop even further to less than 0 6% However one interprets the data, therefore, it appears that the Cecchml commlsslon’s estimates of gains from the Europe 1992 changes of between 2 5% and 6 5% of GDP are too large to be explamed by increasing returns to scale alone unless the degree of returns to scale are substantially greater than have been observed m the past I3 5. Summary and dlscussron This paper has done two things It has described a framework for studying the welfare effects of the shift from customs union to common market m the presence of mcreasmg returns to scale, and It has provided proposltlons showing that welfare gains are guaranteed if the scale of increasing returns to scale firms and industries rises as a result of the shift using an appropriate weighted average to measure output An example was constructed showing that the assumption of output expansion m the increasing returns to scale sectors cannot be dropped m general The formula for gains was applied to data from the Common Market for 1987 to estimate the size of gains that might be expected from the 1992 mltlatlve The results of the present paper relate both to customs union theory and to the theory of gains from trade m the presence of increasing returns to scale In the move from autarky to free trade a sufficient condltlon for gains IS that trade led to an increase m the output of goods produced with increasing returns However, different analysis 1s needed to evalute the move from customs union to common market because the comparison 1s from one imperfect trading situation to another and the influence of the change on the terms must be considered The necessary and sufficient condltlon for welfare gam 1s given by eq (6) with eq (9) substltutmg for Zl In the move to common market, terms of trade welfare effects are controlled through the external tariff and dlstrlbutlon of tariff revenues Given the variety of market types and pricing rules that can arise m imperfectly competltlve condltlons, the condltlon m Proposltlon 3 for welfare gains based on a weighted increase m the output of increasing returns firms 1s surprlsmgly free of quahfymg restrictions It depends solely on the property of decreasing cost without further hmltatlons on functional forms, 13Work by Baldwm (1989) and Rlvera-Battz and Romer (1991) focus on dynamic growth effects of mtegratlon Dynamic Induced mnovatlon can produce welfare gams dramatlcally larger than those estlmdted from static models Whether larger countries grow dramatically faster than smaller countries, ceterls panbus, IS somethmg that must be questloned emplrlcally

pricing rules, or other market mformatlon except non-negative profits l4 Since the needed weights, a,, are functions only of totdl revenues and total costs for the customs umon dnd common market levels of output, the sufticlent condltlon of Proposltlon 3 can be calculated and emplrlcally Implemented based on d relative mmimum of information

Appendix

CGE compututlon Enlurgmg the mtreasung return?, sector IS both nec.esury and sufficient Jor weljure gams m the move to common market Let utility m the customs union and in the rest of the world be given by the constant elasticity of substitution function

where G, and G, are consumption of goods 1 and 2, rcspcctlvely, m the relevant region Good 1 1s produced competltlvely m customs union country 1 using labor input according to the production function

(A 2) and good 2 1s a natural monopoly, produced m customs using labor input acLordmg to the production function

y2J’)

L,-

81

union

country

to 9

2

(A 3)

Country 1 has 0 15 umts of labor dnd country 2 has 9 85 units for d total of 10 For slmphclty, we will assume that the rest of the world is specldlised m the productlon of good 1 dt 80 units In the customs union equlhbrlum labor 1s lmmoblle In the common market equlhbrlum ldbor IS freely mobile between countries 1 dnd 2 The common external tariff on the import of good 1 in the customs union equrhbnum IS 0 756665 To cdlculate the welfare effects of the shift from customs union to common market we need to compute the customs union equlhbrmm and the common market equilibrium In this example it will turn out thdt the common market equlhbrlum 1s also a world free trade equlhbnum, so we compute that equlhbrlum first World demand for good 2 IS given by G,z

mi

(A 4)

P(1 +P)’

14Thlscondltlon I> In\estlgated

more generally

in the u~mpdnlon

paper, Grn~ols

(1991)

EL

Grmols, Increasmg

returns and the shft from custom> umon to common market

where r IS world income m terms of good 1 and p = P,/P, price of good 2 Totally dlfferentlatmg (A 4) for fixed I gives

333

IS the relative

G,(1+2p)ddGp+(p+p’)=O 2

or 1

G2

dp

E

p

dG2

-=-

_

I+P

<1

1+2p

(A 5)

’

where E IS the elastlclty of demand for good 2 The country 2 monopolist determmes output of good 2 by setting marginal revenue equal to marginal cost,

(A 6) where w 1s the wage rate satisfies

Competltlve

production

of good

P, =w Consumption

1 m country

1

(A 7) of good

Gl=&

1 and 2 by union

countries

1s given by

(A 8)

and I

(;2=p(l

+p)’

(A 9)

where I = Y, +pY, IS the income of union countries Rest of world demand for goods 1 and 2 IS given by (A 8) and (A 9), where T-1 replaces I m the formulae Condltlons (A 1)3A 9) must all hold m equlhbrlum Choosmg the wage rate w = 1 as numeralre, market clearing occurs at P, = 1 and and P, =9, with the other variables as given m table A 1 Direct computation of the utility of union countries gives U = 11 11 Computmg next the customs union equlhbrmm where 9 85 units of labor remam m country 2 and 0 15 units of labor remam m country 1, we find that utility IS higher at U= 11 64 (see table A 1) Thus, the shift to common market has lowered welfare Comparing the marginal rate of transformation, -dY,/dY, =02345, marginal rate of substitution MU,/MU, = MRS=O 1952, and world prices Q1/Q2 =0 1111 we find that

334

EL

Grmols, Increasrng returns and the sh$tjiwm

customs unron to common market

Table A 1 Computation

of customs

union

and Common Customs

Domestic prices World prices Production Labor dllOCdtlOn Consumption Umon exports (good 2) Umon imports (good 1) Common external tariff on good

1

ut111tv

Market

equlhbrla

Umon

Common

Market

I. 1, 1. 91 1. 9 9. 1 89 8 0 II 1111

015. 11,7567,9 9 015, 985 8 15, 0 3105 8,/9 8 0 1567 11 6420

%MRS
Q2

Thus, given the trade flows with the rest of the world, it follows that union welfare rises if and only if production of good 2 rises This IS also easily seen m fig 1, where consumption moves from X” mto the preferred region along lMRT if and only if production on the production posslblhtles frontier moves to the south-east

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Grznols, lncreasmg

returns

and the shift from

customs unton to common market

335

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