ISSN O075-6407

ECONOMICBUSINESS&
35th

REPORT
ANNUALl.Ky [gUTE"0
lrc

2.k.,

,t.

eee
1,sNi9RESEARCH INSTITUTE FOR ECONOMICSAND BUSINESS ADMINISTRATIONKOBE UNIVERSITY
1990

KOBE
& BUSINESSECONOMIC
REVIEW
35th

REPORT
ANNUAL

sliU'Elld;.,L
ttk

RESEARCH INSTITUTE FOR ECONOMICSAND BUSINESS ADMINISTRATIONKOBE UNIVERSITY
1990

CONTENTS
Page
Some Implications of the Present-Value-

Based Depreciation Within the
Historical Cost Framework ••••••••••••••••••••••••••••••••••••••• Isao NAKANo

1

Foreign Subsidiaries as Contributors

to Parent Companies-A New Paradigm of Mulimational
Enterprises- •••••••••••••••••••••••••••••••••••••••••••••• Hideki YOSHIHARA

15The Gains from Free Trade for a Monetary
Economy •••••••••••••••••••••••••••••••••••••••••••••••••••••••• Murray C. KEMp

On the Optimal Timing of Foreign Aid••••••••••••••••••••••••• Murray C. KEMp

27
31

Ngo Van LoNG
Kazuo SHIMOMURAA Simple Union-rudden General
Equilibrium Model••••••••••••••••••••••••••••••••••••••••••• Kazuo SHIMOMURA

51

Industrial Policy under International
Oligopoly•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• Kenji KOJIMA

69

Realtime Distributed Control of World Link Models
in the International Computer Networks••••••••••••••••••••• Ko MryAZAKI

77

SOME IMPLICATIONS OF THE PRESENT-VALUE-BASED
DEPRECIATION WITHIN THE HISTOklCAL COST FRAMEWORK

Isao NAKANo

1. Introduction
The purpose of this paper is to re-examine the present-value-based depreciation
concept within the historical cost framework and to report some findings concerning

the selection of a depreciation method. One is that if the profitabMty pattern(as defined later) over time of a fixed asset should remain constant the adoption of

the declining-balance method is consistent within our theory. The other result isthat if the profitabMty should declme linearly then the straight-line depreciation
is a logical choice in our model,

2. The Depreciation Concept as the Historical

Cost of Each Year's Expired Service
The original acquisition cost of a plant asset is usuaky measured by the amountof expenditure made to obtain the good. From the view-point of its user, it may besaid to consist of a series of physical services which are planned to be extracted
from the asset.
If we consider a fixed asset as a lump sum purchase of such a bundle of services,then the annual depreciation expense is nothing but that part of the expenditure
which can naturally be considered as paid for the service being consumed in thisyear. How much was paid for the service expired in each financial year? The answer

is our measure of depreciation strictly based on the historical cost. The arnount

paid for the consumed service is equivalent to what could have been dispensed
with if that service layer had been unnecessary.

In the first year, one year's service of the brand new asset was consumed.

After consumption of this service layer, it becomes a one-year-used asset,
which contains everything except that partScular service. Accordingly, if we canretrospectively find the acquisition price of such a one-year-used good as of theactual purchase date of the new asset, then the historical cost of the first-year-service

2 ISAO NAKANO
gll[el-B.eeard.eiseelgiigeoeoddll).r taking the difigrence between the past prices of the new andStated another way, if that new service 1ayer had been unnecessary, we could
huve bought a one-year-used asset, not a new one, and saved the difference, whichof course is equal to the acquisition price of the first year service from a brand new asset.

This reasoning can be easily generalized, so that we can propose that the i thyear depreciation expense is equal to the dfference between the historical costsof an i-1 year-used asset and of aniyear-used one, both at the date the firm actuakybought the good. It is almost self-evident that this dfference is the money additionallypaid to obtain theith year plant service M.
For later use, symbolic expressions of the above will be made. Let
Ai: the acquisition price of the i year-used fixed asset as of the date thefirm actually bought the good.
Si : the service actuaky consumed during the i th year.
E (Si): the acquisition price of the service consumed during thei th year.
SP : the remaining service capacity of the asset when it reached the end of

the usefu1 ure.
E (SP) : the acquisition price of the service capacity at end of the ure.
D(i) : the historical-cost-based depreciation expense for the i th year.
The historical cost principle dictates that

AO = E(sl) + E(s2) + "----- +E(Sn) + E(SP) (1)Al . E(s2) +E(s3) + ------ +E(sn) +E(sP) (2)Talcing the difference between (1) and (2),

AO-Al =E(si) .D(1). (3)Generalizing,

Ai = E(si+i) + E(si+2) + ----"+ E(s") +E(sP) (4)andAi-1 = E(si) + E(si+1) + w""+ E(sn) + E(sP) (5)Comparing (4) and (5).

