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Sharing the gains from customs unions among less developed countries
Journal of Development Economics 1 (1974) 213-233. 0 North-Holland
Publishing Company
SHARING THE GAlINS FROM CUSTOMS UNIONS AMONG LESS DEVELOPED CO.LJNTRIES A game theoretic approach Dermot
LATELY
*
New York University, New York, N. Y. 10003, U.S.A.
Received March 1974, revised version received August 1974
1. Introduction Finding a mutually acceptable distribution of the gains from cooperation is probably the main barrier to economic integration among developing countries, and the main cause of friction within existing arrangements. In this paper we discuss the sources of these gains, both for the custom:; union as a whole and for the individual countries (section 2). A measure of these: gains and losses is proposed (section 3) and it is then utilized in a framework ofn-peisC n, cooperative game theory to analyze various questions discussed in ths literattire, such as which distributions would be mutually acceptable, whether an actual distribution of the gains is ‘fair’ and whether an individual country wouid be bettei off dropping out or not joining (section 4). Such an approach i$ ‘cht-n illustratetl with an ex-post analysis of the distribution of gains from Ihe East African Common Market (section 5). 2. The gains and losses from cooperation The main economic goal of integration among less developed countries is an increase in the level of output, especially industrial output, over what it TtiGdld be in the absence of integration.’ The economic ratiorale for customs unions, or the sources of gains, fall into two groups, those associal:ed with protection and those associated with cooperation per se.2 *The author is Assistant Professor at New York University. Much of the work on this paper was done while the author was Visiting Lecturer at the Uni\ersi,:y of Ghana, on leave fron the University of Western Ontario, under a twinning arrangement funded by the Canadian International Development Agency. He is grateful fbr the comments of participants at a seminar in the Economics Deparrment of the University of Ghana and for those of R.G. Lipsey; any remaining errors are, of col;rse, the responsibility of the author. ‘Whether a customs union will achieve this goal, or whether it could be better achieved by some other policy, ha.s often been. discussed in the literal ure, most recently in Krauss (1972). ZThe discussion here draws upon Rr?bson (1972) and Lipsey (1960).
214
D. Gately, Slmritrggains among LDC’s
The gains from protection are import.mt inasmuch as a customs union iimong less developed countries might best be thought of as protection on a more efficient scale. The most important argurr,:nts in this group are the infantindustry or learning-by-doing argument, the external economies generated by industrial activity, and the existence ofdomestic cl.istortions (such as the industrial wage exceeding the opportunity cost of labor). The sources of gains from cooperadon per se are several. The most important ones we believe to be: first, economies of larger scale production and operation; second, the increased availability of certain factors, in particular foreign capital; and third, increased efficiency in the use of existing factor inputs. Scale economies can be realized both by new industries and by already existing industries. A new industry can build a single large plant to service the entire customs union, capturing the technological and managerial economies of scale not available to several small plants in the various countries. Existing industries can also become more efficient when capacity underutilization. is reduced or when mlllti-plant firms, each plant previously producing the same variety of products, can be re-organized to specialize production within each plant. For example, if each country has a footware factory producing both shoes and sandals then, after the establishment of the customs union, they can specialize production and export their specialty to the partner country. As the larger market makes new industries feasible and as the common tariff barriers are erected, the supply of capital responds to these new opportunities for profit. Foreign capital inflows (and perhaps also private domestic savings) increase the availability of this important factor; accompanying such inflows are technological and managerial skills. The competitive pressures resulting from the movement toward freer trade can increase the efficiency of existing factor inputs in at least two ways. Allocative efficiency, or increased specialization within exist.ing activities among member countries according to comparative advantage, is well known to economists but its practical importance has been shown to be almost trivial. Less precisely formulated, but probably much more important, is Leibenstein’s notion of X-efficiency, 3 which could be loosely described as motivational efficiency. teibenstein’s examples are illustrative and easily supplemented by some casual empiricism in modern sector activity in the less developed countries: simple reorganization of the work process, payment by results, promotion by merit, and better worker attitudes can often increase output by 25 % or more. All these potential gains are, of course, gains for ,the customs union as a whole. Yet they will noi necessarily be distributed among the members in a way &hat could generally be considered equitable. The distribution of gains is likely to be ighP~:correlated with the distribution of the new industries resulting from the eitabliihment of the customs union, which are likely to concentrate around the
aheady developed centers within the union .4 Peripheral countries in the union which do not share in the distribution of industries might even be worse off under the union, relative to what they could achieve without the union. For example, an independent country might be able to attract and support some small ‘shiftable’ industries by protecting its domestic market; however, if that country were part of a customs union, such plants might instead locate at the already developed centers in the partner countries.5 The losses to the union as a whole stem from the trade-diverting ell’ects of the union, low-cost imports fro% abroad are replaced by higher-cost, protected production within the union. 6 This cost disadvantage would hopefLdly be shortterm, as in the infzmt-industry case, but it is sometimes a permanent feature of the union. Another potential loss, or al least a difficulty created by the union, is the reduction in government tariff revenue, both from the abolition of duties on trade between members and from the reduction of imports from coulitries outside the union.’ This lost revenue would have to be replaced from alternative dependable sources, which are often difficult to find. 3. Measuring the gains and losses To measure the gains or losses to a given country resulting from a customs union requires a comparison between that country’s growth over time as a member of the union and what its growth over time would have !:cen in the absence of the union. Several attempts have been made in the literature to estimate such effects, especially for the European Common Market.* Such studies normally use data for a single ‘representative’ post-union year to examine the union’s effects. Ideally, of course, a se.ries of post-union yeErs should bt: studied in order to evaluate the longer-term effects of the union. schema, although OLII In this section we sketch an ideal measurement numerical example in section 5 is a considerably simplified version. Let’s conside.? three countries about to form a customs union, call them A, B agd C. (Three is the minimum number necessary to illustrate some of the essential problems in sharing the gains from cooperation.) At first glance there might appear to be only tLvo alternatives, either a three-country union or no union at This proccsc is what Hirschma:~ calls ‘polarization’. Such cf?‘ccts arc discussed in Newlyn (193). “See Ncwlyn (1965). “\+‘hilc \vc arc ;l\{are of the theoretical nossibility of Lvelfare improvcm~~nt from ;L tr;ldcdivcrtjng customs union, v/c tJo not conjid :r it to hnxc any likely pr;lc!il.:ll ‘m;x)rt:ince: 111~ issue is treated most recently in Kkauss (197?.). We follow Balassa (1967) in associating the negative effects with trade diversion. ‘In West Africa, for example, the proportion of import duties in total government rcvc’n~c exceeds 50 :‘i for Togo, Dnhome>, and Upper Vuita; see United Nations, Dcpartmcnt of Economics and Social Affairs (1969). 8fjal;ls~:~(1974) survq’s the e\GJt:ncc on trade cr-1-1tion and trade diversion in the Euro?c.1!7 ~‘ontnlo~~Ilk1rkct. n
216
D. Gately, Sharing gains among L DC’s
all. There are however j%x possible ways in which these three countries group themselves into ‘coalitions’; these five ‘coalition structures’ are: (i)
[(A, B, C)] the three-country
(ii)
[(A, B), (C)] A and B in a union, C outside;
(iii)
[(A, C), (B)] A and C in a union, B outside;
(iv)
[(B, C), (A.)] 13 and C in a union, A outside;
(v)
could
customs union;
[(A), (B), (C)] no union at all.
The three additional cases of two-country unions are essential for an understanding of the bargaining power of the individual countries and of the different coalitions. Consider the five coalition structures from the viewpoint of one country,’ say country A. Let us make the assumption that A’s prospects for growth under a stratea of independence do not depend upon whether or not B and C happen to form a union, Given this assumption we need to consider what happens to A in each of four coalitions: (A, B, C:i, t-4, B), (A, C) and (A); that is, from A’s viewpoir t coalition structures (iv) and (v) are the same. 3.1. The three-country wiorl We want to estimate the growth over time in A subsequent to the formation of the three-country union. I0 Benefi,ts (losses) to A c:m occur on the production side and on the consumption side. On the production side the benefits (losses) result from the increased (decreased) output following the setting up of the union, either from newly established industries or from the expansion (contraction) of already existing industries. Note that this output change could occur in industries producing ei;ports for its partners or producing for domestic consumption. The measure of these benefits on the prod:uction side w xtld be the social value added of this increase in catput minus the social opportunity cost of the productive factors involve;i.” Any benefits from employment creation are assumed to be reflected in this measure. The consur option effects follow from the change in the pattern of consumption and imports subsequent to the establishment of the union. These effects are of twc types, the gain (loss) of consumers’ surplus and the loss of government tariff revenue. One o:r both of these will occur for the following four categories of consumption: ‘Our measurement schema does not (bt.:t could) take account of the effects of any benefitsharing mechanisms built into the agreement, such as an administrative scheme to allocate nc;i industries; this and others are discussed in Morawetz (3Q73). ‘01nclu3ed here obviously, is the growth that would have, occurred tiithout the union. Since ihi\ is also inclpldci in the measure of gains to A when indep’znclent of the union, it is netted out At !“?Cend. ’ ‘Thcsc benefi:s on the production side ai:c discussed more extensively in Mead (19G8).
D. Gate&, Sharing gains among L DC’s
(i) goods formerly produced in A, now displaced B or C: a gain of consumer’s surplus;
by lower-cost
217
imports
from
(ii) goods previously imported from outside the union and now imported from B or C : a loss of tariff revenue and a gain (loss) of consumers’ surplus if the new price to consumers is below (above) the former price; (iii) goods formerly and still imported surplus but a loss of tariff revenue;”
from
B or C: a gain of consumers’
(iv) goods formerly and still produced in A; if scale or other effects allow a price reduction there will be a gain of consumers’ surplus. For categories (ii) and (iii) note that lost tariff revenue might be weighted more heavily than gained consumers’ surplus; policy makers within the government would very likely be inclined to do so because of the difficulty of finding alternate sources of government revenue. All these benefits and losses over time, both on the production side and the consumption side, should be discounted to present value and summed to form a scalar measure. 3.2. A two-comiry
customs uniorz
Taking the case of country A in (A, B), the benefits (losses) are calculated similarly to the case of the three-country union. The benefits (losses) on the production side result from the increased (decreased) output subsequent to the establishment of (A, B). In this case the new indusrries in A might not include some which were !oca:ed there under (A, B, C) because the smalier market (A, B) could not support such an industry. On the other hand, some industries that might have located in C under (A, B, C) might now locate in A under (A, B). On ti\e consumption side, the benefits and losses would fall in the same categories as under (A, B, C); there would, however, be smaller price reduction effects from reduced scale economies and there wouLd be a different pattern of consumption and imports in A under (A, B), as compared with the case under (A, B, C>. These calculations of the efiects of the establishment of the union (A, B) can also he used to estimate the eventual eflects on A and B of the following sequence : the three-country union is formed but C drops out, leaving (A, B). This \vil\ ‘x true unless there happen to be some putty-clay asymmetries os!,ociz,ted with C s joining and leaving. One possible asymmetry woulcl be the cast of an industry which would not have been cstablishcd in A hxd (A, B) :xen formed at th: outset but, once established ill A under (A, B, C), it learns-by-doing and can survive the departure of C. ’ 3 l 21f scale effects allow an additional price reduction the gain of consumers even larger. 1-‘Pic~cly~ (1965) discusses other possible asymmctrics.
