FINAL REPORT TONATIONAL COUNCIL FOR SOVIET AND EAST EUROPEAN RESEARC H

TITLE : COSTS AND BENEFITS OF SOVIET TRAD E

WITH EASTERN EUROPE : A THEORETICA L

AND QUANTITATIVE ANALYSI S

PART I I

"OPTIMAL BEHAVIOR IN THE PRESENC E

OF UNCONVENTIONAL GAINS FROM TRADE "

AUTHORS : Michael Marrese, Northwestern University

and

Jan Vaňous, University of Britis hColumbi a

CONTRACTOR : Northwestern University, Evanston, Ill .

PRINCIPAL INVESTIGATORS : Michael Marrese, Department of Economics ,Northwestern University

Jan Vaňous, Department of Economics ,University of British Columbi a

COUNCIL CONTRACT NUMBER : 622- 5

The work leading to this report was supported in whole or i npart from funds provided by the National Council for Sovie tand East European Research .

- 48 -

BIBLIOGRAPHY

Hirschman, Albert O . [1945], National Power and the Structure o fForeign Trade (Berkeley : University of California Press) .

Korbonski, Andrzej [1980], "Eastern Europe : Soviet Asset or Burden ?The Political Dimension," Working paper, Department o fPolitical Science, University of California, Los Angeles ,January .

Marer, Paul [1979], "Is Eastern Europe a Soviet Asset or Burden? Th eEconomic Dimension, Working paper prepared for delivery at th eAnnual Meeting of the American Political Science Association ,Washington, D .C ., August 31 .

Olson, Mancur, Jr ., and Richard Zeckhauser [1966], "An Economic Theoryof Alliances," The Review of Economics and Statistics 48, 3(Cambridge : Harvard University Press, August), pp . 266-279 .

Russett, Bruce M . [1968], "Editor's Comment," in Bruce M . Russett (ed .) ,Economic Theories of International Politics (Chicago : MarkhamPublishing Company), pp . 64-67 .

Schelling, Thomas C . [1960], The Strategy of Conflict (Cambridge ,Massachusetts : Harvard University Press) .

Tasker, Rodney [1980], "Facing Moscow's Pincer Movement," Far EasternEconomic Review, May 9-15, pp . 21-25 .

Theriot, Lawrence H . and JeNelle Matheson [1979], "Soviet Economi cRelations with Non-European CMEA : Cuba, Vietnam, andMongolia," in Soviet Economy in a Time of Change (Washingto nD .C . : Joint Economic Committee, Congress of the United States ,October), pp . 551-581 .

Vaňous, Jan [1980a], "Eastern European and Soviet Fuel Trade," Discussionpaper no . 80-10, Department of Economics, The University o fBritish Columbia, April .

Vaňous, Jan [1980b], "Soviet and Eastern European Foreign Trade in th e1970s : A Quantitative Assessment," Discussion paper no .80-11, Department of Economics, The University of Britis hColumbia, April .

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"OPTIMAL BEHAVIOR IN THE PRESENCE O FUNCONVENTIONAL GAINS FROM TRADE "

by

Michael Marrese and Ja n Vaňous

A B S T R A CT

Unconventional gains from trade are defined as the non-market benefit sof bilateral agreements which are secured through bilateral preferentia ltrade treatment . Unconventional gains from trade arise because of conflict samong different groups in society, which motivate government officials t ochoose bilateral preferential trade treatment as a hidden way of generatin gnon-market benefits . Creating bilateral terms of trade which are differen tfrom world market terms of trade has been an observable example of bilatera lpreferential trade treatment .

The customs union literature addresses the issue of preferential trad etreatment, but focuses on welfare measured in terms of consumption of trade dgoods and services . Our analysis focuses on commodities which under particularsocial traditions and during a particular time period are not traded openly .Moreover, our analysis is applicable in either an auctioneer-type situatio nwith many buyers and sellers or in a bilateral bargaining situation .

The purpose of this paper is to analyze the production, trade and con-sumption behavior of a country facing bilateral terms of trade which diffe rfrom world market terms of trade because of the presence of non-market benefits .Section 1 presents two examples in which social conflict causes the bilatera ldistortion of world market terms of trade . Both examples utilize three hypo-thetical countries : POLECON, representing a politicized economy intereste din obtaining non-market benefits from EXECON : EXECON, which is a potentia lexternal source of non-market benefits for either POLECON or ROW : ROW, th erest of the world, which is also interested in obtaining non-market benefit sfrom EXECON .

In the first example, EXECON's non-market benefits are auctioned to th ehighest bidder . Suppose POLECON is the highest bidder . Why doesn't POLECONsend a lump-sum payment to EXECON for these on-market benefits ?

Assume that a conflict exists within POLECON . Suppose POLECON's govern-ment values highly the non-market benefits from EXECON but POLECON's popula-tion does not . POLECON's government may decide to use a hidden means t opurchase the non-market benfits in order to circumvent domestic conflict .

Why might POLECON decide to alter her bilateral terms of trade wit hEXECON? Anyone not closely associated with POLECON's government would havedifficulty in determining world market prices because of the proliferation o fgrades and qualities of commodities and because of the paucity of detaile dtrade data . So POLECON could covertly pay for non-market benefits by exportin ggoods to EXECON at discount prices and importing goods from EXECON at premiu mprices . Moreover, as long as POLECON either knows, or is able to predic treasonably well, the world market prices of those commodities to whic hdiscounts or premiums are to be added POLECON will be able to calculat ethe "implicit subsidy" that EXECON is receiving .

The term "implicit subsidy" refers to the payment EXECON receive s

from POLECON for non-market benefits . It is calculated as the value o fexports less imports evaluated at world market prices minus the valu eevaluated at the preferential bilateral prices (assuming a standard uni tof account is used through the world) . Therefore, the implicit subsid yis the opportunity loss which POLECON bears by trading with EXECON at pre-ferential bilateral prices rather than with ROW at world market prices .

This example is consistent with the analysis in section 2 as long a sthe increments in the bids of POLECON and ROW for an additional unit o f

non-market benefits increases as the quantity of non-market benefit sincreases .

In the second example, hegemony, defined as a situation in which on ecountry has power superior to that of other countries, plays a crucial role .

Assume POLECON has hegemony over EXECON . In the bilateral bargaining situa-tion between POLECON and EXECON over non-market benefits, hegemony confer s

on POLECON three powers : (1) elimination of ROW as an alternative purchase r

of non-market benefits ; (2) control over the quantity of non-market benefit s

received ; (3) some control over the amount paid to EXECON for the non-marke t

benefits .The first element of hegemony restricts EXECON from auctioning her non -

market benefits to the highest bidder . The second allows POLECON to choos eq*, the quantity of non-market benefits to be transferred . The third refer s

to the set of feasible payments for q* . POLECON will not pay more than th eamount of Vn (q*) to EXECON for q*, and EXECON will not accept less than th eamount V E (q ) from POLECON for q* . So the bilateral bargaining problem is t ochoose

a(q*), the actual payment for q*, such tha tv [ ( q* ) < a ( q* ) < vp( q* ) •

POLECON may not have the power to set a(q*) = v E (q*), possibly because EXECO Nwill argue that POLECON already has imposed restrictions on EXECON by elimina-ting the auction process and by choosing q* . Under a plausible set of assumption s(which includes the presence of conflict between POLECON's government and EXECON' spopulation), we argue that as the quantity of non-market benefits increases ,POLECON's incremental subsidy to EXECON for an additional unit of non-marke tbenefits increases . In other words, there are diminishing returns to an extr aunit of subsidy .