Ai--1 -.. Ai ,. E(si) .. D(i). (6)SOME IMPLICATIONS OF
THE PRESENT-VALUE-BASED
DEPRECIATION WITHIN THE
HISroklCAL COST FRAMEWORK

3. 0n Application of
to Estimate

a Present Value Formula

Used Asset Costs

The past price data of the used assets are often unavailable. This is particularly

the case with such peculiar assets as buildings, chemical plants, etc. How can we
implement our depreciation concept in these situations?

To approach this problem, a new perspective in the relationship between asset

value and depreciation seems to be required. Under the economic depreciation'' as a discounted present value
concept,
for example, the asset value is first definedof the future net cash-inflow series emanating from the asset operation. Since thisconcept seems to happily correspond to the ``probable future economic benefit''
conception of assets [5], we will continue with this definition, Then, as a first-orderdifference of the begiming and end year present values, the depreciation expense
is defined and quantified [2].

Symbolicady,

pv(i) - ,C.(g, + ft//;L' + ----- + ,.2,\n2,-, -"lÅí:;i C[k,IS," (nand

D(i) - PV(i) - PV(i+1)= C(i) - PV(i) r,(8)where PV(i) : the discounted present value of the future net cash-inflows fromthe asset at the beginning of year i,
C(i) : the estimated net cash-infiow for year i,r : the discount rate which equalizes the discounted value of a new
asset to its acquisition cost,n : the usefu1 ure of the asset,
D(i) and A' : as defined above.
In short, the prior established asset values determine the depreciation expensein the conventional theory (for example, a], [3], [4], [6], [8], [9]).

Suppose that under the condition of certainty we have succeeded in findmg
a relation like (7) above between the acquisition cost of a new fixed asset and its
estimated discounted value.

AO-,g., ,ffk,l, (g)34 • ISAO NAKANO'
Then, we will be justified in constructing the equation' Ai = PV(i+1)o ='k"Åíi' ?1(+k,")ik) (i= O, 1, 2, ----, n), (10)where PV(i+1)o : the discounted present value of the future net cash-inflows
from an i year-used asset as estimated at the beginning of year 1.
and using this formula to estimate the (supposedly) lacking historical acquisition
price of an i year-used asset, because there exists logical consistency between (9)and (10).

But everyone knows various difiiculties facing implementation of this kind of
estimation. They include impossibMty of accurately predicting future cash-inflow
values as well as theoretical difficulty of attributing the cash-fiow amounts (or any

other amounts) to the fixed asset without arbitrariness because they are joint
products of al input goods ( [10], [11] ).

We will show below, however, that the present value formula can sti11 be used
if we reconsider it from a new point-of-view.

4. The Fixed Asset Cost as the Discounted Present Valueof the Future Depreciation Values
All writers on the economic depreciation so far have assumed that annual cashinflow values C(i) are completely exogenous variables and that the costs (present
values) derived therefrom determine depreciation expenses. But this is only paniallytrue. As adequately expressed by Ladelle, the object of discounting in the present
value formula consists in the `value of the enjoyment of the assetl during a year [8].

Hence, the use of net cash-inflow values is only a gross, inaccurate approximation,
for they include other inputs' contributions, too. The enjoyment value more closely
relates to the quantity and cost of the service from the fixed asset for each year.

Whereas the depreciation expense is the original acquisition cost of the service

E(Si) provided each year, the value of the service enjoyment - denoted as V(Si)hereafter - may be considered as a current market valuation of the economic
value of the same service extracted from the asset and hence as a function of theannual service Si or of the depreciation expense D(i) = E(Si).
That is,

V(Si) =f(E (Si))=f(D (i)) (11)5
SOME IMPLICATIONS OF
THE PRESENT-VALUE-BASED
DEPRECIATION wrTHIN THE
HISTORICAL COST FRAMEWORK

We can introduce a revaluation or service profitabdity factor M and assume
V(Si) is the product of M and the depreciation expense. M wi11 temporarily be
regarded as constant during the asset's ure. Some effects of its change over time

will be considered later. We can reconstruct the asset cost formula by applying
this relationship (E).

V(Si)-f(D(i)) (2)=M Å~ D(i).