surplus will kc
D. Gately, Sharing gains among LDC’s
218
3.3. A one-country ‘coaiition
Finally, consider ,the case of country A following s policy of independence; this, of collrse, need not imply a policy of autarky under which all trade ceases with B and C. The benefits to A in this case would simply be the growth and development taking place in A over. time, discounted to the present. These benefits for A could conceivably be lrtrger than those to A under a two-country or three-country customs union, as might be the ctse for a peripheral country noted in section 2. The calculations for this case could likewise be used to estimate the eventual effects upc,n A, of joining a customs union but then dropping out, unless there were important putty-clay asymmetries. 4. The garae theoretic framework a measure of the benefits to each country .“;om three-country cooperation, two-country cooperation and non-cooperation brings us to the characteristic function for the game and a wa!r of determining what distributions of the benefits WCuld be mutually acceptable. For each of tht, seven possible coalitions, 14 the clwac.*eristic function oalue for that codition is defined as the sum of the benefits to each member’ 5 (as measured in section 3); it is a scalar measure, the net present value of the future benefits to be shared by the members of that coaii tion. 16 Let us denote the characteristic function value for some coalition S as c(S), Taking the two-country coalition (A, B) as an example, the characteristic function ta!ue ,c(A, B) would equal the sum of the benefits to A and the benefits to B (as measured in section 3) if the tu’o-country union (A, B) were to be formed. We allow for side payments between partners in a coalition, for example, by fiscal compensation (as in the East African Common Market’s Distributable Pool, as a means of redistributing the benefits. ’ 7 Such side payments are assumed to have the properties of transferable utility. l8 The sum of benefits to a given country plus (minus) any side payments received (made) will be denoted, respectively, X,, X,, and Xc. With this background we can now proceed to perhaps the most critical question facing a customs union : what distributions o:f the benefits of cooperation Swh
1‘the sel.en are the three-country coalition, the three two-country coalitions, and the three one-countrJ~ coali tion.5. I ‘This ad3ition of benefits assumes comp;.rability between countries in time preference for &x:,ts and in their perception and evaIuatior of the benefits. i “Whilr this ~aluc will b-_ a single number it is not a ‘static’ measure in the sense of repreCT-ting or!y current benefits. _,. i -This assumption skirts a vihoie range of interesting issues related to the actual imgiementatinn nf benefit sharing. !Horau,etz (1972) discusses several such schemes: compensation via ::;comt: t -ansfcrs, the eqI.iitable allocation cf new industries, balanced intra-unio:l payments, ;ii~d :I b;?~rp& distributicn of not fixal gains. “P +)r ,2 di;c3-iion see Luceand Raiffa(1957, plr. 168-170, l:?A-181).
D. Gclely,
Slrarkggains among LDC’s
219
would be mutually acceptable? The first condition that a distribution of the otal bt-nelits of the three-country union must satisfy is that of individual ration: iit.y, t!lat each country should receive benefits at least as great as it would receive if it were not a member:
If any of these inequalities is llot satisfied then that country rvould be better off outside the union. Note that this is not the same as saying that the measured benefits to each country under the t!xee-country union should be positive. ” All those distributions of the total benefits [K,, X,, Xc such that X,+ S,,+ Xc = r(A, B, C)] which satisfy this condition of individual rationality con: titutc the set of imputations. A second condition of mutual acceptability could also be imposed: th:\t an); pair of countries jointly receives an amount no less han what they could xhicve without the cooperation of the third:
X,+X,
(2bj
2 v(A, C),
If any one of these three inequalities is not satisfied then those two co _mtries could both gain by refusing to cooperate with the third. All those distributions of the total benefits which satisfy conditions (1) :md (2) constitute the cow 0,’ the game. Equivalently: the core can be defined as the >,et of those distributions of the total benefits which satkfy : P(A) =< X, S z(A, 13, C) -r(B,
C),
(12)
220
D. Cutely, Sharing gains among LDC’s
Membership in the core would he a minimal condition of mutual acceptability; distribution outside the core can bc successfully vetoed by a pair of countries or by a single country. 2o Thus, if countrv# A were receiving less than it was guaranteed in the core, X, < u(A), it csuid drop out of the three-countr:y union and increase its benefits to v(A); alternati\rely it could threaten to drop out unless its share of the benefits were increased to an acceptable level. Or, if countries A and B were jointly receiving too small a share of the benefits, X,+ X, < u(A, B) [that is, if country C were receiving too large a share, Xc > u(A, B, C) - v(A, B)], then A and B could refuse to cooperate with C and could increase their joint benefits up to the amount v(A, B); likewise, they could jointly threaten noncooperati’on with C unless their share were sufficiently increased. A. geometrical representation of the set of irr,putations and the core is depicted in the three-dimensional diagram in fig. 1 foi* one example of a characteristic any
function :
c(A) = 0.05 ,
~(5) -= 0.10,
V(C) = 0.15,
zl(A, B) = 0.30,
v(A, C) = 0.40,
U(I3,C) = 0.50,
r(A, B, C) = 1.0. T’ht. triangle P,P2P, describes those distributions (X,, ;Brg,Xc) of t:ie :oltal benefits ix,+ XB+ Xc = tt(A, B, C)] such that each player’s share i- nonnegative. The smaller triangle LMN represents the set of imputation- Tile hexagon’ ’ Q 1Q2Q3Q4Q!iQ6 represents the core. While the core puts a reasonable upper limit on each country’s share of the benefits [the right-hand inequalitks af (3)], the lower limits [the left-hand inequalities of (3)] do not guarantee that each country will be much better off, if at all, than if it did not cooperate. To eliminate such distributions we introduce the concept of a country’s propa~tsity to disrupt the three-country distribution (X, y X,, Xc); for each country it is the ratio of holw much the other two countries would lose, to how much it vvould lose if it refused to cooperate.22 For country A, “Alfhougl; WEwill be discussing characteristic functions with non-empty cores there c!o exist characteristic functions for which the core is empty, e.g., t.(A) = r-(B) = r(C) = 0,
r(riB) = z$AC) = c(BC) = 0.9,
z:(A, B, C) = 1.
P-or such a ;Icro-one normalized characteristic function the core will be empty if and only if 1(A +Bi L 1(X. C‘)- I$B, C) > 2. In such cases, intuitio,ely, the benefits to three-player cooperation XC not very rn?lch bigger than those of two-player cooperation; the three-player coalition ii 11;~sIikcly to form in such cases. For such games other concepts are important; see Luc;ts t P9”l~. Lucc and .Raiha (1957) and Rapoport (I 370). i ’ Depndrng *upon the characteristic function the core can take a variety of shapes: hexagon, ntagon, pa....J~elogram, trapezoid, triangle, line segment or point; see Fischer and Gate!y 1i ‘37.1). 2‘Tijii
concept v.as introduced in Gately (1974) and its properties discussed extensively mn I.lit%.zr snSi b;alcE:. (137-a).
D. Gcrtely, Sharing gains among LDC’s
d,
E
&+ x,--v(B, C) maximum of (0, X,- v(A))
221
*
Note that. a country’s propensity to disrupt a given imputation will be infinite if it receives an amount less than or just equal to what it could achieve by not cooperating. And its propensity to disrupt will be very large if it receives only slightly more than it is guaranteed within the core, while the other Iwo jointly receive significantly more than what they are jointly guaranteed. At such a distribution it could threaten non-cooperation, hoping to receive a larger share of the benefits, with the knowledge that the other two countries would suffer a considerably greater loss (or foregone gain) that it would if it carried out the
Fig. 1
threat. Such a threat would be credible and the country would be rat:ional in actually carrying out such a threat, in the hope of achieving a larger share of the benefits at a later negotiating session. Unlike some games that are played once and only once, such regional negotiations can be terminated and later re-opened if the participants desire. Using this concept we can eliminate, as not mutually acceptable, any core imputation for which any country’s propensity to disrupt is ‘too high’, greater than, say, 2. ’ 3 In ig. 2, the set of mutually acceptable distributions would bc the intersection of the core Q,Q2Q3Q4Q5Q,; and the triangle2” R,H;:,FL,,; the characteristic function used is the same as in fig. 1. 230ther limits on the propensity to disrupt of any country (or of any pair of countries) arc discussed in Fischer a?d Gately (1974). 241n this example The triangle lies entirely within the core. However, this is not nl:ccssnril) true, See Gately (197r) and Fischer and Gately (19741.
‘7 ,‘, ._ __
D. Gately, Sharing gains amojtg L DC’S
Since we could still be left with a fairly large set of mutually acceptable distributions we could proceed to consider several specific imputations that might be proposed as candidates for the ‘best’ distribution, such as the Shapley value, the kernel imputation, the equal-shares imputation, or the imputation equalizing tile propensities to disrupt. This has been done elsewhcre15 and we shall do it briefly in sectioa 5. Yet, however interssting the rationale for any of these specific imputations, we don’t believe that any of them ‘ought’ to occur, either in a predictive or a normative sense. Th?ls, what we’ve done in this section is to specify the set of mutually acceptable distributions of the benefits, within which *he actual distribution ought to lie. If it does rlot, then the agreement which proaticed such a distribution is not likely to endure; either the dissatisfied country will opt out entirely or a new
Fig. 2
agreement, acceptable to that country, will be negotiated. The dynamics of negotiating an agreement and arriving at a particular distribution of the gains are not considered here. 5. AR illustrative example from the East African Common Market
We now apply our analytic framework to the case of the East African Common Market (EACEJ), formed in 1957 by Kenya (K), Uganda (U), Tanganyika [Tar,zania] (T). !6 The extent and thf: distribution of benefits from the EACM hale been much debated in the literature27 and within the EAChl itself, 25S
D. Gately, Sharing gains
among LDC’s
223
especially in the mid 1960’s. Zt seems generally agreed that the region as a whole had benefited but the distribution of the gains had beer. uneven, with Kenya having gained the most and Tanzania the least. There was no agreement, however, about whether Tanzania and perhaps Uganda had suffer?“, 2 IF’! loss and would have been better cff dropping out. The controversy reached a critical point in the mid-1960’s and threatened to dissolve the EACM. A compromise solution was agreed upon in the 1967 Treaty for East African Cooperation, which gave certain concessions to Tanzania and, in lesser degree, to Uganda. We shall now examine the distribution of benefits within the EP,CM, using data for the year 1963. Much of the debate in the literature has focussed on the data for that year an? we shall also use it as representative of the situation in the early 1960’s. Of course, as pointed out earlier, the benefits should be evaluated over a number of years; we do not do this because of data limitations and because the purpose of this example is only illustrative. Listed in table 1 are each country’s 1963 exports to its EACM partnc::s, irs ‘EACM expc’ts’, broken down into SITC categories. In order to use this to estimate thl: actual distribution of benefits in 1963 we must make some simplifying assumptions: (Al) Net all of a country’s EACM exports are dependen; upon the existence of the EACM; some would continue even without the EACM. Assume that the percentage which is independent of EAC,M’s existence is the same as the percer tage of that country’s E#9CM exports receiving no external tariff protection, 14 % of Kenya’s EACM exports, 20 % of Uganda’s and 46 y/, of Tsnzani:t ‘s.” (A2) The percentage commodity composition of a country’s EACM exports to each of the other two countries is the same as that of its total EACM exports. Furthermore, each country’s EACM-dependent exports have the same percentage commodity composition as its total EACM exports. (A3) In EACM-dependent industries, tion is equal to that country’s production
the production for domestic fur EACM export.
consump-
(A4) A country’s trade &version exports consist of one-half its EACiLG dependent exports in SITC categories 1, 5, 6, 7, 8 (call these categories ‘manu7 ‘-y/o of its EACM esport,s are in ‘LJ~escc:1tegoric:;. 50 i’,:, factures’); for Kenya 7_.3 for Uganda and 36.7 7,; for Tanzania. 1ts trade-crcatlon export% cmsist O; all its other EACM-dependent exi3orts.