The analysis in section 2 takes place from POLECON's point of view . Wit ha fixed endowment of inputs, POLECON produces goods A,B and C . Only A and Bare traded internationally, with POLECON importing A and exporting B . In de-ciding on the optimal pattern of trade with ROW or EXECON or both, POLECO Nweighs the relative importance of two considerations . On one hand, the termsof trade offered by ROW are more favorable to POLECON than those offered b yEXECON . On the other hand, non-market benefits, obtainable by exchanging B fo rA with EXECON at relatively disadvantageous terms of trade, act as a substitut efor POLECON's domestic production of C .

Two models are presented which incorporate this tradeoff : maximization o fthe utility derived from both conventional and unconventional gains from trade ,and maximization of convetional gains from trade subject to a constraint whic his influenced by unconventional gains from trade .

-iii -

The results of Models 1 and 2 indicate that whether POLECON trades wit hROW or EXECON or both depends on the extent to which non-market benefit ssubstitute for C and on POLECON's relative preference for C . When makin gmarginal trade decisions POLECON always chooses the greater of world marke tterms of trade and the marginal terms of trade inclusive of EXECON's non-marke tbenefits . Finally, POLECON's ability to secure unconventional gains from trad eincreases her utility, and in the case when A,B and C are normal goods, create soptimal patterns of production and consumption which include greater A and B .

OPTIMAL BEHAVIOR IN THE PRESENCE O F

UNCONVENTIONAL GAINS FROM TRADE *

by

Michael Marrese** and Jan Variou s

Discussion Paper No . 80-29

Department of Economic s

The University of British Columbi a

August 198 0

*We are indebted for financial support to the National Council for Sovie tand East European Research in the United States . We are grateful to Davi dDonaldson, Craig Hakkio, Ronald Harstad and John Pomery for useful comment son an earlier draft of this paper, and to Martha Weidner for researc hassistance .

**Department of Economics, Northwestern University .

OPTIMAL BEHAVIOR IN THE PRESENCE OF

UNCONVENTIONAL GAINS FROM TRAD E

by

Michael Marrese and Jan Vaňous1

Unconventional gains from trade are defined as the non-market benefit s

of bilateral agreements which are secured through bilateral preferential trad e

treatment . Unconventional gains from trade arise because of conflicts among

different groups in society, which motivate government officials to choos e

bilateral preferential trade treatment as a hidden way of generating non-marke t

benefits . Creating bilateral terms of trade which are different from worl d

market terms of trade has been an observable example of bilateral preferentia l

treatment . 2

The customs union literature addresses the issue of preferential trad e

treatment, but focuses on welfare measured in terms of the consumption of trade d

goods and services . 3 Our analysis focuses on commodities which under particula r

social traditions and during a particular time period are not traded publicly .

Moreover, a bilateral bargaining model often provides a better framework withi n

which to analyze non-market benefits than does an auctioneer-type model wit h

many buyers and sellers .

Non-market benefits of bilateral agreements may be categorized into fou r

classes : military, political, economic and ideological . 4 The most importan t

type of military benefits are : (i) creation and maintenance of military al-

liances ; (ii) absence of threat (pacification impact) ; (iii) availability o f

military bases in strategic locations ; (iv) access to military technology ,

know-how, and training ; (v) proxy intervention (availability of modern-day

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international mercenaries) ; (vi) possibility of importing military service s

in the case of an internal conflict ; and (vii) ability to consume another

country ' s defense services (free-rider aspect of defense as a public good) .

Potential political benefits include voting along alliance lines in interna-

tional forums, informal foreign government and media support, and the suppor t

and friendship of a foreign population . While most economic benefits of

bilateral trade agreements are conventional in nature, several may be considere d

unconventional : increased economic stability, reduced risk of disrupted flow o f

strategic commodities, and reduced risk of refusal to purchase a country's ex -

ports for reasons other than their price-competitiveness . 5 Possible ideological

byproducts of bilateral agreements primarily occur in three areas : acceptance

of a desired political ideology and its propagation to other countries ; achieve-

ment of religious unity ; and strengthening of ethnic solidarity .

The purpose of this paper is to analyze the production, trade and consumptio n

behavior of two countries facing bilateral terms of trade which differ from worl d

market terms of trade because of the presence of non-market benefits . Section 1

presents two examples in which social conflict causes the bilateral distortio n

of world market terms of trade . The first example involves a covert auction o f

non-market benefits, while the second is based on bilateral bargaining . Both ex-

amples illustrate how the amount paid for the non-market benefits might be deter -

mined . In section 2, the effects of purchasing non-market benefits via trad e

conducted at prices which are more favorable to the seller and less favorable t o

the buyer than world market prices, are studied . Two models are presented : maxi-

mization of the utility derived from both conventional and unconventional gain s

from trade ; and maximization of conventional gains from trade subject to a con-

straint which is influenced by unconventional gains from trade .

-3-

Section 1 : The Presence of Two Sets of Terms of Trade Due to Social Conflic t

In the introduction, unconventional gains from trade are said to aris e

because of conflicts among the preferences of different groups in society .

Two abstract examples serve to illustrate why social conflict is the reaso n

for the existence of unconventional gains from trade .

Consider three countries : POLECON, representing a politicized econom y

interested in obtaining non-market benefits from EXECON ; EXECON, which is a

potential external source of non-market benefits for either POLECON or ROW ;

ROW, the rest of the world, which is also interested in obtaining non-marke t

benefits from EXECON .

In the first example, EXECON's non-market benefits are auctioned to th e

highest bidder . Suppose POLECON is the highest bidder . Why doesn't POLECON

send a lump-sum payment to EXECON for these non-market benefits ?

Assume that a conflict exists within POLECON . Suppose POLECON' s

government values highly the non-market benefits from EXECON but POLECON' s

population does not . POLECON's government may decide to use a hidden means to

purchase the non-market benefits in order to circumvent domestic conflict .

Why might POLECON decide to alter her bilateral terms of trade with EXECON ?

Anyone not closely associated with POLECON's government would have difficulty i n

determining world market prices because of the proliferation of grades an d

qualities of commodities and because of the paucity of detailed trade data . S o

POLECON could covertly pay for non-market benefits by exporting goods to EXECO N

at discount prices and importing goods from EXECON at premium prices . Moreover ,

as long as POLECON either knows, or is able to predict reasonably well, th e

world market prices of those commodities to which discounts or premiums are t o

be added, POLECON will be able to calculate the " implicit subsidy " that EXECON

is receiving .

-4-

The term " implicit subsidy " refers to the payment EXECON receives fro m

POLECON for non-market benefits . It is calculated as the value of exports les s

imports evaluated at world market prices minus the value evaluated at the pre-

ferential bilateral prices (assuming a standard unit of account is used throughou t

the world) . Therefore, the implicit subsidy is the opportunity loss which POLECO N

bears by trading with EXECON at preferential bilateral prices rather than wit h

ROW at world market prices . 6

This example is consistent with the analysis in section 2 as long as th e

increments in the bids of POLECON and ROW for an additional unit of non-marke t

benefits increase as the quantity of non-market benefits increases .