Ai = "ii v(sk+i)
k=1 (1+s)k=:Åíi' M(Å~i.D,()kk+i.) (i=o, i, 2, ---, n) ' (B)where s: the discount rate which equakzes the present value to the original
cost A' of an i year-used asset at time O.
D(i) is the usual depreciation expense, while V(Si) can be called 'depreciation
value', for that denotes the enjoyment value of each year's fixed asset service. Hence,by this formula (13), we are proposing a new fixed asset concept as a `discounted
present value of the future depreciation values'.

What is the exact meaning of formula (13), especiaky the term M Å~ D(k+i)?
We are assuming here (1) that the valid object of discounting must be that amountof annual cash-inflow which reflects the true contribution of the fixed asset for eachyear; (2) that this object is the depreciation value M Å~ D(k+i) and not the usuallyadopted annual net cash-inflow C(k+i) per se because this reflects other inputs'
contributions too; (3) that this depreciation value as the annual service value does

exist even though not accurately measurable; and (4) that this value does notexceed annual cash-inflow amount, being usually equal or less. This last requirementmeans that we are positing each year's depreciation value can be totally recoveredfrom annual revenue, whatever amount it may be. In the last analysis, therefore,
we admit we are assuming an oligopolistic or monopolistic firm.

We also note that D(k+i) in (B) is not intended to solely represent annual`technical' operation service (i.e., the quantity of annual output products) of a fixed

asset alone. As will be made clear in next section, D(i+k) in the present value
model does include - in addition to that operating service cost - the imancial
cost of having the future year service layers wait for this year, because suchfinancial service is necessary to realize annual operating service. So, in formula(B), we in effect are assuming that this sum total of annual operating and financial

6 ISAO NAKANO
service costs can be wholely recoverable from revenue (and a proponional amount of
net profit obtained).

Even though service enjoyment value V(Si) usually is unmeasurable, some
operations on equation (B) wru be shown to enable us to reach an annual depreciation

expense formula. In this sense, we may say that our making the annual service value
variable panially endogenous and our interpreting a fixed asset cost as a discounted

present value of the future depreciation values do have some theoretical merit.

5. Logical Consistency of the Declining-Balance Method

When the Profitability of the Annual Service Remains
Constant Over Time
Just as an annual decrease in the volume of water in a reservoir is equal to the amountflowing out during the same period, so can the depreciation expense as the service
flow be measured as a difference between the beginning and end year present valuesof the asset involved. Accordingiy, from (13),Ai -1 =MX D(i) . MÅ~ D(i+1) . .. - .. . MÅ~ D(n)(1+ s)1 (1+ s)2(1+ s)n+1 -i

Ai =MxD(i+1) +Mx D(i+ 2) + . -+ Mx D(n.) a4)(1+ s)1(i+ s)2 a+ s)n-i
Hence, Ai-i (1+s) - Ai =M Å~ D(i).
That is, (Ai-i - Ai) + s Ai-i =M Å~ D(i).
Since Ai-i - Ai is the depreciation expense,

D(i) + s Ai-i = M Å~ D(i).

Therefore, D(i) = S Ai-1 (i=1, 2, ---, n). (15)M-1

Thus, we have proven that a particular depreciation expense pattern as indicatedby (va) is consistent with our `discounted depreciation value' concept of fixed
assets. If we continue with the assumption that the discount rate s and the service

revaluation factor M remain constant during the whole usefu1 ure of the asset,
then a decreasing asset cost balance Ai-i is multiplied by the constant factor

SOME IMPLICATIONS OF THE PRESENT-VALUE-BASED 7

DEPRECIATION WITHIN THE HIS'IOklCAL COST FRAMEWORK(depreciation rate) s/(M-1). So, a sort of decreasing charge depreciation has been
derived as logically consistent within our theory. In the following, we wil1 provethat this in fact is the declining-balance method. The depreciation rate sl(M -1) must be

quantified as 1-(S/A)i/" where S is the salvage value.

(Theorem 1)
Let the depreciation be defined as the difference between the begiming andend year discounted present values of the future service values of the tixed asset.

Further, assume that those service values are not the year-end cash-inflows per
se but some values proportional to the annual depreciation expense measures. If,
in this case, the revaluation factor M of the annual asset service should remain

constant every year, then the declining-balance method is consistent with thoseassumptions.

(ProoDThe characteristics of the declining-balance method consist in (1) that each

year's depreciation amount is determhed by multiplying a constant rate by the
beginning year undepreciated fixed asset cost and (2) that that rate equals 1 -(SIAO)il",

where S is the salvage value. Of these two points, the former has been shownto hold in (15). The constant rate - labelled DR hereafter - is sl(M-1).
The latter point can be easily proven as follows.

DR=s/(M-1). Since D(1) = AO - Al,
Al=AO - D(1) = AO •-- AOsl(M-1) = (1-DR) AO.
A2 = Al -- D(2) = Al - AIDR = (1 --- DR) Al = (1 -DR)2 AO.