- --___-__
1oC:‘, (75.8%) (24.2 %)
8,243 6,250 to Kenya 1,993 to Tanzania --
33.2% 17.2% 1.6% 4.2% 10.9% 4.0 % 27.7 % 0.3 % 0.8 % 0.1%
100% 19,790 9,400 to (47.6 %) Uganda 10,390 to (52.4 %) Tknzania
‘Taken from Ndegwa (1968, pp. 50-51, 58-63).
--
T0ta.l: of which
Food Bcveragcs ~tnd tobacco Crude mntcrials FUClS Oils and fats Chemicals Manufactured goods Machinery Miscellanco:~: mrutufactcres Other
Description
Proporticu af its total (11)
Uganda’s EGCM exports (3) __-.2,738 1,419 133 349 901 ^__ 531 2,280 20 66 6
___-
Kenya’s Proportion EACM exports of its tctal (1) (2) ~- _~.____ ..-._--. 4.904 24.8 % 15.1% 2,995 0.9% 184 0.3 % 49 1.0% 205 1. .l.Y>, z.“,, 2,5-X3 27.3 :< 5,404 C.9”/, 179 17.3% 3,428 o.!i % 94
--_--.--._-_-__.
Commodity composition of EACM exports, 1963 (in thousand f).”
Tnblc 1
_
Proportion of its total (6) 36.4% 3.1% 17.2% 1.1% 8.4% 1.4% 16.5% 0.2% 15.5% 0.2 “/, loC% (85.2%) (34.8 %)
Tanzania’s EACM exports (5) 1,247 107 590 38 287 iT\ 5:: 6 526 7 3,423 2,920 to Kenya 503 to Uganda
-
D. Gaiely, Sharing gains among LDC’s
225
(A5) Value added as a proportion of total value is 65 % for all industries in the three countries. 2g (A6) The opportunity cost of all resources involved in EACM-dependent industries is only one-half of their value added in such production. (A7) The additional cost to the country importing trade-diversion exports is 20 % of the value of the goods. (A8) The benefits to the country importing trade-creation exports equal IO % of the value of the goods. Needless to say, these assumptions are heroically simple. Some of them [(A2), (A3), (A4j, (A7), (WI could be modified by access to relevant data which probably exist already. For example, if the EA(ZM export data in table 1 were further broken down according to country o ’ destination, assumption (A2) would not be necessary. Other assumptions, such as (A6) and perhaps (Al), might not yie;? to a closer scrutiny of existing data and a certain element of judgement would continue to be necessary. It should be stressed again that our example is illustrative and no more confidence should be placed in the numerical results than in the underlying assumptions. By contrast, Segal(1969, 1970) assumed that all EACM exports were EACMtiependent (if any country dropped out then all its trade with the other two would cease) and that they were entirely trs.de-creation exports. Assuming zero opportunity costs for resources involved in EACM exports,30 his measure of total gain was the value added in all EACM exports. This measure would seriously overstate the gains from coopera:ion. On the basis of our assumptions the EACM exports are broken down in table 2 and the calculation of the actual benefits are made in table 3. From this distribution of benefits - 11642 to K, 4223 to U, and 1161 to T - we calculate the sum, 17026, which is the characteristic function value u(K, U, T) for the three countries together. In order Lo estimate the effects c,F one country dropping out of the threecountry EACM we must make some additionai assumptions: (A9) If one country refuses to cooperate, then all its EACM-dependent exports and imports will cease and its production for domestic c’zasumption in EACM-dependent Lldustries will be reduced by half. it can import-substitl;tc for “Segal(l969) calcuiated these percentages as 65 y.; for Kenya and Uganda but only 45 1: fcr Tanzania. Our mcasbre of the actual distribution of gains will therefore be biased, relative to Segal’s, in favor of Tanzania. 30With respect to labor, he jus:lficd wch an assumption consisted of labor-surplus economies. A; for foreign capital only by the establishment of the EACM Our assumption of but less than value added, is clearly a corny. romise between the
on the grounds that the EAChI he assumed that it \\\‘a~ attracted opportunity costs being positive. extreme position:;.
8080 2925 5155
EACM-indcpendentS
EACM-dependent 1, tra& diversionb ?. trade creation
_
d_
.~-
-
.%
,_-
_
.-
‘Calculated using the percentagts from (Al). bCalculated using (A2), (A4) and table 1.
9400 1320
Tofui exports
to u (1)
-
-
a935 3255 5700
10390 1455
toT I-’ (LI -
-
-
I
17115 6160 10855
I
total (3) ______ 19790 2775
-
-__-
_.
.- -- .-_-. Kenya’s EACM exports
L
5000 1250 3750
L-
-,
.
.
r,
--
-____--
1595 399 1197
II
_
6595 1649 4947
_-.. .-. Uganda’s EACM exports -----total to K to T is) (6) (4) _-_6250 1993 8243 1250 395 I$“‘:
_
_
Lag.
1578 290 1289
272 50 222
-
.,.-
--
1850 340 151:
__
Tanzania’s ZACM exports --to U to K total (8) (7) (9) ____ 2920 503 3423 1342 23i 1573
___----
A breakdown of EACM exports, resulting from our assumptions (in thousand 0.
Table 2
: CF b-
z $
2 f? 2’ :
P P $? CrJ z0 g.
P
D. Gale/y, Sharing g~~iilsamong .CDC’s
227
Table 3 Distribution of benefits in the three-country common market (i,z thousand E). Benefits (losses) to Kenya eficfs: value added minus resource opportunity cost 1. trade creation exportsa 2. trade diversion export? 3. production in EACM-dependent’ industries for domestic consumption
Benefits (losses) to Uganda
Benefits (Ilosses) to Tanzania ---
Prohction
Consutrykm effects 1. trade diversion importsd
2. trade creation imports” Net benefits to each country
3525 2000
1605 535
490 111
5725
2140
601
(308) 500
(595) 538
(731) 690
4223
1161
11642
“Calculated as 65 “/, of the ‘trade creation’ values of table 2, less the resource oppo:.tunity cost of 50% from (A6); for example, in column I,3525 = (0.65)(0.50)(10855). bCalculated as above, but using ‘trade diversion’ of table 2; e.g., in column 1.2000 = (0.35) (0.50)(6160). “FrOM (A3) it follows that amounts on this line equal the sum of the two lines immetlial ely above. ‘From (A7) and the ‘trade diversion’ figures of table 2; e.g., in column 1,308 = (0.20)(1250+ 290). eFrom (AS) and the ‘trade creatio2’figuires of table 2; e.g., in column 1,500 = (0.10)(!750+ 1289).
only a fraction, say 60 ‘A, of its former EACM-dependent would represent the ‘shiftable’ industries.
imports;
this fra,:tilln
(A 10) The non-cooperation Jf one c0untr.y will have an effect upon the EAZ’N;dependent industries in the union of the other two countries; only 80% of the EACM-dependent exports betueen those two countries and SOY4 of their domestic production in EACM-dependent industries will survive. Those two countries will be able to import--substitute for a fraction, say 70%, of Their former EACM-dependent imports from the non-cooperating third country, These assumptions likewise are rather arbitrary, again for purposes of illustration. There is, of course, no reason why one would expect the identical percentages of (A9) and (AlO) to apply to exh country or to each pair of countries. The benefits to each country in a two-country ultion are e:timatetl ar,d listed in table 4, for each of the three possible two-country unions, And the benefits of non-cooperation are calculated for each country and listed in table 5. The characteristic function values, for each of the seven coalitions, XC listed in table 6. Rounding these values OR to the nearest hundred for the sake of sim-
-
.___-
.
. .._..
-_.__ -_
~~_
7156 -__
-~
3029
65
1720
4580 3’7’6
975 325
Benefits (losses) to u
1340 760
(;zj
. __
W, U) ---.- ~--~--- .~~-~-------
__
Benefits (lOSSPSj to K
_ ---___
8080
(47) 103
1113
4580
1480 845
__ ____.-
1206
(520) 455
380
480
335 76
Benefits (losses) toT _.___~~
-Jo ---
_.~_.__
Benefits (losses) tcK __.~ ~-
K __ -.
(Zj 2503
4266
1920
480
58 13
Benefits (losses) :0 T
(8) 18
2120
1720
312 104
Benefits (losses) to u
u-4 n
_.____-_
~
“Caiculated using (A5), (AG), (AlO), and the values from tab.,, ‘L 7 _, ‘trade creation’; e.g., in the first column, 1340 equals 65 % (from A5) of 80% (from AlO) of 5155, less 50%(fromA6). bCalcu!at~d using (AS), (A@: (AlO) and the values from table 2, ‘trade diversion’; e.g., in column I, 760 = (0.65) (0.80) (0.50)(2925). 2 of Production effects; e.g., in cc”::~n 1,458O equals 80 % (frcm AlO) of 5725 (from ‘Cakuiated using (AlO) and the values from table 3, line + table 3, line 3 of Production effects). *Calculated Gig (A5), (A6), (AlO) and the values from table .’ , ‘EACM-dependent’; e.g., in the first column, 376 equals 65 % (from AS)ot 70% (from AlO) of 1578, less 50 % (from A6). ‘Calculated using (ATj, LLIL.. ’ -A (AlO); , e.g., in the first column, 200equals 20% (from A7) of 8076 (from AlO) of 1250, from table 2, ‘trade diversion’, column 4. “c-aiculated _ using (A8) and (AlO); e.g., in column 1, 300 equals lo”/, (from AS) of 80% (from AlOj of 3750. from table 2, ‘trade creation’, co!u;nn 4.
Net benefits to each couniry ~~____. _______ __
2. trade creation imports’
Corlsritq7tiot~effects I. trade diversion i;.lportse
opportunity cost 1. trade creation expotW 7h. trade diversion exportsb in IC U-dependent industries 3. prodwtion ‘or domestic consumpt ionC 4. import substitution for imports from third country*
Prorbc~tiotleJecrs: value added minus resource
_-..
._
Benefits to each of the three tbvo-country common markets (in thousand f).
Table 4
D. Gately, Sharing gclins mnong LDcls
Benefits of non-cooperation
229
Table 5 for each country (in thousand f).
Production eficts: value added minus resource opportunity cost 1. production for domestic consumption from surviving EACM-dependent industries” 2. import substitution for goods previously imported from former partnersb
Benefits to Kenya
Benefits to Uganda ___.