In the second example, hegemony, defined as a situation in which one countr y

has power superior to that of other countries, plays a crucial role . Assume

POLECON has hegemony over EXECON . In the bilateral bargaining situation betwee n

POLECON and EXECON over non-market benefits, hegemony confers on POLECON thre e

powers : (1) elimination of ROW as an alternative purchaser of non-market benefits ;

(2) control over the quantity of non-market benefits received ; (3) some contro l

over the amount paid to EXECON for the non-market benefits .

The first element of hegemony restricts EXECON from auctioning her non-marke t

*benefits to the highest bidder . The second allows POLECON to choose q , th e

quantity of non-market benefits to be transferred . The third refers to the set

*of feasible payments for q . POLECON will not pay more than the amoun t

vp (q*) to EXECON for q * , and EXECON will not accept less than the amount v E (q*)

from POLECON for q* . So the bilateral bargaining problem is to choose a(q*), the

actual payment for q*, such that v E (q*) < a(q*) < v p (q*) . POLECON may not hav e

power to set a(q*) = vE (q*), possibly because EXECON will argue that POLECO N

already has imposed restrictions on EXECON by eliminating the auction process an d

by choosing q* . However, POLECON's control over price can be quantified, at least

- 5-

conceptually, by an index of price control 0(q*), which is calculated as :

6(q*) = 1 -

a(q*) - vE (q * )

vp (q*) - vE (q* )

If 6(q*) = 0, then POLECON has no price control ; if 0(q*) = 1, then POLECON ha s

complete price control .

In the case in which the transfer of non-market benefits from EXECON t o

POLECON is advantageous or at least non-detrimental to all parties in both coun-

tries, then the solution to the bilateral bargaining problem may well be a zero

payment to EXECON because EXECON does not have a viable threat position [this i s

certainly so if 6(q'*) = 1] . However the modelling in section 2 requires tha t

POLECON behaves as if there exists a functional relationship indicating tha t

for an additional unit of non-market benefits, the incremental implicit subsid y

increases as the quantity of non-market benefits increases .

The following assumptions provide a framework in which this functional re-

lationship seems plausible : POLECON realizes that EXECON's population, as distinc t

from EXECON's government, interprets greater military and political associatio n

with POLECON as meaning less sovereignty ; sovereignty is a commodity desired by

EXECON's population . Even if the governments of POLECON and EXECON have th e

same preferences, as long as EXECON's population has a threat position that

forces POLECON to pay a greater additional increment of subsidy for each additiona l

increment of benefits, the analysis in section 2 is valid . So it is the conflic t

between POLECON's government and EXECON's population which causes the distortio n

of world market terms of trade .

- 6 -

Section 2 : Optimal Behavio r

The analysis in this section takes place from POLECON's point of view .

POLECON has the option of trading with ROW or EXECON or both . ROW offer s

POLECON better terms of trade than EXECON (see Table 1, part 6), but w e

will demonstrate that it may be optimal to trade with both countries simul-

taneously .

With a fixed endowment of inputs, POLECON produces goods A,B and C .

Only A and B are traded internationally, with POLECON importing A and export-

ing B at existing relative prices . However, non-market benefits obtainabl e

by exchanging B for A with EXECON at relatively disadvantageous terms of trade ,

act as a substitute for POLECON's production of C .

E(•) (see Table 1, part 10) is a strictly concave and increasing functio n

which maps the implicit subsidy, Tr, into non-market benefits, E . Thus EXECON

is modelled as providing an additional increment of non-market benefits for a n

increment of implicit subsidy which increases as the quantity of non-marke t

benefits increases .

The implicit subsidy, rr, is the opportunity loss which POLECON bears fo r

trading with EXECON (see Table 1, part 8) . 7 Given the balance of trade con-

straints with ROW and EXECON (see Table 1, part 7), it may be reduced to th e

value of all exports less imports evaluated at world market prices (see Table 1 ,

part 9) . So 7 is equal to POLECON's hypothetical balance of trade surplu s

that would have existed if POLECON would have conducted all of her trade a t

world market prices .

D{•} (see Table 1, part 11) captures the substitution between domesticall y

produced C and E . D is the amount of C that yields the same level of service s

to POLECON as the combination C( C) and E(T) . So the concave and increasin g

function D{•} allows the extent to which non-market benefits act as a

- 7-

Table 1 : Characteristics of POLECON

1 . Fixed Endowment of Inputs (x1, . . .,xN) where xi > 0 for i = 1, . . ., N

Inputs may be used domestically to produce A,B or C . Inputs may not be traded .

For i = 1, N

xiA

amount of i th input used to produce A

xiB

amount of i th input used to produce B

xiC

xi

xiA

xiB amount of i th input used to produce C

> 0x,

> xiA

xi

> xiB > 0 L

Input feasibility constraint s

X .

> x

>1

-

1 C

2 .

Production functions A ( . ),

B(•) and C(•)

ar econcave and increasing functions of inputs .tives .

twice differentiable, strictlySubscripts denote partial deriva -

A = A(x1A,. . .,xNA)

EA(RA) where A(0) = 0 and Aj (0) _ for some j

B = B(x1B,. . .,xNB)

E B(RB ) where B(0) = 0 and BJ.(0)

= oo for some j

C = C(x1C, . . .,xNC)

E C(RC ) where C(0) = 0 and C . (0) = for some j

3. A° amount of A domestically consume d

B° amount of B domestically consume d

4. At existing relative prices, POLECON imports A and exports B

- [A(RA) - A°] amount of A which is importe d

[B(xB) - B°] amount of B which is exporte d

5. a

fraction of - [A(cA) - A°] imported from ROW

(1-a) fraction of - [A(xA) - A°] imported from EXECON

S

fraction of

[B(xB ) - B°] exported to ROW

(1-S) fraction of [B(x B ) - B°] exported to EXECO N

6. PA trading price for A with RO W

PB trading price for B with ROW

RA trading price for A with EXECO N

RB trading price for B with EXECO N

PB > RB > 0 and RA > PA > 0

AA E PAa + RA(1-a) average trading price for A

AB - PBS + RB (1-S) average trading price for B

- 8-

7. POLECON's

balance of trade constraints with

ROW

PAa[A(RA) - A°] + P B 8[B(RB) - B°] = 0 ;

EXECON

RA (1-a)[A(RA) - A°] + RB (1-S)[B(RB ) - B°] = 0

8 . 7 is the implicit subsidy in terms of a common international currenc ytransferred to EXECON by POLECON .

7 = (PA - RA)(1-a)[A(RA) - A°] + (PB - RB)(1-S)[B(RB) - B° ]

9. Given that balance of trade constraints with ROW and EXECON will alway sbe required to hold, 7 may be simplified as follows :

7 = (PA RA)(1-a)[A(RA) - A°] +,(PB-RB)(1-8)[B(RB) - B°] +

{PAa[A(RA) - A°] + PB8[B( RB) - B°]} + {RA(1-a)[A(RA) - A°] + RB (1-S)[B(RB) -B°] }

= PA [A(RA) - A°] + PB [B(RB) - B° ]

10. E is a one-dimensional measure of the non-market benefits which POLECO Nreceives from EXECON . E( . ) is twice differentiable, strictly concave an dincreasing in Tr .