An =s = a-DR) An-1 = a-DR)2An-2 = ---- = (1-DR)nAO.
Therefore,(1-DR)" = SIAO.
DR = 1 - (s/AO)1/n.
(Q. E. D.)
In conclusion, DR = s/(1-M) = 1-(S/AO)i/". As stated above, we cannot
determine s or M directiy. In practice and also in theory too, we must rely on
this formula to determine the depreciation rate.

An implication of our conclusion here is the rigidity of depreciation method
choice, i.e., the proposition that the declining-balance method is always logical for

any consumption pattern of the fixed asset service during the usefu1 ure, as far

ISAO NAKANO

8

as the service profitabmaty factor M should remain constant every year. This may
appear absurd and unacceptable. But it is not so. If very intensive use of the asset

is planned in a year, then, the estimated remaming amount of its service capabmaty

for ab future years is correspondmgly lower, so that the cost for some relatively
greater consumption of service in a year tends to be offset by the correspondingly

lower `stocking cost' of the remaining servjce jayers with respect to the good so
as to generate an unchanged depreciation pattern (i.e., the declining-balance method

pattern) in every case, if the depreciation expense is defined as the sum of those
two costs.

6. Depreciation as a Measure of the Annual Aggregate
Operating and Stocking Service Costs.
What is the semantic content of such depreciation information? To see this, we will
expand the depreciation formula (15) as follows.

sAi'i 1v(si) V(Si+1)

D(i)= M-1 = M-1 Å~SÅ~+((1+s)1"-----t--- + (1+s)2+ (1.V,()S.n-)i.1 )V((Si+1)-- (1+ V(Si)s)1 Å~ S1Å~ M-1+ ( (1+s)2+ ---------+ V(Sn) ).,. i a6)a+s)n-i+i M-i

In considering the service enjoyment value of a fixed asset, we can devide`operating' and `stocking' service values. The former concerns actual annual
operation of the fixed asset, while the latter involves the necessity of stocking
future years' plant service layers simultaneously, which is indispensable, in case ofa multi-year good, for this year's asset operation. Therefore, a realistic depreciation

measurement must include both service costs in its annual expense.
' The first term •in (16) represents the cost for the i th year operating service

value from the asset. V(Si)/(1+s) shows the acquisition cost of the i th year net

service value and hence when multiplied by s (the rate of return) the profit
from the operating service. Since M is, as defined above, the ratio of the annual

service value V(Si) from the fixed asset to the depreciation expense D(i), the9SOME IMPLICATIONS OF THE PRESENT-VALUE-BASED
DEPRECIATION WITHIN THE HISroruCAL COST FRAMEWORK

value M - 1 represents the ratio of V(Si) - D(i) (i.e., net sewice profit for year i)to the depreciation expense. Consequently, 1/(M-1) may be said to denote the ratioof the i th year depreciation expense to the annual net service profit. By multiplying

this to the estimated net operadng service profit s, V(Si)/(1+s), we get theoperating service cost component of the depreciation expense.
The other element, that is, the annual stocking service cost is precisely reflectedby the second term of (16). V(Si+1)/(1+s)2 -- + V(Sn)1(1+s)"-i'i is thetotal cost of the yet unused operating service layers as of the end of year i, so that when
multiplied by s this produces the required annual net profit for justifYing this financial

investment. Hence, when this is further multiplied by 1/(M-1), the depreciationprofit ratio, then we see that the stocking service cost portion of the annual depreciation

expense results.

In consequence, we have proven that our depreciation formula has the semantic
content of `annual aggregate operating and stocking service costs' for using the fixed
asset each year. Even if the operating service value should remain level every year,

the stocking service cost declines corresponding to the decreasing undepreciatedcost balance. So, even in this case, too, we see that the decreasing charge method(the declining balance method) wi11 be judged as consistent within our theory.

If M should vary over time, some other depreciation method than the decliningbalance method may possibly be derived. Some consideration wi11 be given to thisproblem in next section.

7. Validity of the Straight-line Method When the Asset
Service Profitability Declines Linearly over Time
Just in contrast to our assenion on appropriateness of the declining-balancemethodin a constant net service value situation, we will show that the straight-line

methodis logicaky consistent within our theory only if the annual net service value

declines

in a spechic periodic pattern.

If the straight-lme method is to be supported in our theory,

D(i) = D (i+1)
for i = 1, 2, -----, n-1.
That is,S Ai -1 ., S Ai

Mi -1 Mi+1 -1(ID

ISAO NAKANO

10

where Mi and Mi+1 are the variable revaiuation factors of the i th and i+1 th year
depreciation expenses.