Benefits to Tanzania
2863
1070
300
1280
1630
2030
Net benefits
2700 4143 2330 -__. ___-__ ---__ “Calculated using (AS) and the values from table 3, line 3 of Production effects; e.g., in column 1.2863 equ& 50 7; (from A9) of 5725 (from table 3, line 3 of Production effectsi. bCalculated using (A5), (A@, (A9) and the values from table 2, ‘EACM-dependcni’; e.g., in the first column, 16’30equals 65 74 (from A5) of 60 % (from A9) of the sum of 5060 and I.578 (from table 2, ‘EAC H-dependent’), less 50 % (from A6). Table 6 Values of the characteristic function (in thousand f). Coalition Value r:(K, U,T) t$K, (J) c(K, Tj cW, T) r!K) l(U) L’(T)
I: % ?‘j (K: Tj (U, T) (Kj Wj \T) -
= 17026 = 11642+4223+1161 = 10185 = 7156f3029 = 91S6 = 8083+1’06 = 6769 = 4266+2503 = 4143 = 2700 = 2330
plicity, the core then consists of those distributions 17000 and, from ,:onditions (3) in section 4,
itable3) (table 4) (table 4) (table 4) (table 5) (table 5) (table 5)
such that X, + _I’,,+ XT =
4100 s X, 5 10200 = 17000-6800, 2700 5 X, 5
7700 = 17000-9300,
2300 5 XT 5
6800 = 17000 - 10200.
Geometrically, the hexagonal
in the three-dimensional distribution space of fig. 3, the core is area ABCDEF” within the triangle of imputations LMN. If we
31The lines through the following pairs of points in fig. 1 are represented follows: XK = 4100, ,u,+x, = 12900; AB: BC : XIJ = 7700, x,+ _YT = 9300; PE : EF :
CD :
XT = 2300, ,:li+x, x, = 10200, x,+x, ,-u,: = 3700, x,-l- x;
= 14700; = ‘;XOD; = 14300;
AF :
XT =
= 10230.
6800,
X~+Xu
annly~ically
as
D. Gate/y, Slrclring gains among L DC’s
236
impose the addition;11 criterion of mutual acceptability, that no country’s propensity to disrupt have a value greater than, say, 3, then we are left with the i mpurations within the triangle WY 3’ in fig. 3. kote that, according to our calculations, the actual distribution from table 3, rounded off to the nearest hundred, X, = 11600, Xu = 420@,X = 12OQ,is not a member of the core (in fact it’s not even an imputation) since Tanzania receive? an amount (1161) less than it would receive under self sufficiency, 2300 = v(T). (This distribution is denoted as point Z in fig. 1.) From this it follows that Tanzania could improve its position by dropping out of the three-country
;‘7-
pu
:l @ L c-_---
A
6
----
\
\
i
(:?2;/ , ’
\
;
\
,’
/’
A’ _,’/ -__
--
_I
\ ,’ ,” ,,,’
/,’
7!” ,,
‘).
, ,‘/. ‘c j//;, i, _, / Y’ :. E I D ‘\ ‘4’ i, ; 3
_i;
r,
%
Fig. 3. The triangle of imputations and the core.
Li~iOR.'3Tanzania’s
unilateral action in 1965 to impose restrictions on many imports from Kxya and Uganda was therefore understandable; it amounted to park1 non-cooperation and a threat of total non-cooperation. Also understandal~le w’as the reluctance of all parties to have Tanzania drop out of the EACM entire-l;:: Tanzania preferred to be a member of the EACM so that it j2The ;i~e iflm_lgh the points XY, for example, has dT = 2; it lies two-thirds of the distance Tr~rnline AF (Tanzania’s maximum payment in the core) to line CD (Tanzania’s minimum p:,:,ment in the con:). 3 TThis conclusior: would hold even if we were to takp qccount of the effects of the EP CM Di:;trihutable 1’001, through which 48.5 thousal:d E were transferred from Kenya to Ur.nnda a!,:1 ‘8X thouianci f from Kenya to Ta.?zania II-I1 ?I?-63.
D. Gately, Sharing gains among LDC’s
231
could realize gains greater than it could achieve alone, c(T), and both Kenya and FJganda wanted Tanzania’s cooperation so that they could jointly achieve gains greater than those of the two-country union, u(K, U), Let us digress for a moment to consider two specific imputations which might be suggested as candidates for the ‘fairest’ distributicn, the equal-sh.ares distribution and the Shapley value distribution. The equal-shares distribution (A’, = X, = X, = 17000/3 = 5667) has the simplest rationale for being equitable, divide the t&al gains into three equal shares. 34 It is a member of the core in this example, although this will not be true in genera13’ Kenya’s propensity to disrupt under such an imputation would be greatest, at a ::alue close to 3. The Shapley value imputation has also been suggested as a benchmark of fairness. 36 For our exemg le it is the distribution X, = 7190, Xu = 5230, X, = 458C (point S in fig. 1). This also is a member of the core3’ and it approximately equalizes each country’s propensity to disrupt. 38 So far our analysis of the mutually acceptable distributions of the gains has considered only the set of imputations. But if the countries are unwilling to make (or accept) monetary side payments, or if shifting industries between countries does not conserve the gains, then we must also consider distributions which are not imputations. One might argue that these countries were in fact willing to agree to side payments, given the way the distributable pool and the common services were operated. 39 However, Tanzania’s main demand in the 196Ys was not for greater monetary compensation but for a greater share of industrial development. Similarly, the assumption that shifting industries conserves the 34Making shares proportional to each country’s population would result in the distribution Xk = 5780, Xu = 4590, X, = 6630: (34x, 27x, 39x, respectively); in fig. 3 this would be a p”‘~~?~~~l~ ?%lely (1974) and Fischer and Gately (1974). 36For example,‘in Segal(l969). The Shapley procedure assumes that three-country coalition is formed by some sequence such as country A joining the two-country coalition (B, C), which in turn was formed by country B joining the one-country ‘coalition’ (C); there are six possible sequences, each assumed equally likel:r. It also assumes that the country joining the coalition receives the entire increment resulting from his joining. The Shapley value for country A is its expected final payment under this procedure t XA
=
W(A,
B,
a-v@,
al-t-b%
B,
O--u@,
-t
[v(A, B; -u(B)] + ‘o(A, C - a(C)]
+
[u(A)1 + MA)ll.
C>l
See Lute and Raiffa (1957) or Rapoport (1970). 37The Shapley value is no: necessarily a men.ber of the core even when the core is non-empty; for the conditions under which it is not see Fischer and Gateiy (1974). j*The Sha,pley value is, in general, not the same as the imputation which equalizes the propensitiesto disrupt; 1or a zero-one normalized characteristic function with non-empty core they will only be eqtlal if either the three players are symmetric or if o(A, B)+u(A, C); o(B, c) = 1. [See Fiscier and Gately (1974).] It also happens that, for the particular characteristic function considered here, the kernel imputation and the core’s center of gravity arc virtually the same as the Shapley value. 39See Robson (1968) and Hdewo0d(1967). E
23:!
D. Gately, Shacing gains among L DC’s
gains is a questionable one. Since the choice of industrial location under laissezfaire would be made to minimize the cost of production and distribution, higher costs would presumaibly be involved if the industry were 1.0 be located in a different country, rlesulting in smaller total gains to the EACM as a whole.40 !Suchan alternative approach will not be considered in detail here, even though it might be helpful for a complete understanding of the agreement reached in the 1967 Treaty for East African Cooperation. This treaty resolved the tensions of the mid4Q’s and averted the dissolution of the EACM. Based on the principle of each country havir;g a ‘baiance’ in its EACM imports and exports of manufactures, it provided for a system of temporary ‘transfer taxes’ (a euphemism for unilateral inter-country tariffs) on some manufactured exports from Kenya to Uganda and to Tanzania, and from Ug;anda to Tanzania. This agreement presumably resulted in a mutually acceptable distribution, but at the cost of reduced total gains. 6. Smne concluding comments
The example from section 5 was, of course, merely illustrative. It was not meant as the final word on the debate within the literature about the division of benefits from the East African Common Market. Given the heroic nature of our assumptions in handling the data and the back-of-the-envelope character of the calculations, little confidence should be placed in the actual numerical results. Two important things, however, do stand out. One is that rt-person game theory provides the most appropriate framework for considering questions of a fair di.,ision of the gains from intlegtation, as advocated by Segal. The other is that the proper measure of the gains and 10s~: ought to follow the lines sketched out in section 3. 40However,as Morawetz(13721has shown, when distortions are present, administrative locationof in#&cstries nlu~increasethe we1far,l=of the union as a whole.
References Balassa, B., 1967, -Trade creation anid trade diversion in the Eu::opean Common pdfarket, Economic Journal 77, i-21; Reprinted in: Robsaa, (1972). B&&l, 5.. 3974, Trade creation and tradr: diversion in the European Common Market : An appraisal of the evidence, mimeo. Brovx~,. A.J., 1961, Econom.; separation versus a common market in developing countries, Yorkshire Bc:L:tin of Ecc,lomic al?d Sociiil Research 13,33-40,88-96. Fiscbtx, D. and D. Gate’!y, 1974, A. compari!son of various solution concepts for three-person cooperative s,xmes with non-empty cores, mimeo. (New York University, New York). Lately, D., 197rL,Sharing the gains from regional cooperation: A game theoretic application to pfannilg nvestment in e&t& power, International Economic Review 15, no. 1, 195XI%. GIG, II., 1964, Temitorial distribution of tl-e benefits and costs of the East African Common slarkct, E&i African Economics Review i 1.
D. Cutely, Sharing gains among L DC's
233
Hadewood, A., 1966, The ‘shiftability’ of industry and measurement of gains and losses in the East African Common Market, Bulletin of the Oxford University lnstitute of Economics and Statistics 28, no. 2,63-72. Hazlewood, A., ed., 1967, African integration and disintegration (Oxford University Press, London). Krauss, M.B., 1972, Recent developments in customs union theory: An interpretive survey, Journal of Economic Literature 10, no. 2,413+36. Leibenstein, H., 1966, Allocative efficiency versus X-efficiency, American Economic Review 56,392-415. Lipsey, R.G., 1960, The theory of customs unions: A general survey, Economic Journal 70, no. 279,496-513; reprinted in: R.E. Caves and H.G. rohnson, eds., 1968, A.E.A. Readings in international economics (Richard D. Irwin, Homewood, Ill.). Lute, R.D. and H. Raiffa, 1957, Games and decisions (Wiley, New York). Mead, D.C., 1968, The distribution of gains in customs unions betwe:n developing countries, Kyklos 21, no. 4,713-734; reprinted in: Robson (1972). Morawetz, D., 1972, Equitable distribution of benefits in integration schemes among less c&eloped countries: The Andean group, Economic Development Report no. 216 (Harvard University, Cambridge, Mass.). Nev;lyn, W.G., 1965, Gains and losses in the East African Common Market, Yorkshire Bulletin of Economic and Social Research, Nov.; reprinted in: Robson (1972). Ni?gwa, P., 1968, The common market and deveilopment in East Africa (East African Publishing House, Nairobi, Kenya). Rapoport, A., lf70, N-person game theory [University of Michigan Press, Ann Arbor, Mich.). Robson, P., 1968, Economic integration in Africa (Northwestern University Press, Evanston, Ill.). Robson, P., ed., 1972, International economic integration: Selected readings (Penguin Books, Middlesex, England). Segai, D., 1969, East African Common Market inequities of the 1960’s: An arbitration scheme, unpublished Ph.D. dissertation (Yale University, New Haven, Conn.). Segal, D., 1970, On making customs unions fair: An East African example, Yale Economic Essays 10, no. 2, pp. 115-I 60. United Nations, Department of Economics and Sncial Affairs, 1969, Economic cooperation and integratron in Africa: Three case studies, E.69.11.K.7.