E = E(Tr) for 7 > 0 where 0 = E(0 )

11. D is the amount of C that yields the same level of services as the combinatio nC(RC) and E(T) . D{•} is twice differentiable, concave and increasing in bot h

arguments .

D = D{C(RC ), EM} where 0 = D{C(0), E(0)}, C(R C) = D{C(RC), E(0)}

-9 -

substitute for domestically produced C to vary with the level of domesticall y

produced C and the level of non-market benefits .

Assume that in the absence of unconventional gains from trade, POLECO N

would trade with the country which offers the more favorable terms of trade ,

implying that no quality or transportation differences exist .

Finally, assume that POLECON accepts both sets of terms of trade as fixe d

(though the analysis also holds for terms of trade represented by non-linea r

offer curves) . 8 This assumption ignores

POLECON's role in the deter-

mination of RA and RB , the trading prices for A and B with EXECON . However

the analysis in this section does not focus on the determination of R A and RB ,

but on POLECON's behavior once world market prices P A and PB , and RA and RB

are known .

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Model 1 : Maximization of Conventional and Unconventional Gains from Trad e

Model 1 assumes that POLECON maximizes the utility derived from con-

ventional and unconventional gains from trade subject to production efficiency ,

a balance of trade constraint with each trading group and feasibilit y

constraints . We posit a utility function, U[ . ], which is twice differentiable ,

strictly quasi-concave and increasing in its arguments :

(1)

U = U[A0,B0,D{C(XC),E(7)}] ;Ul[0,6, .]=co,U2[ .,0, .]=o.,U3[ ., .,0]=°° .

Another restriction on the utility function is that A, B and C are normal goods .

So an increase in POLECON'S endowment implies increased consumption of A, B an d

C .

The constraint of production efficiency is embodied by definin g

xiC

xi

xiA - xiB

i = 1, . . .,N and by the input feasibility conditions .

The balance of trade constraints have been embodied by reducing 7 (see Table 1 )

from

7 = (PA QA)(l-a)[A(RA) - A°] + (PB-QB)(l-S)[B(RB) - B°] t o

7 = PA [A(RA ) - A°] + P B [B(x) - B°] . Actually, this simplification requires onl y

an overall balance of trade constraint with both groups . However only when both

individual balance of trade constraints are included, are we able to solve for

unique values of a and S . The unique values for a and S enable us to determin e

POLECON's import and export patterns .

Let us begin by deriving the unique value for a and S . From the balanc e

of trade constraint with ROW,

P

[B(x ) - B° ]P a[A(x )- A°] + P S[B(x ) - B°] = 0 => a = - B SB .A

A

B

B

PA

[A(RA)-A0 ]

Substitute this value of a into a balance of trade constraint with EXECON,

- 11-

P B [ B (RB ) - 13° ]

—

[A(X ) - A°] + R (1-S)[S(X ) - B°] = 0A [A(XA) - Ao]

A

B

B

[A(RA) - A°]

PB

RB

[B(XB ) - B°]

PA

RA

(PB

BS = - [A(RA)-A0]

B -_> PA

RA

[B(xB)

B°]

RA

(2)

[A(RA)-A°]

RB

[B(RB )-B°]

RA

B

RB

PA

RA

P

P B [B(xB ) - B°3a =- P

A [A(RA) - A°] S and (2) = >

[A(RA)-A°]

RB

PB [B(XB ) - B°]

- [B(RB ) - B°]

RA

- PA [A(XA) - A°]

PB

RB

_ >

PA

RA

P B

P B R B

1[B(RB ) - B° ]

PA + PA RA

[A(RA ) - A° ]

P B

RB

PA

RA

So once POLECON's production and consumption of A and B are determined ,

POLECON's exports to and imports from ROW and EXECON can be calculated by usin g

(2) and (3) respectively .

From

a =

(3)

a

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The feasibility conditions are non-negative inputs and non-negativ e

trade with ROW and with EXECON . Since the production functions are define d

only on the non-negative quadrant, the only feasibily condition is 0 < a < 1

(if this condition is

met, then 0 <

< 1 because of the individual balanc e

of trade constraints) . Substituting (3) into 0 < a < 1 = >

PB

P B RB

[B(RB )-B° ]0 < PA + PA A

R

[A(RA)_A°]

< 1 =>

P

RB

B

P

RA A

PB

PB RB

[B(RB)-B"]

RBPA — PA RA [A(RA)-Ao]

RA =>

(4)

RB

[A(RA)- A° ]_ PBRA

[B(RB ) - B o ] — PA

Hence, including constraint (4) in the model is equivalent to includin g

the restriction of non-negative trade with ROW and with EXECON . If the

right-hand weak inequality in (4) holds as an equality at the optimum, the n

POLECON trades only with ROW . If the left-hand weak inequality holds as a n

equality at the optimum, then POLECON trades only with EXECON . If (4) is a

strict inequality at the optimum, then POLECON trades with ROW and EXECON .

Thus we define L by including the utility function and constraint (4 )

as :

(5) L = U [ A° , B° , D {C(RC ), E( r )}]

- 1 3

P B

[A(RA) - A° ]

RB

[A(RA) - A° ]

PA

[B(RB ) - B°] - ~ 2

RA + [B(RB ) - B°]

J

Since U[•] is continuous and the constraint set is compact, there exists a

feasible solution which maximizes (5) . 9 Furthermore, U[•] is strictly quasi -

concave and the constraint set is convex, 10 thus the maximizer is unique . 11

Finally, if the Kuhn-Tucker conditions hold at a feasible point, then thi s

feasible point maximizes (5) . 12 Consequently, we wish to test the Kuhn-Tucke r

conditions over the set of feasible points . Using subscripts attached t o

functions to denote the first partial derivatives, the Kuhn-Tucker condition s

with respect to A°, B°, x . ,x, and the constraints are :IA 1B

(-X l +A2)(6) U1 [• ] - U3 [• ]D 2 {• } E1 (Tr)PA + [B(xB)-B°1 = 0 ;

(7) U 2 [•] - U3 [ • ]

D2{•} El(w)PB +(A1-A2)

0 2[B(XB)-B ]

[D1

Ai (RA)(8) U3 [•]

C i (Rc) +

E1 (Tr)PAAiA +(a l -a 2 )B(RB)-B°] = 0

;

[A(R )-A° ](9) U3[•][-D1{•}C .(Rc) + D 2 {•}E 1 (Tr)PBB .(RB )] + (-X1+A2)[B(xB)-B°]2 B i (RB ) = 0 ;

[A( RA)-A°]= 0 ;

PB

[A(RA)-A° ]

PA

[B(RB ) - B° ](10)

X 1 = 0 ;

_,RB

[A(RA)-A° ]+

RA

[B(RB )-B° ](11) X2 = 0 ;

(12 )

a l > 0 ;

(13) A2 > 0 .