After some arrangements.

Mi+1 -1 Ai

Mj -i =Ai-i<i' as)

Equation (24) demonstrates that Mi+1 must be smaller than Mi if the straight-line
method is to be consistent. That is Mi must decrease over time. Since Mi is the net'

service value to depreciation ratio, we may restate that the straight-line method isjustified only if the asset service profitabMty in the above sense decreases over timeand all other conditions remain the same.

More spechically, we wilI prove below that a lmeariy decreasing pattern of Mi
just suthces to generate the straight-line depreciation.

(Theorem 2)
Under the same depreciation concept as stated in theorem 1 above, if the service
profitabdity factor M of the fixed asset service should decline lmearly every year,
then, the straight-lme method follows within our theory.

(ProoD
From (17) above,Al -1 Al. -1
Mi -1 Mi+1
Ai-1 Mi+1 - Ai-1 = Ai Mi - Ai .

Mi.1 - 4' Mi . Ai -'l- Ai = p(i) .
Ai-1 Ai-1
Ai-1
This is a first-order linear dfierence equation with respect to Mi. D(i) on its rightside can be set as K (a constant), as we are refening to the straight-line depreciation.
So,

Mi+i-Al:, Mi-AiK-,• (te)We will solve equation (te).

M2 = Al Ml + K.
AO

AO

M3. A2 M2+ K = A2 Al Ml+ A2 K+ K
AI

AI AI AO AI AO AI

SOME IMPLICATIONS OF THE PRESENT-VALUE-BASED 11

DEPRECIATION WITHIN THE HISroklCAL COST FRAMEWORK.. A2 Ml + A2 K+ -!Lr.
AO AI AOAI

M4 ., A3 M3+ K = A3 A2 Al Ml + A3 A2 K+ A3 K
A2 Al AO
A2 Al AO
A2 Al
A2 A2

K

+ A2 •.,, A3 Ml + A3 K+ A3 K+ K.
AO AI AOA2 Al A2
Al-1 Ai-1 Ai-1

Mi=
Ml+
A2 Al K+ K+--AO Al AO
AI-1+Ai-2K Ai-3 K+ Ai-2• (2o)Accordingly, we also get the following.

Ai Ml+ Ai K+ Ai K+""-+.Ai. K+ IS .

Mi+1 =(21)
AO Al AO
A2 Al AI-IAI-2
Ai-1

Taking the difference between Mi and Mi+1,

Mi-Mi+1 ,. Ai-1-Ai Ml. Ai-'1-Ai K+ Ai-1-Ai K+.....

AO Al AO A2 Al. 4i-i-.Ai K- E
AI-2 Al-1Al-1= K MI+ K2 + K2 +-""+ . K2.
AO Al AO
A2 Al AI-2Al-1

K

in Ai-1 (22)

To calculate the difference between Mi-1 and Mi, we will replace i in (28)with i- 1. Then,

Mi -1 - Mi = K MI + K2 + K2 + -"" + . K2.
AO AI AO
A2 Al Ai-3Ai-2

K-Ai-2 (23)rz ISAO NAKANO'

Talring the difference between (22) and (23), we will compare the adjacent two pairs ofMi's durerence.

(Mi - Mi+1) - (Mi-1 - Mi) = . K2. - .K . s
Ai-2 Ai-1 Al-1

Ai-2

K2 K(Ai-2-Ai-1)
Al-2 Al-1 Al-2 Al-1

K2 K2=, .-. . -o.

Al-2 Al-1Al-2 Al-1

Hence, any two consecutive pairs of Mi has been shown to decrease by the sameamount. So, we have proven that Mi must decrease linearly so as to justify the
adoption of the straight-line depreciation within our theory.

(Q. E. D.)(Example)
A fixed asset has been acquired at $220, with its estimated usefu1 hie of 4 years

and its salvage value of $20. Its future net service revenues are assumed to be
as follows:Year amount

1 60.02 za .O

3 86.44 145.ts •The discount rate s which equates the present value of these future values to its
acquisition cost $220 is O.20. In this case, the following, linearly decreasing service

profitabthty series is just suthcient to generate a set of straight-line depreciation

amounts.

Year Mi values Depreciation

1 1.88* 50.0
2 1.68** 50.0
3 1.48 50.0

4 1.28 50.0

* 22o . O•2 . so.
1.88 - 1

O.2** (22o - 50) Å~ 1.6s -1 = 50•

SOME IMPLICATIONS OF THE PRESENT-VALUE-BASED B

DEPRECIATION WITHIN THE HIS'IDRICAL COST FRAMEWORK

8. Conclusion
The purpose of this paper is to advance a new depreciation theory within the confineof the historical cost principle which can provide some perspective into the problem
of selecting an appropriate deprecation method in each business situation.