Publishing Company
SHARING THE GAlINS FROM CUSTOMS UNIONS AMONG LESS DEVELOPED CO.LJNTRIES A game theoretic approach Dermot
LATELY
*
New York University, New York, N. Y. 10003, U.S.A.
Received March 1974, revised version received August 1974
1. Introduction Finding a mutually acceptable distribution of the gains from cooperation is probably the main barrier to economic integration among developing countries, and the main cause of friction within existing arrangements. In this paper we discuss the sources of these gains, both for the custom:; union as a whole and for the individual countries (section 2). A measure of these: gains and losses is proposed (section 3) and it is then utilized in a framework ofn-peisC n, cooperative game theory to analyze various questions discussed in ths literattire, such as which distributions would be mutually acceptable, whether an actual distribution of the gains is ‘fair’ and whether an individual country wouid be bettei off dropping out or not joining (section 4). Such an approach i$ ‘cht-n illustratetl with an ex-post analysis of the distribution of gains from Ihe East African Common Market (section 5). 2. The gains and losses from cooperation The main economic goal of integration among less developed countries is an increase in the level of output, especially industrial output, over what it TtiGdld be in the absence of integration.’ The economic ratiorale for customs unions, or the sources of gains, fall into two groups, those associal:ed with protection and those associated with cooperation per se.2 *The author is Assistant Professor at New York University. Much of the work on this paper was done while the author was Visiting Lecturer at the Uni\ersi,:y of Ghana, on leave fron the University of Western Ontario, under a twinning arrangement funded by the Canadian International Development Agency. He is grateful fbr the comments of participants at a seminar in the Economics Deparrment of the University of Ghana and for those of R.G. Lipsey; any remaining errors are, of col;rse, the responsibility of the author. ‘Whether a customs union will achieve this goal, or whether it could be better achieved by some other policy, ha.s often been. discussed in the literal ure, most recently in Krauss (1972). ZThe discussion here draws upon Rr?bson (1972) and Lipsey (1960).
214
D. Gately, Slmritrggains among LDC’s
The gains from protection are import.mt inasmuch as a customs union iimong less developed countries might best be thought of as protection on a more efficient scale. The most important argurr,:nts in this group are the infantindustry or learning-by-doing argument, the external economies generated by industrial activity, and the existence ofdomestic cl.istortions (such as the industrial wage exceeding the opportunity cost of labor). The sources of gains from cooperadon per se are several. The most important ones we believe to be: first, economies of larger scale production and operation; second, the increased availability of certain factors, in particular foreign capital; and third, increased efficiency in the use of existing factor inputs. Scale economies can be realized both by new industries and by already existing industries. A new industry can build a single large plant to service the entire customs union, capturing the technological and managerial economies of scale not available to several small plants in the various countries. Existing industries can also become more efficient when capacity underutilization. is reduced or when mlllti-plant firms, each plant previously producing the same variety of products, can be re-organized to specialize production within each plant. For example, if each country has a footware factory producing both shoes and sandals then, after the establishment of the customs union, they can specialize production and export their specialty to the partner country. As the larger market makes new industries feasible and as the common tariff barriers are erected, the supply of capital responds to these new opportunities for profit. Foreign capital inflows (and perhaps also private domestic savings) increase the availability of this important factor; accompanying such inflows are technological and managerial skills. The competitive pressures resulting from the movement toward freer trade can increase the efficiency of existing factor inputs in at least two ways. Allocative efficiency, or increased specialization within exist.ing activities among member countries according to comparative advantage, is well known to economists but its practical importance has been shown to be almost trivial. Less precisely formulated, but probably much more important, is Leibenstein’s notion of X-efficiency, 3 which could be loosely described as motivational efficiency. teibenstein’s examples are illustrative and easily supplemented by some casual empiricism in modern sector activity in the less developed countries: simple reorganization of the work process, payment by results, promotion by merit, and better worker attitudes can often increase output by 25 % or more. All these potential gains are, of course, gains for ,the customs union as a whole. Yet they will noi necessarily be distributed among the members in a way &hat could generally be considered equitable. The distribution of gains is likely to be ighP~:correlated with the distribution of the new industries resulting from the eitabliihment of the customs union, which are likely to concentrate around the
aheady developed centers within the union .4 Peripheral countries in the union which do not share in the distribution of industries might even be worse off under the union, relative to what they could achieve without the union. For example, an independent country might be able to attract and support some small ‘shiftable’ industries by protecting its domestic market; however, if that country were part of a customs union, such plants might instead locate at the already developed centers in the partner countries.5 The losses to the union as a whole stem from the trade-diverting ell’ects of the union, low-cost imports fro% abroad are replaced by higher-cost, protected production within the union. 6 This cost disadvantage would hopefLdly be shortterm, as in the infzmt-industry case, but it is sometimes a permanent feature of the union. Another potential loss, or al least a difficulty created by the union, is the reduction in government tariff revenue, both from the abolition of duties on trade between members and from the reduction of imports from coulitries outside the union.’ This lost revenue would have to be replaced from alternative dependable sources, which are often difficult to find. 3. Measuring the gains and losses To measure the gains or losses to a given country resulting from a customs union requires a comparison between that country’s growth over time as a member of the union and what its growth over time would have !:cen in the absence of the union. Several attempts have been made in the literature to estimate such effects, especially for the European Common Market.* Such studies normally use data for a single ‘representative’ post-union year to examine the union’s effects. Ideally, of course, a se.ries of post-union yeErs should bt: studied in order to evaluate the longer-term effects of the union. schema, although OLII In this section we sketch an ideal measurement numerical example in section 5 is a considerably simplified version. Let’s conside.? three countries about to form a customs union, call them A, B agd C. (Three is the minimum number necessary to illustrate some of the essential problems in sharing the gains from cooperation.) At first glance there might appear to be only tLvo alternatives, either a three-country union or no union at This proccsc is what Hirschma:~ calls ‘polarization’. Such cf?‘ccts arc discussed in Newlyn (193). “See Ncwlyn (1965). “\+‘hilc \vc arc ;l\{are of the theoretical nossibility of Lvelfare improvcm~~nt from ;L tr;ldcdivcrtjng customs union, v/c tJo not conjid :r it to hnxc any likely pr;lc!il.:ll ‘m;x)rt:ince: 111~ issue is treated most recently in Kkauss (197?.). We follow Balassa (1967) in associating the negative effects with trade diversion. ‘In West Africa, for example, the proportion of import duties in total government rcvc’n~c exceeds 50 :‘i for Togo, Dnhome>, and Upper Vuita; see United Nations, Dcpartmcnt of Economics and Social Affairs (1969). 8fjal;ls~:~(1974) survq’s the e\GJt:ncc on trade cr-1-1tion and trade diversion in the Euro?c.1!7 ~‘ontnlo~~Ilk1rkct. n
216
D. Gately, Sharing gains among L DC’s
all. There are however j%x possible ways in which these three countries group themselves into ‘coalitions’; these five ‘coalition structures’ are: (i)
[(A, B, C)] the three-country
(ii)
[(A, B), (C)] A and B in a union, C outside;
(iii)
[(A, C), (B)] A and C in a union, B outside;
(iv)
[(B, C), (A.)] 13 and C in a union, A outside;
(v)
could
customs union;
[(A), (B), (C)] no union at all.
The three additional cases of two-country unions are essential for an understanding of the bargaining power of the individual countries and of the different coalitions. Consider the five coalition structures from the viewpoint of one country,’ say country A. Let us make the assumption that A’s prospects for growth under a stratea of independence do not depend upon whether or not B and C happen to form a union, Given this assumption we need to consider what happens to A in each of four coalitions: (A, B, C:i, t-4, B), (A, C) and (A); that is, from A’s viewpoir t coalition structures (iv) and (v) are the same. 3.1. The three-country wiorl We want to estimate the growth over time in A subsequent to the formation of the three-country union. I0 Benefi,ts (losses) to A c:m occur on the production side and on the consumption side. On the production side the benefits (losses) result from the increased (decreased) output following the setting up of the union, either from newly established industries or from the expansion (contraction) of already existing industries. Note that this output change could occur in industries producing ei;ports for its partners or producing for domestic consumption. The measure of these benefits on the prod:uction side w xtld be the social value added of this increase in catput minus the social opportunity cost of the productive factors involve;i.” Any benefits from employment creation are assumed to be reflected in this measure. The consur option effects follow from the change in the pattern of consumption and imports subsequent to the establishment of the union. These effects are of twc types, the gain (loss) of consumers’ surplus and the loss of government tariff revenue. One o:r both of these will occur for the following four categories of consumption: ‘Our measurement schema does not (bt.:t could) take account of the effects of any benefitsharing mechanisms built into the agreement, such as an administrative scheme to allocate nc;i industries; this and others are discussed in Morawetz (3Q73). ‘01nclu3ed here obviously, is the growth that would have, occurred tiithout the union. Since ihi\ is also inclpldci in the measure of gains to A when indep’znclent of the union, it is netted out At !“?Cend. ’ ‘Thcsc benefi:s on the production side ai:c discussed more extensively in Mead (19G8).