-14-

We will divide our analysis of the Kuhn-Tucker conditions into thre e

cases which depend on whether the constraints are binding . Case 1 indicate s

that POLECON only trades with ROW . This implies that constraint 1 is binding ,

a2 = 0, it = 0, E(0) = 0, a =

= 1 . The solution to case 1 is equivalent t o

the solution that POLECON would choose in the absence of unconventional gain s

from trade . Let us denote the solution to case 1 with the superscript "+" .

x l(6) => U [ . ] - U 3 [-] D

2{• }E

1(0)P

A1

-[B(RB)-B°+

]

(14) X 1 = rU l [•] - U 3 [•]D2 {•}E l (0)PA I[ B (XB) - Bo+] .

(7) and (10) _>

=0= >

=0= >

(7) => U2 ['] - U3 [ . ] D2 {•}El (0) PB -PB

A

[B(KB)-B°+ ]

(15) A l = U2 [ . ] - U3 [•] D2 {•} El (0) PB PA [B(RB) - B°+ ] .B

P

PSetting (14) = (15) => U 1 [ . ] - U3 [ .] D 2 { . } El (0) PA = U2 ['] 17-- - U3[•]D2{ .}El(0)PA .

Thus (16)

U 2 [Ao+,Bo+

D{C(Rc),0}]

A 1 A,(R+A

)

(8)

=> U3 ['] [_u1 .c1(Xc)

+ D2{.}El(0)PAAi(iA)i i+ [B(RB)-Bo+] = O .

Substituting (14) => U3 [•] [_D1 .c1 ( hc) + D2{ .}El(0)PAAi(k'+)] + U1 [ .] Ai (xA) -

U3[ .]D2{ .}gl(0)PAAi( ;:A) = 0 => (17) A i(e)

U3 f .]D 1 { . }

C .(x C )

Ul [']

P

A(9) and (10) _> U 3 ['][- Dl { . }Ci ( xc) + D2 { • }E1 (0)P

BBi (RI + PA [B(_B)-B°+] - 0 .

PB

U1[A0+,B0+,D{C(c),0}]

PA

-15 -

Substituting (15) => u3[•] [ D1 (.}c .( c ) + D2 { •

}E 1 (0)PBBi (xB', + U2[•]Bi(4:,)

-

c .(5)

U2 [• ]

(17) and (18) _> (19)

Ai (kA)

U2 [• ]

B i (5 )

U1 [• ]

So at the optimum for case 1, (16) indicates that the marginal rate o f

substitution equals world market prices, whereas (19) says that the margina l

rate of transformation in production equals the marginal rate of substitution .

Thus the standard results hold for case 1 .

We have not yet indicated the conditions under which X 1 > 0 . From (14 )

and (15) we know that a l > 0 if f

U3 [•]D2 {•}E 1 (0)PBB i ( x+B )= 0 =>

B i (x 8 )

U3 [']D 1 { • }(18)

U1 [• ]

PA> U

D {•}E (0) and U2[ ] ? U3 [ • ] 2

1

P

3 [ ]D2 { }E1 (0)' Equality of these relation-B

ships implies that a l = 0, which is the limit of case 2 (trade with both coun -

tries) as a and 8 approach 1 .

U1 [•]

U2 [• ]> 0 <_>

P

> U3[•]D2{•}E1(0) and P

> U3[•]D2{ .}E1(0) . These inequali-

A

B

ties indicate that no trade with EXECOiN occurs because the marginal cost of obtain-

ing non-market benefits is greater than the marginal gain from non-market benefits .

Consequently the unique solution for case 1 (a l > 0) is denoted by S 1 :

A .(R+)

I ' B

[•]

A . (ti+ )

L' [•]D 1 {• }1

+ 0+

+

o+

+ 1 A

B 2 1 A 3S

{[n(}.A),A ,B( B ), B ,c( Rc), o ] Bi(xB )_ = PA _ U1[ , ] , C .(hc) _ y- ]

> U3[•]D2{.}E1(0) ; x iA > 0

;x. > 0 ; x. > 0

i = 1, . . .,`i} .

-16-

Case 2 refers to the instance in which POLECON trades with ROW and

EXECON . We know from case 1 that POLECON does not trade with EXECON because

the marginal cost of obtaining additional non-market benefits is greater tha n

the marginal gain from additional non-market benefits . Therefore case 2

occurs iff POLECON receives more non-market benefits from EXECON for each

amount of implicit subsidy (a shift in E(•), at least near Tr = 0) or there i s

an increase in the extent to which each quantity of non-market benefits substi-

tutes for C (a shift in D{•} . So let us assume that either E(•) or D{•} shift s

so that that at S1 the following holds :

Ul [•]

U 2 [• ]

PA

< U [•]D {•}E (0) and p

< U [•]D {•}E (0) ,A

3

2

1

B

3

2

1

For case 2 neither constraint is binding, which implies a l = 0, A 2 = 0 ,

> 0, E(i) > 0, 0 < a < 1, 0 <

< 1 . Let us denote the solution to case 2

with the superscript "'*" .

(6) U 1 [•] = U3[•]D2{•}El(7*)PA .

(7) _> U2 [•] = U3[•]D2{•}El(7*)PB . Thus ,

(20) .

u2[A°*,B°*,D{c(X*), E(Tr*)}]

P B

andA

(21)

U 1 [']

U 2 [• ]

P

=

P

=U 3[ .]D2{•}El(7*) .

A

B

( 8 )

=> U 3 [•]

- D1( .}Ci(R*) + D 2 {•}E l (7*)PAAi (R*) = 0 = >

D ( .}C (R*)

U [• ](72 ) Ai (RA) = D2{•}El(Tr*)PA = U1[•]

D1{•}Ci(xC) .

U1[Ao J.„,B0*,D{C(R*),E(Tr*) } P

-17

-

(9) => U3[•] [ -D l {•} c .(~C ) + D2 {-}E

*)PBBi(R*)] = 0 = >

*

D l{•} Ci (Rc) U 3 [•]

*(23) B Dl{•}Ci(hC) .

U

[• ]D 2 {•}El (u*)PB 2

(22) and (23)A . (R )

_>

(24) B .(YA

)

P= PB

i

B A

Consequently the unique solution for case 2 is denoted S 2 :

y

A .(x*)

P

U2 [- ]

S 2 = {[A(W~), Ao^,B(RB),Bo^,C(KC),E(Tr*)] ; B.(i ) = PA = Ul[•],

A(iA)

U 3 [•] Dl{ . }

C i (RC)

Ul [• ]

x*

> 0 ; x* > 0 ;iA —

iB —

Ul [• ]

P

=U 3 [ . ]D2{ • }

E1 (Tr*) ;A

> 0

i = 1,

,N} .

POLECON is better off in case 2 than in case 1 because of the greater valu e

of non-market benefits in case 2 [due to the shift in E(•) or D{•}] . However accordin g

to (24) the ratio of world market prices still equals the marginal rate of transforma-

tion in production because POLECON, on the margin, trades with ROW . (22) and (23) yiel d

another standard result : POLECON'S level of trade with EXECON and level of domesti c

production of C are determined so that the marginal rates of transformation in produc-

tion between A and C and between B and C equal the respective marginal rates of substi-

tution . (21) indicates that at S2 , the marginal gain from acquiring non-market benefit s

equals the marginal cost .