We have started by adopting the economic depreciation concept where the historicalcost of a fixed asset is regarded as the discounted present value of the future net
service values (or the future net cash-inflows) to be generated by the good. In thistheory, the authors have so far considered those future service values (or net cash-

inftows) as a pure 'exogenous variable'. From this, a serious doubt about thepredictabMty of those future values has arisen and the feasibdity of this depreciation

model has been questioned. ,' In opposition to this view, I have taken the standpoint that the future service
value of a fixed asset is to be considered as a partially `endogenous' variable. Thatis, the depreciation is those annually consumed service quantity as valued by its
historical cost, whereas the service value is the same provided service as measured

by its current market vaiue. Hence, we have proposed the idea that multiplying
a revaluation factor by the annual depreciation expense will produce the annual net
service value from a fixed asset, which is the object of discounting in the present
value model.

By inserting this idea into the model, we have derived a depreciation expense
formula. According to this, if the revaluation factor should remain constant every

year, then - contrary to the commonsence prediction - the declining-balancemethod has been obtained as consistent within our theory. And if this factor should

fal linearly (by the same amount) every year, then - again contrary to the usual
presumption - the straight-line depreciation has been shown to be logical in our
specific model.

These apparently paradoxical results may be explained by the fact that a fixed

asset will annuaby provide two kmds of services: operating service and stocking
service. The former service can only be reakzed by the support of the latter. In thissense, there is some rationale for the depreciation concept which reflects the annual

costs for both kinds of services. This is our proposed depreciation concept. Since

the stocking service cost tend to decline every year because of diminishng unused

asset service layers, a flat operadng service pattern over time does produce a

decreasing-charge depreciation. •Another paradoxical result about straight-line method choice in case of a linearlydecreasing profitabdity (i.e., revaluation factor) comes from the increased proponion

ISAO NAKANO

14of the depreciation expense in the annual service revenue V(Si) in this situation.
If this should stay flat over time, then, an increase in Mi wM result in a tendency toraise depreciation. Hence, at a certain decreasing pattern (i.e., a linealy decliningcase) of Mi, this tendency will be just offset by the above stated element of decreasing

stockmg cost so as to generate a constant annual depreciation expense every year.

No consideration has been given to the utdity of the accounting information

our depreciation measure wil1 produce. So, we cannot as yet recommend ourdepreciation method choice to the practice. All we have done is a reponing of some
implications of the present-value-based depreciation within the historical cost framework.

References[1]

Anton, H.R., Depreciation, Cost Ailocation and Investment Decision''. Accounting Research[2]

Beaver, W.H., and R.E.Dukes, "6-Depreciation Methods: Some Analytical Results'1 Journal of(Apnl te56), pp. 117-134.

Accountirrg Research (Autumn lg74), pp. 205-2ts.
[3]

Bierman, H., Jr., "Depreciable Assets - T;iming of Expense Recognition'', The Accounting Review[4]Dixon, R. L., ``Decreasing Charge Deprecjation - A Search for Logic'', The Accounting Review[5]-

Financial Accounting Standards Board, Statement of Financial Accounting Concepts No. 6, ``Elements(October te61), pp. 6B-618.

(October D60), pp. 590-5or.

of Financial Statements" (Financial Accour]ting Standards Board, re85).
[6]

Hotelling, H., "A General Mathernatical Theory of Depreciation'1 Journal of American Statistical
Association (Septernber D25), pp. 340-353.

[zNakano, I., ``On Monetary-Sacrifice-Based Depreciation'', The International Journal of Accounting[8]

Ladelle, O. D., "The Calculation of Depreciation", The Accountant (November 29, 1890 and(Spring, 1978), pp. 41-56.

December 6, re90), pp. 659-660 and pp. 669-671.
[9]

[10]

Reynolds, I. N., "Selecting the Proper Depreciation Method", The Accounting Review (April te61),

Thomas, A. L., ``The Allocation Problem in Financial Accounting Theory" (American Accounting
Association re69).

[11]

Thomas, A. L., "The Allocation Problem: Part Two'' (American Accounting Association 1974).