D. Gate&, Sharing gains among L DC’s
(i) goods formerly produced in A, now displaced B or C: a gain of consumer’s surplus;
by lower-cost
217
imports
from
(ii) goods previously imported from outside the union and now imported from B or C : a loss of tariff revenue and a gain (loss) of consumers’ surplus if the new price to consumers is below (above) the former price; (iii) goods formerly and still imported surplus but a loss of tariff revenue;”
from
B or C: a gain of consumers’
(iv) goods formerly and still produced in A; if scale or other effects allow a price reduction there will be a gain of consumers’ surplus. For categories (ii) and (iii) note that lost tariff revenue might be weighted more heavily than gained consumers’ surplus; policy makers within the government would very likely be inclined to do so because of the difficulty of finding alternate sources of government revenue. All these benefits and losses over time, both on the production side and the consumption side, should be discounted to present value and summed to form a scalar measure. 3.2. A two-comiry
customs uniorz
Taking the case of country A in (A, B), the benefits (losses) are calculated similarly to the case of the three-country union. The benefits (losses) on the production side result from the increased (decreased) output subsequent to the establishment of (A, B). In this case the new indusrries in A might not include some which were !oca:ed there under (A, B, C) because the smalier market (A, B) could not support such an industry. On the other hand, some industries that might have located in C under (A, B, C) might now locate in A under (A, B). On ti\e consumption side, the benefits and losses would fall in the same categories as under (A, B, C); there would, however, be smaller price reduction effects from reduced scale economies and there wouLd be a different pattern of consumption and imports in A under (A, B), as compared with the case under (A, B, C>. These calculations of the efiects of the establishment of the union (A, B) can also he used to estimate the eventual eflects on A and B of the following sequence : the three-country union is formed but C drops out, leaving (A, B). This \vil\ ‘x true unless there happen to be some putty-clay asymmetries os!,ociz,ted with C s joining and leaving. One possible asymmetry woulcl be the cast of an industry which would not have been cstablishcd in A hxd (A, B) :xen formed at th: outset but, once established ill A under (A, B, C), it learns-by-doing and can survive the departure of C. ’ 3 l 21f scale effects allow an additional price reduction the gain of consumers even larger. 1-‘Pic~cly~ (1965) discusses other possible asymmctrics.
surplus will kc
D. Gately, Sharing gains among LDC’s
218
3.3. A one-country ‘coaiition
Finally, consider ,the case of country A following s policy of independence; this, of collrse, need not imply a policy of autarky under which all trade ceases with B and C. The benefits to A in this case would simply be the growth and development taking place in A over. time, discounted to the present. These benefits for A could conceivably be lrtrger than those to A under a two-country or three-country customs union, as might be the ctse for a peripheral country noted in section 2. The calculations for this case could likewise be used to estimate the eventual effects upc,n A, of joining a customs union but then dropping out, unless there were important putty-clay asymmetries. 4. The garae theoretic framework a measure of the benefits to each country .“;om three-country cooperation, two-country cooperation and non-cooperation brings us to the characteristic function for the game and a wa!r of determining what distributions of the benefits WCuld be mutually acceptable. For each of tht, seven possible coalitions, 14 the clwac.*eristic function oalue for that codition is defined as the sum of the benefits to each member’ 5 (as measured in section 3); it is a scalar measure, the net present value of the future benefits to be shared by the members of that coaii tion. 16 Let us denote the characteristic function value for some coalition S as c(S), Taking the two-country coalition (A, B) as an example, the characteristic function ta!ue ,c(A, B) would equal the sum of the benefits to A and the benefits to B (as measured in section 3) if the tu’o-country union (A, B) were to be formed. We allow for side payments between partners in a coalition, for example, by fiscal compensation (as in the East African Common Market’s Distributable Pool, as a means of redistributing the benefits. ’ 7 Such side payments are assumed to have the properties of transferable utility. l8 The sum of benefits to a given country plus (minus) any side payments received (made) will be denoted, respectively, X,, X,, and Xc. With this background we can now proceed to perhaps the most critical question facing a customs union : what distributions o:f the benefits of cooperation Swh
1‘the sel.en are the three-country coalition, the three two-country coalitions, and the three one-countrJ~ coali tion.5. I ‘This ad3ition of benefits assumes comp;.rability between countries in time preference for &x:,ts and in their perception and evaIuatior of the benefits. i “Whilr this ~aluc will b-_ a single number it is not a ‘static’ measure in the sense of repreCT-ting or!y current benefits. _,. i -This assumption skirts a vihoie range of interesting issues related to the actual imgiementatinn nf benefit sharing. !Horau,etz (1972) discusses several such schemes: compensation via ::;comt: t -ansfcrs, the eqI.iitable allocation cf new industries, balanced intra-unio:l payments, ;ii~d :I b;?~rp& distributicn of not fixal gains. “P +)r ,2 di;c3-iion see Luceand Raiffa(1957, plr. 168-170, l:?A-181).
D. Gclely,
Slrarkggains among LDC’s
219
would be mutually acceptable? The first condition that a distribution of the otal bt-nelits of the three-country union must satisfy is that of individual ration: iit.y, t!lat each country should receive benefits at least as great as it would receive if it were not a member:
If any of these inequalities is llot satisfied then that country rvould be better off outside the union. Note that this is not the same as saying that the measured benefits to each country under the t!xee-country union should be positive. ” All those distributions of the total benefits [K,, X,, Xc such that X,+ S,,+ Xc = r(A, B, C)] which satisfy this condition of individual rationality con: titutc the set of imputations. A second condition of mutual acceptability could also be imposed: th:\t an); pair of countries jointly receives an amount no less han what they could xhicve without the cooperation of the third:
X,+X,
(2bj
2 v(A, C),
If any one of these three inequalities is not satisfied then those two co _mtries could both gain by refusing to cooperate with the third. All those distributions of the total benefits which satisfy conditions (1) :md (2) constitute the cow 0,’ the game. Equivalently: the core can be defined as the >,et of those distributions of the total benefits which satkfy : P(A) =< X, S z(A, 13, C) -r(B,
C),
(12)
220
D. Cutely, Sharing gains among LDC’s
Membership in the core would he a minimal condition of mutual acceptability; distribution outside the core can bc successfully vetoed by a pair of countries or by a single country. 2o Thus, if countrv# A were receiving less than it was guaranteed in the core, X, < u(A), it csuid drop out of the three-countr:y union and increase its benefits to v(A); alternati\rely it could threaten to drop out unless its share of the benefits were increased to an acceptable level. Or, if countries A and B were jointly receiving too small a share of the benefits, X,+ X, < u(A, B) [that is, if country C were receiving too large a share, Xc > u(A, B, C) - v(A, B)], then A and B could refuse to cooperate with C and could increase their joint benefits up to the amount v(A, B); likewise, they could jointly threaten noncooperati’on with C unless their share were sufficiently increased. A. geometrical representation of the set of irr,putations and the core is depicted in the three-dimensional diagram in fig. 1 foi* one example of a characteristic any
function :
c(A) = 0.05 ,
~(5) -= 0.10,
V(C) = 0.15,
zl(A, B) = 0.30,
v(A, C) = 0.40,
U(I3,C) = 0.50,
r(A, B, C) = 1.0. T’ht. triangle P,P2P, describes those distributions (X,, ;Brg,Xc) of t:ie :oltal benefits ix,+ XB+ Xc = tt(A, B, C)] such that each player’s share i- nonnegative. The smaller triangle LMN represents the set of imputation- Tile hexagon’ ’ Q 1Q2Q3Q4Q!iQ6 represents the core. While the core puts a reasonable upper limit on each country’s share of the benefits [the right-hand inequalitks af (3)], the lower limits [the left-hand inequalities of (3)] do not guarantee that each country will be much better off, if at all, than if it did not cooperate. To eliminate such distributions we introduce the concept of a country’s propa~tsity to disrupt the three-country distribution (X, y X,, Xc); for each country it is the ratio of holw much the other two countries would lose, to how much it vvould lose if it refused to cooperate.22 For country A, “Alfhougl; WEwill be discussing characteristic functions with non-empty cores there c!o exist characteristic functions for which the core is empty, e.g., t.(A) = r-(B) = r(C) = 0,
r(riB) = z$AC) = c(BC) = 0.9,
z:(A, B, C) = 1.
P-or such a ;Icro-one normalized characteristic function the core will be empty if and only if 1(A +Bi L 1(X. C‘)- I$B, C) > 2. In such cases, intuitio,ely, the benefits to three-player cooperation XC not very rn?lch bigger than those of two-player cooperation; the three-player coalition ii 11;~sIikcly to form in such cases. For such games other concepts are important; see Luc;ts t P9”l~. Lucc and .Raiha (1957) and Rapoport (I 370). i ’ Depndrng *upon the characteristic function the core can take a variety of shapes: hexagon, ntagon, pa....J~elogram, trapezoid, triangle, line segment or point; see Fischer and Gate!y 1i ‘37.1). 2‘Tijii
concept v.as introduced in Gately (1974) and its properties discussed extensively mn I.lit%.zr snSi b;alcE:. (137-a).
D. Gcrtely, Sharing gains among LDC’s
d,
E
&+ x,--v(B, C) maximum of (0, X,- v(A))
221
*
Note that. a country’s propensity to disrupt a given imputation will be infinite if it receives an amount less than or just equal to what it could achieve by not cooperating. And its propensity to disrupt will be very large if it receives only slightly more than it is guaranteed within the core, while the other Iwo jointly receive significantly more than what they are jointly guaranteed. At such a distribution it could threaten non-cooperation, hoping to receive a larger share of the benefits, with the knowledge that the other two countries would suffer a considerably greater loss (or foregone gain) that it would if it carried out the
Fig. 1
threat. Such a threat would be credible and the country would be rat:ional in actually carrying out such a threat, in the hope of achieving a larger share of the benefits at a later negotiating session. Unlike some games that are played once and only once, such regional negotiations can be terminated and later re-opened if the participants desire. Using this concept we can eliminate, as not mutually acceptable, any core imputation for which any country’s propensity to disrupt is ‘too high’, greater than, say, 2. ’ 3 In ig. 2, the set of mutually acceptable distributions would bc the intersection of the core Q,Q2Q3Q4Q5Q,; and the triangle2” R,H;:,FL,,; the characteristic function used is the same as in fig. 1. 230ther limits on the propensity to disrupt of any country (or of any pair of countries) arc discussed in Fischer a?d Gately (1974). 241n this example The triangle lies entirely within the core. However, this is not nl:ccssnril) true, See Gately (197r) and Fischer and Gately (19741.
‘7 ,‘, ._ __
D. Gately, Sharing gains amojtg L DC’S
Since we could still be left with a fairly large set of mutually acceptable distributions we could proceed to consider several specific imputations that might be proposed as candidates for the ‘best’ distribution, such as the Shapley value, the kernel imputation, the equal-shares imputation, or the imputation equalizing tile propensities to disrupt. This has been done elsewhcre15 and we shall do it briefly in sectioa 5. Yet, however interssting the rationale for any of these specific imputations, we don’t believe that any of them ‘ought’ to occur, either in a predictive or a normative sense. Th?ls, what we’ve done in this section is to specify the set of mutually acceptable distributions of the benefits, within which *he actual distribution ought to lie. If it does rlot, then the agreement which proaticed such a distribution is not likely to endure; either the dissatisfied country will opt out entirely or a new
Fig. 2
agreement, acceptable to that country, will be negotiated. The dynamics of negotiating an agreement and arriving at a particular distribution of the gains are not considered here. 5. AR illustrative example from the East African Common Market
We now apply our analytic framework to the case of the East African Common Market (EACEJ), formed in 1957 by Kenya (K), Uganda (U), Tanganyika [Tar,zania] (T). !6 The extent and thf: distribution of benefits from the EACM hale been much debated in the literature27 and within the EAChl itself, 25S
D. Gately, Sharing gains
among LDC’s
223
especially in the mid 1960’s. Zt seems generally agreed that the region as a whole had benefited but the distribution of the gains had beer. uneven, with Kenya having gained the most and Tanzania the least. There was no agreement, however, about whether Tanzania and perhaps Uganda had suffer?“, 2 IF’! loss and would have been better cff dropping out. The controversy reached a critical point in the mid-1960’s and threatened to dissolve the EACM. A compromise solution was agreed upon in the 1967 Treaty for East African Cooperation, which gave certain concessions to Tanzania and, in lesser degree, to Uganda. We shall now examine the distribution of benefits within the EP,CM, using data for the year 1963. Much of the debate in the literature has focussed on the data for that year an? we shall also use it as representative of the situation in the early 1960’s. Of course, as pointed out earlier, the benefits should be evaluated over a number of years; we do not do this because of data limitations and because the purpose of this example is only illustrative. Listed in table 1 are each country’s 1963 exports to its EACM partnc::s, irs ‘EACM expc’ts’, broken down into SITC categories. In order to use this to estimate thl: actual distribution of benefits in 1963 we must make some simplifying assumptions: (Al) Net all of a country’s EACM exports are dependen; upon the existence of the EACM; some would continue even without the EACM. Assume that the percentage which is independent of EAC,M’s existence is the same as the percer tage of that country’s E#9CM exports receiving no external tariff protection, 14 % of Kenya’s EACM exports, 20 % of Uganda’s and 46 y/, of Tsnzani:t ‘s.” (A2) The percentage commodity composition of a country’s EACM exports to each of the other two countries is the same as that of its total EACM exports. Furthermore, each country’s EACM-dependent exports have the same percentage commodity composition as its total EACM exports. (A3) In EACM-dependent industries, tion is equal to that country’s production
the production for domestic fur EACM export.
consump-
(A4) A country’s trade &version exports consist of one-half its EACiLG dependent exports in SITC categories 1, 5, 6, 7, 8 (call these categories ‘manu7 ‘-y/o of its EACM esport,s are in ‘LJ~escc:1tegoric:;. 50 i’,:, factures’); for Kenya 7_.3 for Uganda and 36.7 7,; for Tanzania. 1ts trade-crcatlon export% cmsist O; all its other EACM-dependent exi3orts.