For case 2,as compared to case 1, the minimum resource cost of consuming C ha s

decreased due to the shift in the value of non-market benefits . This is equivalent t o

a non-linear decrease in the per unit cost of C (or a non-linear price decrease), so mor e

C will be consumed due to the pure substitution effect and due to the income effec t

is a normal good) . Also, more A and B are consumed because they are normal goods . Thus ,

- 18 -

POLECON must produce more A and B for two reasons : to subsidize EXECON and to in-

crease domestic consumption . Given POLECON ' s fixed endowment and the greate r

production of A and B, POLECON must produce less C .

Case 3 refers to the situation in which POLECON trades only with EXECON .

Therefore, relative to case 2, 3 occurs if POLECON receives more non-marke t

benefits from EXECON for each amount of implicit subsidy (a shift in E(•), a t

least near Tr = Tr*) or there is an increase in the extent to which each quantity

of non-market benefits substitutes for C (a shift in D{•}), Furthermore, th e

shift in either E(•) or D{•} must be great enough so that at the solution fo r

case 3 (A2 > 0), the marginal gain of acquiring additional non-market benefit s

is greater than the marginal cost . For case 3, constraint 2 is binding, which

implies A l = 0 , 1 T > 0 , a = = 0 . Let us denote the solution to case 3 with the

superscript

A 2(6) => U1 [•] - U3 [•]D2 {•} El (lr ' )PA +

[B(R')-B°' ]

(25)

A 2 = {U3[•]D2{•}E1(Tr')PA - U1[•]}[B(R') - B° ] .

[A(x')-A°~ ]

(7)

U2 [•] - U3 [•]D 2 {•}El (7r ' )PB - A 2A

°

= 0 = >[B(R')-B ] 2

(26) A 2 = {U3[•]D2{-}E1(Tr')PB - U2[-]}xRA

[B(xB) - B° ' ] sinceB

RE

[A(3.-A)-A° ]R -A

[B(y-B°•]

from (11) .

Setting (25)=(26)=>

U 3 [•]D2{'}EJ

(Tr ' )PA - U 1 ['] =[U3[•]D2{•}El(Tr')PB - U2 [-]RA

_>R B

- 1 9-

RU3[•]D2{•}E1(Tr') = Ul [•] - U

2[•] -j'

P - P RA

B A

R B

(27) U3[A°,BoD{C(Rc),E(Tr')}]D2{•}El(Tr') =Ul [ • ]RB-U2 RA[ •]P R - P R

A B

B A

(~

~] A A, (x' )(8) => u3[•] L -Dl{•}C .(R.') + D2 {•}E1 (Tr ' )PAAl (RA)1 - 2 i Aof

0J [B(RB) - B ]

Substituting (25) => - U3[•]Dl{•}Ci(y + Ul [•]Ai ( RA) = 0 = >

A . (RA) = U3 [•] D l {- }

(28) _> c .(RC )

U 1 [• ]

(~

[A(x')-A°'](9) _> U 3 [•]

L- Dl{•}C .(R~) + D2 {•} E1 (Tr' )PB Bi (RB)1 + X2 [B(xA

° 2B .0-‹) = 0

B )

-B0

Substituting (21) _> - U3[•]Di{•}C .(R') + U2 [•]Bi (RB) = 0 =>

(29) B .(R')

U3 [•] Dl {• }

0i ( 1C )

U 2 [• ]

(28) and (29) => (30)

A .(RA)

U2[A°',Bo',D{C(RC),E(Tr')} ]

B .(RB) - U1[Ao',Bo',D{C(R'),E(Tr')} ]

We have not yet indicated the conditions under which A 2 > O . From (25) ,

we know A2 > 0 iff U 3 [ . ] D 2 {•} El (Tr ' )PA > Ul [•] . So at the solution for case 3

when A 2 > 0, the marginal gain of acquiring additional non-market benefits exceed s

marginal cost . Now let us examine the necessary and sufficient conditions fo r

this to hold . To begin, we return to (27) .

B

- 20-

U [•]

U2[•]R

A(27)

U3[, ]D 2{ • }E 1 (Tr') =

P R B P R

=>

A B

B A

U 3 [ • ]D 2 { • }E1 (Tr') = Ul [ • ]RBU2 [ .]RA

Ul [ • ]RB

1 - _>

1 - P BRAPARB

U2 [ .]RA

PB RA

1 - PA RB

1

.

PARB

(31) U3 [• ]D2 {• }E1 (Tr ' )PA = Ty . ]

Consequently U3 [• ] D2 {• } El ( Tr ' ) PA > Ty . ] <->Ul[-] RB

Po RA1 -

> 1 . From (25) and (31) ,

U 2 [-] RA1 -

PA RB

U2 [']

PBa 2 = 0 <=> U3 [•]D2 {•}E1 (Tr')PA = Ul [•] <=>

_ U[']

P1

Case 3 with a2 = 0 is the limit of case 2 as a and S approach O .

Now we must determine when a 2 > O . Notice that the assumptio n

P

RB

PBRA

PB RAB >

->

> 1=> 0> 1 -P

R

P R

A

A

A

A B

PA RB

a

U2 [ • ]RAThus if 1 - U l [•]RB

U 2 [•]RA

PBRA> l => l -

< 1 -PE R

A

-

Ul[ • ]RB

PAREPA RB

=> (32) U2[•]

PB l[ .] > PA <_>

In (32), U 2 [•] may be interpreted as the marginal terms of trade with EXECON

U1 [ • ]

inclusive of the non-market benefits . So POLECON does not trade with ROW becaus e

the marginal terms of trade with EXECON inclusive of the non-market benefits ar e

greater than world market terms of trade .

Therefore the unique solution for case 3 with A2 > 0 is denoted as S 3 :

A .(x')

U2[ .]

PS 3 = {[A(%',), A°' , B(xB), B°',C(X~),E(ir')] : B1 (XB ) =

Ul[•] > PA

A .(x ' )

U [•]D { .}

U , [•]R - U [•] R ACi (x~)

3U1 [•]

U3[•]D2[•]E1(~!)

PARE -BPBRA 2 A

x A > 0 ; x' > 0 ; x': > 0

i = 1, . . .,N} .

For case 3 as compared to case 2, the minimum resource cost of consumin g

C has decreased due to the shift in the value of non-market benefits . This i s

equivalent to a non-linear decrease in the per unit cost of C (or a non-linea r

price decrease), so more C will be consumed due to the pure substitution effec t

and due to the income effect (C is a normal good) . Also, more A and B will b e

consumed because they are normal goods . Thus POLECON must produce more A an d

B for two reasons : to subsidize EXECON and to increase domestic consumption .

Given POLECON ' s fixed endowment and the greater production of A and B, POLECO N

A 2 > 0 .

- 2 2-

must produce less C .

Adding these results to those previously discussed, we find that :

(33) A(R) > A(RA) > A(R+) ; B(R) > B(XB) > B(XB

) ;

+

o'

o* > Ao+ ;B o' > °;: > Bo+ ;C(R ' )

C(Y*)

C(XC ) ; A> A

D{C(Xp, E(r')} > D { C (R ), E(r*)} > D{C(R ), E(0)} ;

U[A°',B°

',D{•}] > U[A°*,B°*,D{•}] > U[A° + ,B°, D{•}] .