FOREIGN SUBSIDIARIES AS CONTRIBUTORSTO PARENT COMPANIES- A NEW PARADIGM OF MULTINATIONAL ENTERPRISES -Hideki YoslHARA

1. Technological Superiority of Parent Companies

Foreign Companies in Prewar JapanThe first foreign company that expanded its operations to Japan in prewar days was

the American firm Western Electric, whose Japanese subsidiar}', Nippon Electric,
was established on July 17th, rs9g.1)

Nippon Electric was in the telephone business. Backed up by the overwhelming
technological superiority of its American parent company, Nippon Electric experienced

rapid growth in Japan, and was able to achieve excellent financial performance.
Before long, competing iirms were founded in Japan, and they grew to be competitorsof Nippon Electric. In te31 the Manchurian Incident occurred, and, foHossring thisevent, the Japanese govemment adopted a negative attitude towards foreign cornpanies.

As a consequence, a difficult period started for Nippon Electric. Later, when the
Pacinc War broke out, Western Electric was compelled to withdraw from Japan.

During the Meiji era, many foreign experts had been irwited to work in Japan,

so that this country could acquire Western knowledge and technology. After thisacquisition was completed, the foreigners, having fu1filled their function, were fired

and returned to their countries of origin. In a simlar way, while there exists
technological disparity between Japanese and foreign firms, the latter are a usefuland strong presence, but, as the Japanese side -such as the Japanese partner ina joint venture or Japanese competitors -- catches up, the usefulness of the foreigncompany decreases and its competitive position loses strength. Since, sooner orlater, the technological gap is closed, the success of foreign companies is unavoidably

temporary. M. Mason, who studied the expansion of foreign companies (Western
1) Regarding rrty considerations on foreign companies in Japan during the pre-war years, I benefited
ffom the papers -and stibsequent discussions- presented at the rath Fuji Conference of the Society
for the Sudy of Business History, in which I participated Uan., 1-4, D89). The conference topic was"Foreign Businesses in Prewar Japan.''

16

HIDEKI YOSHIHARAElectric and other companies) in Japan in the prewar years, concludes that foreigncompanies in Japan during this period could be compared to the oyatoi gaikokuji(hired foreign experts).2)

The oyatoi-gaikokujin theory is built around two variables -i.e., heavy involvementof the Japanese govemment and technological superiority of the parent company.
In this paper I wil1 concentrate exclusively on the second aspect, technological superiority.

The variable ``technological advantage" may be considered from two aspects.
The first is the idea that the technological gap between the foreign company and its

Japanese competitors is a key factor in the former's success. That is, whether aforeign company in Japan will succeed is determined by whether there is a technological

gap between the foreign firm and its Japanese competitors.

The second idea is that the superior technology is unidirectionally transferredfrom the parent company in the country of origin to the subsidiary in Japan. The
parent company has superior technology which, when transferred to the subsidiaryin Japan, becomes a source of competitive strength.

The Traditional Paradigm of Multinational Companies
The two points mentioned above -i.e., that the technological superiority of theforeign company over the indigenous firms is a key success factor for the former,
and that the superior technology fiows from the parent company in the country oforigin to the subsidiary in foreign countries- are ideas shared by many theories ofmultinational firms developed up to the present.

The basic idea of Vernon's product cycle model is that the driving force for
American multinational companies to enter foreign markets is the superior resources(capacity for product development, marketing know-how, managerial and administrativeknow-how, etc.) developed in the U.S. These superior resources are transferredfrom the parent company in the U.S. to the foreign subsidiary. Subsidiaries in each

foreign country take this advanced technology and marketing know-how and use
them as competitive weapons against indigenous firms.3)

One of the features of S. Hymer's theory of multinational firms is its emphasison the hierarchical relationship existing between the parent company in the countryof origin and its foreign subsidiaries. Excellent resources, which are the foundatjonof competitive strength, are transferred from the parent to the foreign subsidiaries.

In order to make good use of these resources at every foreign subsidiary, the2) M. Mason, "Temporary Guests: Western Electric and ITT in Prewar Japan." (Paper presented
at the Fuji Conference mentioned ab(rve.)3) R. Vernon, Soveneignty at Bay, Basic Books, rm, p. 65-77.

FOREIGN SUBSIDIARIES AS CONTRIBU'IORS 17
10 PARENT COMPANIES

parent has to build a global organizational stmcture, and develop an adequate4) system.
management control
Multinational corporations are also treated in international economics as a topic

in the theory of direct foreign investment. Direct foreign investment is considered

as an international transfer of corporate resources. International tmsfer actuahymeans movement of resources from the parent in the country of origin to the foreigncountries where subsidiaries are located. Transfer of resources in other direction,such as from the foreign subsidiary to the parent or mutual transfers among foreignsubsidiaries, are not considered.