- --___-__
1oC:‘, (75.8%) (24.2 %)
8,243 6,250 to Kenya 1,993 to Tanzania --
33.2% 17.2% 1.6% 4.2% 10.9% 4.0 % 27.7 % 0.3 % 0.8 % 0.1%
100% 19,790 9,400 to (47.6 %) Uganda 10,390 to (52.4 %) Tknzania
‘Taken from Ndegwa (1968, pp. 50-51, 58-63).
--
T0ta.l: of which
Food Bcveragcs ~tnd tobacco Crude mntcrials FUClS Oils and fats Chemicals Manufactured goods Machinery Miscellanco:~: mrutufactcres Other
Description
Proporticu af its total (11)
Uganda’s EGCM exports (3) __-.2,738 1,419 133 349 901 ^__ 531 2,280 20 66 6
___-
Kenya’s Proportion EACM exports of its tctal (1) (2) ~- _~.____ ..-._--. 4.904 24.8 % 15.1% 2,995 0.9% 184 0.3 % 49 1.0% 205 1. .l.Y>, z.“,, 2,5-X3 27.3 :< 5,404 C.9”/, 179 17.3% 3,428 o.!i % 94
--_--.--._-_-__.
Commodity composition of EACM exports, 1963 (in thousand f).”
Tnblc 1
_
Proportion of its total (6) 36.4% 3.1% 17.2% 1.1% 8.4% 1.4% 16.5% 0.2% 15.5% 0.2 “/, loC% (85.2%) (34.8 %)
Tanzania’s EACM exports (5) 1,247 107 590 38 287 iT\ 5:: 6 526 7 3,423 2,920 to Kenya 503 to Uganda
-
D. Gaiely, Sharing gains among LDC’s
225
(A5) Value added as a proportion of total value is 65 % for all industries in the three countries. 2g (A6) The opportunity cost of all resources involved in EACM-dependent industries is only one-half of their value added in such production. (A7) The additional cost to the country importing trade-diversion exports is 20 % of the value of the goods. (A8) The benefits to the country importing trade-creation exports equal IO % of the value of the goods. Needless to say, these assumptions are heroically simple. Some of them [(A2), (A3), (A4j, (A7), (WI could be modified by access to relevant data which probably exist already. For example, if the EA(ZM export data in table 1 were further broken down according to country o ’ destination, assumption (A2) would not be necessary. Other assumptions, such as (A6) and perhaps (Al), might not yie;? to a closer scrutiny of existing data and a certain element of judgement would continue to be necessary. It should be stressed again that our example is illustrative and no more confidence should be placed in the numerical results than in the underlying assumptions. By contrast, Segal(1969, 1970) assumed that all EACM exports were EACMtiependent (if any country dropped out then all its trade with the other two would cease) and that they were entirely trs.de-creation exports. Assuming zero opportunity costs for resources involved in EACM exports,30 his measure of total gain was the value added in all EACM exports. This measure would seriously overstate the gains from coopera:ion. On the basis of our assumptions the EACM exports are broken down in table 2 and the calculation of the actual benefits are made in table 3. From this distribution of benefits - 11642 to K, 4223 to U, and 1161 to T - we calculate the sum, 17026, which is the characteristic function value u(K, U, T) for the three countries together. In order Lo estimate the effects c,F one country dropping out of the threecountry EACM we must make some additionai assumptions: (A9) If one country refuses to cooperate, then all its EACM-dependent exports and imports will cease and its production for domestic c’zasumption in EACM-dependent Lldustries will be reduced by half. it can import-substitl;tc for “Segal(l969) calcuiated these percentages as 65 y.; for Kenya and Uganda but only 45 1: fcr Tanzania. Our mcasbre of the actual distribution of gains will therefore be biased, relative to Segal’s, in favor of Tanzania. 30With respect to labor, he jus:lficd wch an assumption consisted of labor-surplus economies. A; for foreign capital only by the establishment of the EACM Our assumption of but less than value added, is clearly a corny. romise between the
on the grounds that the EAChI he assumed that it \\\‘a~ attracted opportunity costs being positive. extreme position:;.
8080 2925 5155
EACM-indcpendentS
EACM-dependent 1, tra& diversionb ?. trade creation
_
d_
.~-
-
.%
,_-
_
.-
‘Calculated using the percentagts from (Al). bCalculated using (A2), (A4) and table 1.
9400 1320
Tofui exports
to u (1)
-
-
a935 3255 5700
10390 1455
toT I-’ (LI -
-
-
I
17115 6160 10855
I
total (3) ______ 19790 2775
-
-__-
_.
.- -- .-_-. Kenya’s EACM exports
L
5000 1250 3750
L-
-,
.
.
r,
--
-____--
1595 399 1197
II
_
6595 1649 4947
_-.. .-. Uganda’s EACM exports -----total to K to T is) (6) (4) _-_6250 1993 8243 1250 395 I$“‘:
_
_
Lag.
1578 290 1289
272 50 222
-
.,.-
--
1850 340 151:
__
Tanzania’s ZACM exports --to U to K total (8) (7) (9) ____ 2920 503 3423 1342 23i 1573
___----
A breakdown of EACM exports, resulting from our assumptions (in thousand 0.
Table 2
: CF b-
z $
2 f? 2’ :
P P $? CrJ z0 g.
P
D. Gale/y, Sharing g~~iilsamong .CDC’s
227
Table 3 Distribution of benefits in the three-country common market (i,z thousand E). Benefits (losses) to Kenya eficfs: value added minus resource opportunity cost 1. trade creation exportsa 2. trade diversion export? 3. production in EACM-dependent’ industries for domestic consumption
Benefits (losses) to Uganda
Benefits (Ilosses) to Tanzania ---
Prohction
Consutrykm effects 1. trade diversion importsd
2. trade creation imports” Net benefits to each country
3525 2000
1605 535
490 111
5725
2140
601
(308) 500
(595) 538
(731) 690
4223
1161
11642
“Calculated as 65 “/, of the ‘trade creation’ values of table 2, less the resource oppo:.tunity cost of 50% from (A6); for example, in column I,3525 = (0.65)(0.50)(10855). bCalculated as above, but using ‘trade diversion’ of table 2; e.g., in column 1.2000 = (0.35) (0.50)(6160). “FrOM (A3) it follows that amounts on this line equal the sum of the two lines immetlial ely above. ‘From (A7) and the ‘trade diversion’ figures of table 2; e.g., in column 1,308 = (0.20)(1250+ 290). eFrom (AS) and the ‘trade creatio2’figuires of table 2; e.g., in column 1,500 = (0.10)(!750+ 1289).
only a fraction, say 60 ‘A, of its former EACM-dependent would represent the ‘shiftable’ industries.
imports;
this fra,:tilln
(A 10) The non-cooperation Jf one c0untr.y will have an effect upon the EAZ’N;dependent industries in the union of the other two countries; only 80% of the EACM-dependent exports betueen those two countries and SOY4 of their domestic production in EACM-dependent industries will survive. Those two countries will be able to import--substitute for a fraction, say 70%, of Their former EACM-dependent imports from the non-cooperating third country, These assumptions likewise are rather arbitrary, again for purposes of illustration. There is, of course, no reason why one would expect the identical percentages of (A9) and (AlO) to apply to exh country or to each pair of countries. The benefits to each country in a two-country ultion are e:timatetl ar,d listed in table 4, for each of the three possible two-country unions, And the benefits of non-cooperation are calculated for each country and listed in table 5. The characteristic function values, for each of the seven coalitions, XC listed in table 6. Rounding these values OR to the nearest hundred for the sake of sim-
-
.___-
.
. .._..
-_.__ -_
~~_
7156 -__
-~
3029
65
1720
4580 3’7’6
975 325
Benefits (losses) to u
1340 760
(;zj
. __
W, U) ---.- ~--~--- .~~-~-------
__
Benefits (lOSSPSj to K
_ ---___
8080
(47) 103
1113
4580
1480 845
__ ____.-
1206
(520) 455
380
480
335 76
Benefits (losses) toT _.___~~
-Jo ---
_.~_.__
Benefits (losses) tcK __.~ ~-
K __ -.
(Zj 2503
4266
1920
480
58 13
Benefits (losses) :0 T
(8) 18
2120
1720
312 104
Benefits (losses) to u
u-4 n
_.____-_
~
“Caiculated using (A5), (AG), (AlO), and the values from tab.,, ‘L 7 _, ‘trade creation’; e.g., in the first column, 1340 equals 65 % (from A5) of 80% (from AlO) of 5155, less 50%(fromA6). bCalcu!at~d using (AS), (A@: (AlO) and the values from table 2, ‘trade diversion’; e.g., in column I, 760 = (0.65) (0.80) (0.50)(2925). 2 of Production effects; e.g., in cc”::~n 1,458O equals 80 % (frcm AlO) of 5725 (from ‘Cakuiated using (AlO) and the values from table 3, line + table 3, line 3 of Production effects). *Calculated Gig (A5), (A6), (AlO) and the values from table .’ , ‘EACM-dependent’; e.g., in the first column, 376 equals 65 % (from AS)ot 70% (from AlO) of 1578, less 50 % (from A6). ‘Calculated using (ATj, LLIL.. ’ -A (AlO); , e.g., in the first column, 200equals 20% (from A7) of 8076 (from AlO) of 1250, from table 2, ‘trade diversion’, column 4. “c-aiculated _ using (A8) and (AlO); e.g., in column 1, 300 equals lo”/, (from AS) of 80% (from AlOj of 3750. from table 2, ‘trade creation’, co!u;nn 4.
Net benefits to each couniry ~~____. _______ __
2. trade creation imports’
Corlsritq7tiot~effects I. trade diversion i;.lportse
opportunity cost 1. trade creation expotW 7h. trade diversion exportsb in IC U-dependent industries 3. prodwtion ‘or domestic consumpt ionC 4. import substitution for imports from third country*
Prorbc~tiotleJecrs: value added minus resource
_-..
._
Benefits to each of the three tbvo-country common markets (in thousand f).