Another comparison focuses on the marginal gain from acquiring non-marke t

benefits evaluated at S l ,S 2 and S 3 . At S 1 , it is less than the marginal cost ,

whereas at S 2 and S 3 it is equal to the marginal cost . However, while th e

marginal gain is expressed by the same functional form in cases 1, 2 and 3 ,

the expression for marginal cost i s

U2[•] RA1 -U 1 [ .] RBUl

PA

1PB

RA

PA

RB

for case 3 and U1 [ • ]

for cases 1 and 2 . The expression for marginal cos tPA

in cases 1 and 2 is the normalized utility loss of not consuming A . In case 3 ,

the expression for marginal cost is the normalized utility loss of not consumin g

A multiplied by a factor which adjusts for the implicit subsidy to EXECON .

Finally, at S 3 the marginal rate of transformation in production equal s

U2[ .]

P B

1

2Ul[•i but not PA as at S and s .

- 23-

Model 2 : Maximization of Conventional Gains from Trade Given the Existenc eof Unconventional Gains from Trad e

Model 2 assumes that decisionmakers wish to maximize the utility derive d

from conventional gains from trade subject to maintenance of a target level o f

D, production efficiency, a balance of trade constraint with each country an d

feasibility conditions .

Under Model 2, the objective function of decisionmakers, V[•], is twic e

differentiable, strictly quasi-concave and increasing in A° and B° :

(34) V = V[A°, B°] .

The maintenance of a target level of D,D, is expressed as :

(35) D = D { C ( RC ), EMI .

All other constraints are embodied in the same manner as in Model 1 .

Now let us define L as :

(36) L = V[A°,B°] + A o [D{C(RC ), E(Tr)} - D ]

[A(RA)-A°]

RB

[A(RA)-A° ]

[B(RB)-B°]

A 2 RA + [ B (RB)- B° ]

Just as for Model 1, if the Kuhn-Tucker conditions for Model 2 hold at a

feasible point, then the feasible point is a unique maximum . The Kuhn-Tucke r

conditions are :

(37) V [•] - a D { . }E (7)P + (-al+a2) = 0 ;1

o 2

1

A

[B(RB )-B° ]

(38) V2 [•] - A D 2 {•}E l (x)PB + (X 1 -X 2 ) [A(RA)-A

° ]

= G ~[B(x8 )-B ]2

A .(x )(39) A o [-Dl {•}Ci (RC ) + D 2 {•}El ( Tr)PAAi (RA)] + (A 1 - A2) 1 A = 0 ;

[B(RB )-B°]

-2 4-

(40) ao[-D1{•}C .(RC) + D 2 {•}E l (~r)PBB i (xB )] + (- A

(41) A o[D{C(xc),E(TT)} - D] = 0

(42 ) A lPB [A(RA )-A°]

= 0 ;

(43) X 2

PA [B(RB )-B°]

= 0 ;RB

[A(RA)-A° ]

+RA

[B(X B ) - B °]

[A(RA)-A° ]12)[B(RB)_Bo]2 B i (RB) = 0 ;

(44) a > 0 ;o (45) A > O . (46) A 2 > O .

A comparison of (37)-(40), (42), (43), (45) and (46) with (6)-(13)indicates tha t

the two sets of equations are exactly alike except that A appears in the Model 2

set of equations instead of U 3 [•] . Furthermore, the Kuhn-Tucker condition s

for Model 2 contain (41) and (44) . A , the shadow price of C, is non-zero by (1) ,

so (41) implies a smaller set of feasible production optima for Model 2 relative t o

Model 1 . This means that the decisions in Model 2 concerning the domestic pro-

duction of C are less sensitive to the full range of relative prices . This may

be seen in Figures 1 and 2 .

Figure 1 depicts the set of feasible production optima for Model 1 as th e

checkered surface in (A,B,C) space . This set is the same regardless of how POLECON

evaluates the non-market benefits available from EXECON .

In order to understand Figure 2, we define the maximum amount of A, B an d

C that can be produced if all inputs are employed to produce one type of outpu t

good as follows :

_AM = A(x, . . .,x N), BM = B(x1, . . .,xN) and CM = C(x1, . . .,RN )

Next we denote as A and B the maximum amounts of A and B that can be produced ,

given that 5 is maintained solely through domestic production of C :

- 25 -

A = max{A :A = A(xA ),D = D{C(xC),0}, RA+ C = (xl , . . .

)} ;

B = max{B :B = B(XB ),D = D{C(XC),0}, xB + RC

= (xl, . . .,xN)} .

Let us assume that D < C M . Immediately it is evident that the set o f

feasible production optima is reduced by the extent to which D is less than C M .

Figure 2's smaller checkered area (relative to that of Figure 1) depends upon th e

extent to which the non-market benefits received from EXECON can substitut e

for POLECON's production of C . Let D{C(0),E(u)} denote the upper bound o n

such substitution . Then the checkered area of Figure 2 is the set of feasible

production optima for Model 2 . If non-market benefits do not exist, then (41 )

restricts the set of feasible production optima to the frontier segmen t

S(D) = {[A(xA),B(xB),D] :D = C(xc ) = D{C(xC ),0} ;xA + xB + RC =

) } .

The similarity between Model 1 and Model 2 becomes especially apparent b y

expressing Model 2 as a particular form of Model 1 :

(47) U[A°,B°,D{C(XC),E(Tr)}] = V[A°,B° ] + A [D - D{C(XC),E(7)} ]

for A° > 0, B° > 0, RC

> 0, Tr > 0 ;

(48) U 1 [•] = V 1 [•], U2 [•] =_ V2 [•], U3 [•] = ao .

Hence the Kuhn-Tucker conditions for Model 2 only differ from those for Model 1

in the addition of (41) and (44) .

Thus the Model 2 solution sets for case s

1,2 and 3 (A 2 > 0), denoted by T1 ,T2 and T3 , may be constructed directly b y

adding

1 2

3(41) to restrictions found in S ,S and S 3 and by substituting Vl[•],V2[• ]

and Ao everywhere that U1 [ . ], U2 [•] and U 3 [•] appear . Direct construction yield s

the following result where the superscript "+" denotes a case 1 solution, "* "

a case 2 solution and "'" a case 3 solution :

- 2 6-

Figure 1 : Set of feasible production optima for Model 1

Set of feasible productio noptima is the checkeredsurface in (A,B,C) space .This set is the same whethe ror not the non-market benefit sexist .

Figure 2 : Set of feasible production optima for Model 2

Case when D < CM . Set of feasibl eproduction optima is the checkere dsurface in (A,B,C) space . Thisset is dependent upon the exten tto which the non-market benefit scan substitute for POLECON ' sproduction of C . If suc hnon-market benefits do not

C

S(D)exist, then the set of feasibl eproduction optima is th efrontier segment S(D) .

C

CM

- 2 7-

A .(R+)

P

V2 [-]

A .(R+)

A D {• }1

+

o+

+ o+

+ 1 A

B 1 A o 1T E {[A(RA), A ,B(XB), B ,C(RC ), 0 ] : B1(R+) = P

= VL , ]

C .(R+) = V [•]

'B

A

1

C

1

C(RC) = D ;V1 [•] > A D2{•}E1(0) .xt > 0 ; xiB > 0 ; xiC > 0

T2 E {[A(R*),A°,,,B(RB),B°",C(R*), E(Tr*)] : B(RA) = PB = V2 [' ]i B

A

1

A .(RA)

X Dl {•}

VI [' ]c .(RC)

= V1[ .]

D{C(c),E(Tr*)} = D ;

PA

= AoD2{•}E1 (Tr*) ;

x

> 0 ; x `

> 0 ; x* > 0iA —

iB —

iC —

T 3 E {[A(XA), A° ,B(XB),B ,C( .y, E(Tr')] : B .(XB) _ V1[ • ] > PA

A1 (RA)

aoDl {•}

v [•]RB-V2[•]RA

; D{C(R ' ), E(Tr')} = D ;

= a D {•}E (Tr ' ) ;Ci (xC)

Vi [•]

C

PARE - P BRA

o2 1

xiA > 0 ; xiB > 0 ; xiC > 0

i = 1,

,N} .

Cases 1, 2 and 3 for Model 2 are distinguished by the increasing valu e

which non-market benefits received from EXECON have for POLECON . The inequali-

ties describing the solutions for cases 1,2 and 3 appearing in (33) hold for Model 2

as well, except that D{•} = D for all cases .

PB The results of Model 2 as compared to Model 1, for identicalP,

B ,A A

A(•),B(•),C(•), D{•}, and E(•), exhibit differences for cases 2 and 3 .

Ignoring the presence of non-market benefits, suppose Model 2's and Model 1 ' s

consumption of C is the same, namely D = D{C(R C ), 0} . Now let us take into

account non-market benefits of a magnitude which will produce new case 2 an d

case 3 solutions in both models . Each new Model 2 solution relative to it s

Model 1 counterpart is characterized by greater production and consumption o f

A and B, less production and consumption of C, and less trade with EXECON .

i=1,

,N} .

i = 1,

,N} .

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Section 3 : Concluding Remarks

Social conflict encourages government decisionmakers to seek hidden way s

to pay for the non-market benefits associated with bilateral agreements . This

search has resulted in the presence of unconventional gains from trade, that is ,

securing these non-market benefits through bilateral preferential trade treatment .

The idea that non-market benefits are purchased consciously through bilateral pre-

ferential trade treatment provides an explanation for the existence of more tha n

one set of international terms of trade .

The results of Models 1 and 2 indicate that whether POLECON trades with RO W

or EXECON or both depends on the extent to which non-market benefits substitut e

for C and on POLECON ' s relative preference for C . When making marginal trad e

decisions POLECON always chooses the greater of world market terms of trade an d

the marginal terms of trade inclusive of EXECON's non-market benefits . Finally ,

POLECON's ability to secure unconventional gains from trade increases her utility ,

and in the case when A,B and C are normal goods, creates optimal patterns of pro-

duction and consumption which include greater A and B .

-29-

Footnotes

1We are indebted for financial support to the National Council fo rSoviet and East European Research . We are grateful to David Donaldson ,Craig Hakkio, Ronald Harstad and John Pomery for useful comments on an earlie rdraft, and to Martha Weidner for research assistance .

2See Marrese and Vaňous [6] for two observable examples of governmen tdecisionmakers engaging in preferential bilateral trade in order to purchas enon-market benefits .

3 For literature on customs unions, see Kemp [1] and Lipsey [2] .

4This classification is fairly similar to the one proposed by Korbonsk i[3] who considered the political value to Soviet Union of each Eastern Europea ncountry as an aggregate sum of its economic, strategic-military, "proxy," an dideological "values " (p . 5) .

An alternative framework for explaining how a country with superpowe raspirations can use trade policy to advance her political-economic power wa sdeveloped by Hirschman [1] thirty-five years ago . Hirschman sees foreigntrade having two principal effects upon the power position of a country wit hsuperpower aspirations . First, Hirschman defines the supply effect to includ eeconomic gains from trade that increase the economic power of the dominan tcountry . Second, foreign trade becomes a direct source of power if other smalle rcountries become economically dependent on the dominant country and thus provid eit with an instrument of coercion . This effect Hirschman calls the influenc eeffect . Then the power to interrupt or redefine commercial relations with adependent country is the root cause of the influence or power position which th edominant country acquires over other nations . The influence effect requires tha tthe dependence of the trade partners on foreign trade must be greater than tha tof the dominant power . Under such circumstances, dependent countries will likel ygrant the dominant country certain economic, political, and military advantage sin order to maintain stable trade relations . Such dependency is enhanced to th eextent that the smaller countries cannot dispense with trade with the dominan tcountry, or replace it as a market and a source of supply . See Marer [5], pp .27-28 .

Also notice that in the case of benevolent interdependent utility functions ,purely altruistic motives could lead to preferential trade treatment .

5An excellent example of the calculus of conventional economic benefit sand costs in the case of Soviet-East European economic relations from th eSoviet perspective is presented in Marer [5] Sections A and B of the tabl epresented on p . 9a .

6Even quota rights, preferential (below market) credit arrangements fo rbilateral trade and preferential tariff treatment can be translated int ochanges in the terms of trade . Thus they, too, may be viewed as implici texport and import subsidies .

7 ir is defined in terms of a common international currency . Naturallyif trade with ROW occurred in one currency and trade with EXECON in another ,exchange rate considerations would have to be incorporated in the calculatio nof Tr .

8We do not discuss the determination of the magnitudes of specific pe runit export and import subsidies . As explained in section 1, the crucia lassumption from the point of view of section 2 is that the incremental paymen tfor an additional unit of non-market benefits increases as the quantity of non -market benefits .

9Varian [7, p . 258] .

10The set of feasible consumption points is closed and convex due to th enon-negativity constraints . The set of feasible production points is close dand bounded since it is defined on a closed set and is subject to weak inequalit yconstraints ; moreover, it is convex because the production functions are convex .Each set of feasible trades with each trading group is closed and convex becaus eeach balance of trade constraint is an equality condition . Each set of feasibletrades is bounded due to the boundedness of the feasible production set . Thus ,the constraint set, an intersection of the above sets, is compact and convex .

11Varian [7, p. 266] .

12Varian [7, p . 261] .

References

[1] HIRSCHMAN, ALBERT, 0 . : National Power and the Structure of Foreign Trade .Berkeley : University of California Press, 1945 .

[2] KEMP, M .C . : A Contribution to the General Equilibrium Theory o fPreferential Trading . Amsterdam : North Holland, 1969 .

[3] KORBONSKI, ANDRZEJ : "Eastern Europe : Soviet Asset or Burden? The Politica lDimension, " Department of Political Science Working Paper, Universit yof California, Los Angeles, January, 1980 .

[4] LIPSEY, RICHARD G . : The Theory of Customs Unions : A General EquilibriumAnalysis . London : London School of Economics and Political Science ,1970 .

[5] MARER, PAUL . : " Is Eastern Europe a Soviet Asset or Burden? The Economi cDimension , " Working Paper prepared for delivery at the Annual Meetin gof the American Political Science Association, Washington, D .C . ,August, 1979 .

[6] MARRESE, MICHAEL AND JAN VAŇOUS: "Unconventional Gains from Trade, "Department of Economics Discussion Paper No . 80-23, The Universityof British Columbia, July, 1980 .

[7] VARIAN, HAL R . : Microeconomic Analysis . New York : Norton & Company ,1978 .