Table 4
D. Gately, Sharing gclins mnong LDcls
Benefits of non-cooperation
229
Table 5 for each country (in thousand f).
Production eficts: value added minus resource opportunity cost 1. production for domestic consumption from surviving EACM-dependent industries” 2. import substitution for goods previously imported from former partnersb
Benefits to Kenya
Benefits to Uganda ___.
Benefits to Tanzania
2863
1070
300
1280
1630
2030
Net benefits
2700 4143 2330 -__. ___-__ ---__ “Calculated using (AS) and the values from table 3, line 3 of Production effects; e.g., in column 1.2863 equ& 50 7; (from A9) of 5725 (from table 3, line 3 of Production effectsi. bCalculated using (A5), (A@, (A9) and the values from table 2, ‘EACM-dependcni’; e.g., in the first column, 16’30equals 65 74 (from A5) of 60 % (from A9) of the sum of 5060 and I.578 (from table 2, ‘EAC H-dependent’), less 50 % (from A6). Table 6 Values of the characteristic function (in thousand f). Coalition Value r:(K, U,T) t$K, (J) c(K, Tj cW, T) r!K) l(U) L’(T)
I: % ?‘j (K: Tj (U, T) (Kj Wj \T) -
= 17026 = 11642+4223+1161 = 10185 = 7156f3029 = 91S6 = 8083+1’06 = 6769 = 4266+2503 = 4143 = 2700 = 2330
plicity, the core then consists of those distributions 17000 and, from ,:onditions (3) in section 4,
itable3) (table 4) (table 4) (table 4) (table 5) (table 5) (table 5)
such that X, + _I’,,+ XT =
4100 s X, 5 10200 = 17000-6800, 2700 5 X, 5
7700 = 17000-9300,
2300 5 XT 5
6800 = 17000 - 10200.
Geometrically, the hexagonal
in the three-dimensional distribution space of fig. 3, the core is area ABCDEF” within the triangle of imputations LMN. If we
31The lines through the following pairs of points in fig. 1 are represented follows: XK = 4100, ,u,+x, = 12900; AB: BC : XIJ = 7700, x,+ _YT = 9300; PE : EF :
CD :
XT = 2300, ,:li+x, x, = 10200, x,+x, ,-u,: = 3700, x,-l- x;
= 14700; = ‘;XOD; = 14300;
AF :
XT =
= 10230.
6800,
X~+Xu
annly~ically
as
D. Gate/y, Slrclring gains among L DC’s
236
impose the addition;11 criterion of mutual acceptability, that no country’s propensity to disrupt have a value greater than, say, 3, then we are left with the i mpurations within the triangle WY 3’ in fig. 3. kote that, according to our calculations, the actual distribution from table 3, rounded off to the nearest hundred, X, = 11600, Xu = 420@,X = 12OQ,is not a member of the core (in fact it’s not even an imputation) since Tanzania receive? an amount (1161) less than it would receive under self sufficiency, 2300 = v(T). (This distribution is denoted as point Z in fig. 1.) From this it follows that Tanzania could improve its position by dropping out of the three-country
;‘7-
pu
:l @ L c-_---
A
6
----
\
\
i
(:?2;/ , ’
\
;
\
,’
/’
A’ _,’/ -__
--
_I
\ ,’ ,” ,,,’
/,’
7!” ,,
‘).
, ,‘/. ‘c j//;, i, _, / Y’ :. E I D ‘\ ‘4’ i, ; 3
_i;
r,
%
Fig. 3. The triangle of imputations and the core.
Li~iOR.'3Tanzania’s
unilateral action in 1965 to impose restrictions on many imports from Kxya and Uganda was therefore understandable; it amounted to park1 non-cooperation and a threat of total non-cooperation. Also understandal~le w’as the reluctance of all parties to have Tanzania drop out of the EACM entire-l;:: Tanzania preferred to be a member of the EACM so that it j2The ;i~e iflm_lgh the points XY, for example, has dT = 2; it lies two-thirds of the distance Tr~rnline AF (Tanzania’s maximum payment in the core) to line CD (Tanzania’s minimum p:,:,ment in the con:). 3 TThis conclusior: would hold even if we were to takp qccount of the effects of the EP CM Di:;trihutable 1’001, through which 48.5 thousal:d E were transferred from Kenya to Ur.nnda a!,:1 ‘8X thouianci f from Kenya to Ta.?zania II-I1 ?I?-63.
D. Gately, Sharing gains among LDC’s
231
could realize gains greater than it could achieve alone, c(T), and both Kenya and FJganda wanted Tanzania’s cooperation so that they could jointly achieve gains greater than those of the two-country union, u(K, U), Let us digress for a moment to consider two specific imputations which might be suggested as candidates for the ‘fairest’ distributicn, the equal-sh.ares distribution and the Shapley value distribution. The equal-shares distribution (A’, = X, = X, = 17000/3 = 5667) has the simplest rationale for being equitable, divide the t&al gains into three equal shares. 34 It is a member of the core in this example, although this will not be true in genera13’ Kenya’s propensity to disrupt under such an imputation would be greatest, at a ::alue close to 3. The Shapley value imputation has also been suggested as a benchmark of fairness. 36 For our exemg le it is the distribution X, = 7190, Xu = 5230, X, = 458C (point S in fig. 1). This also is a member of the core3’ and it approximately equalizes each country’s propensity to disrupt. 38 So far our analysis of the mutually acceptable distributions of the gains has considered only the set of imputations. But if the countries are unwilling to make (or accept) monetary side payments, or if shifting industries between countries does not conserve the gains, then we must also consider distributions which are not imputations. One might argue that these countries were in fact willing to agree to side payments, given the way the distributable pool and the common services were operated. 39 However, Tanzania’s main demand in the 196Ys was not for greater monetary compensation but for a greater share of industrial development. Similarly, the assumption that shifting industries conserves the 34Making shares proportional to each country’s population would result in the distribution Xk = 5780, Xu = 4590, X, = 6630: (34x, 27x, 39x, respectively); in fig. 3 this would be a p”‘~~?~~~l~ ?%lely (1974) and Fischer and Gately (1974). 36For example,‘in Segal(l969). The Shapley procedure assumes that three-country coalition is formed by some sequence such as country A joining the two-country coalition (B, C), which in turn was formed by country B joining the one-country ‘coalition’ (C); there are six possible sequences, each assumed equally likel:r. It also assumes that the country joining the coalition receives the entire increment resulting from his joining. The Shapley value for country A is its expected final payment under this procedure t XA
=
W(A,
B,
a-v@,
al-t-b%
B,
O--u@,
-t
[v(A, B; -u(B)] + ‘o(A, C - a(C)]
+
[u(A)1 + MA)ll.
C>l
See Lute and Raiffa (1957) or Rapoport (1970). 37The Shapley value is no: necessarily a men.ber of the core even when the core is non-empty; for the conditions under which it is not see Fischer and Gateiy (1974). j*The Sha,pley value is, in general, not the same as the imputation which equalizes the propensitiesto disrupt; 1or a zero-one normalized characteristic function with non-empty core they will only be eqtlal if either the three players are symmetric or if o(A, B)+u(A, C); o(B, c) = 1. [See Fiscier and Gately (1974).] It also happens that, for the particular characteristic function considered here, the kernel imputation and the core’s center of gravity arc virtually the same as the Shapley value. 39See Robson (1968) and Hdewo0d(1967). E
23:!
D. Gately, Shacing gains among L DC’s
gains is a questionable one. Since the choice of industrial location under laissezfaire would be made to minimize the cost of production and distribution, higher costs would presumaibly be involved if the industry were 1.0 be located in a different country, rlesulting in smaller total gains to the EACM as a whole.40 !Suchan alternative approach will not be considered in detail here, even though it might be helpful for a complete understanding of the agreement reached in the 1967 Treaty for East African Cooperation. This treaty resolved the tensions of the mid4Q’s and averted the dissolution of the EACM. Based on the principle of each country havir;g a ‘baiance’ in its EACM imports and exports of manufactures, it provided for a system of temporary ‘transfer taxes’ (a euphemism for unilateral inter-country tariffs) on some manufactured exports from Kenya to Uganda and to Tanzania, and from Ug;anda to Tanzania. This agreement presumably resulted in a mutually acceptable distribution, but at the cost of reduced total gains. 6. Smne concluding comments
The example from section 5 was, of course, merely illustrative. It was not meant as the final word on the debate within the literature about the division of benefits from the East African Common Market. Given the heroic nature of our assumptions in handling the data and the back-of-the-envelope character of the calculations, little confidence should be placed in the actual numerical results. Two important things, however, do stand out. One is that rt-person game theory provides the most appropriate framework for considering questions of a fair di.,ision of the gains from intlegtation, as advocated by Segal. The other is that the proper measure of the gains and 10s~: ought to follow the lines sketched out in section 3. 40However,as Morawetz(13721has shown, when distortions are present, administrative locationof in#&cstries nlu~increasethe we1far,l=of the union as a whole.
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D. Cutely, Sharing gains among L DC's
233
Hadewood, A., 1966, The ‘shiftability’ of industry and measurement of gains and losses in the East African Common Market, Bulletin of the Oxford University lnstitute of Economics and Statistics 28, no. 2,63-72. Hazlewood, A., ed., 1967, African integration and disintegration (Oxford University Press, London). Krauss, M.B., 1972, Recent developments in customs union theory: An interpretive survey, Journal of Economic Literature 10, no. 2,413+36. Leibenstein, H., 1966, Allocative efficiency versus X-efficiency, American Economic Review 56,392-415. Lipsey, R.G., 1960, The theory of customs unions: A general survey, Economic Journal 70, no. 279,496-513; reprinted in: R.E. Caves and H.G. rohnson, eds., 1968, A.E.A. Readings in international economics (Richard D. Irwin, Homewood, Ill.). Lute, R.D. and H. Raiffa, 1957, Games and decisions (Wiley, New York). Mead, D.C., 1968, The distribution of gains in customs unions betwe:n developing countries, Kyklos 21, no. 4,713-734; reprinted in: Robson (1972). Morawetz, D., 1972, Equitable distribution of benefits in integration schemes among less c&eloped countries: The Andean group, Economic Development Report no. 216 (Harvard University, Cambridge, Mass.). Nev;lyn, W.G., 1965, Gains and losses in the East African Common Market, Yorkshire Bulletin of Economic and Social Research, Nov.; reprinted in: Robson (1972). Ni?gwa, P., 1968, The common market and deveilopment in East Africa (East African Publishing House, Nairobi, Kenya). Rapoport, A., lf70, N-person game theory [University of Michigan Press, Ann Arbor, Mich.). Robson, P., 1968, Economic integration in Africa (Northwestern University Press, Evanston, Ill.). Robson, P., ed., 1972, International economic integration: Selected readings (Penguin Books, Middlesex, England). Segai, D., 1969, East African Common Market inequities of the 1960’s: An arbitration scheme, unpublished Ph.D. dissertation (Yale University, New Haven, Conn.). Segal, D., 1970, On making customs unions fair: An East African example, Yale Economic Essays 10, no. 2, pp. 115-I 60. United Nations, Department of Economics and Sncial Affairs, 1969, Economic cooperation and integratron in Africa: Three case studies, E.69.11.K.7.