The following three points can be indicated as features of existing theories ofmultinational enterprises. The first point is the idea that the driving force that
leads multinational corporations to expand their businesses to foreign markets is thetechnological superiority of the parent firm. (Here and in the following paragraphs
I use the term ``technological superiority" in a broad sense, which includes not only

product and production technology, but also marketing and managerial know-how.)
The second point is the idea that this technological superiority is transferredfrom the parent company to the foreign subsidiaries. The third point is a hierarchicalrelationship between the parent in the country of origin and the subsidiaries
abroad. Foreign subsidiaries are considered to be controlled by the parent company.

2. Transfer of Technology from the Subsidiary to the Parent

The Two Objectives of Japanese Investment by Foreign Companies
It is said that history repeats itself. But a detailed examination will show that things

which occurred in the past are not reproduced with precision in the future. The
same can be said about foreign companies in Japan.

The number of foreign companies expanding their businesses into Japan is
growing steadily. In spite of the abrupt appreciation in the value of the yen that

occurred after the autumn of 1985 and the stabMzation of the new high value ofthe currency, this trend has not changed. What then, are the objectives pursued byforeign companies in coming to Japan?

President K. R. wutmore of the U.S. firm Eastman Kodak, talking about theobjectives of enteimg Japan, says.

4) Y. Miyazaki, Gendai no Nthon Kigyo wo Kairgaeru (Thoughts on Contemporary Japanese Enterprises),
Iwanami Shoten, lg74, p. ts8-208.

HIDEKI YOSHIHARA

ts

Japan is not only an important rnarket, but it is alsoasource of technology. We are aiming at gatheringsuperior resources in Japan, such as advanced technology and excellent human resources. Putting towork our company's resources and the Japanese technology and market information, we will be able
to display a powerful strength:' (Nihon Keizai Shimbun, Oct. 30, te85.)

As this statement makes clear, foreign companies have two basic reasons toenter Japan. The first reason is the 1arge size of the Japanese market. Japan is thesecond 1argest market in the world after that of the U.S., and due to the recent
appreciation in the value of the yen the scale of the Japanese market has become
even wider. Foreign firms cannot afford to ignore the Japanese market.

The second major reason that foreign firms have to expand operations into
Japan is their eagerness to acquire Japanese technology and know-how.

Accordjng to executives of European firms, since Japan js ahead of othercountries in a number of advanced technologies such as electronics, companies needa base in Japan if they are to rank among the world's leadmg enterprises in the
future. European companies want to become fully fiedged players in the Japanesemarket, and acquire the advanced technology of the Japanese.5)
Recently, American and European companies, mainly in the electrical and chemical
fields, have successively began to establish product development centers and researchlaboratories in Japan. The purpose of expanding R&D activities into Japan is not totransfer the technology of the parent company to this country, but rather to employ
Japanese engineers and researchers to fumher develop a technology in Japan, then to usethat technology in the Japanese subsidiary and transfer it back to the parent company.

For those companies which expand to Japan for the first reason mentioned
above, i.e., to take advantage of a very big market, the technological superiorityof the parent company becomes a competitive weapon. Regarding this point, theapproaches that have been taken until now in the theory of multinational enterprises
may be applicable. But with regard to the second reason, i.e., the acquisition of superior

Japanese technology, the existing theories seem to be unwarranted. Technologicalsuperiority is not in the country of the parent, but in Japan. Foreign companies
establish themselves in Japan in order to obtain valuable Japanese technology andnot to develop in Japan the superior technology of their parent companies.

The Case Of Fuji-Xerox
Fuji-Xerox was established in D62 as a joint venture of the British Rank Xerox,
a subsidiary of the U.S.'s Xerox, and Japan's Fuji Film. In other words, Fuji-Xerox is5) H. Mirza, P. J. Buckley and J. R. Sparkes, "Swimming against the Tide?: The Strategy of European
Manufacturing Investors in Japan," presented at the Fourth Japanese-European Conference on Management(Tokyo, Sep. 29 and 30, Dg7).

FOREIGN SUBSIDIARIES AS CONTRIBUroRS tero PARENT COMPANIESa `` grandchild" company (subsidiary of a subsidiary) of the U.S.'s Xerox.

At the beginning, Fuji'-Xerox was able to develop smoothly and obtained goodbusiness results in Japan thanks to the overwhelming technological superiority of

its parent company. The company could be counted -together with IBM Japan,
Coca Cola Japan and a handfu1 of other foreign firms- as one which was very
successfu1 in this country.

In 1970, the selenium drum patent and other basic patents expired, and, due
to the gradual strengthening of Japanese firms (rucoh, Canon, and others), FujiXerox's technological superiority quickly disappeared, resulting in a fierce competitive
situation.

It was during this competitive process that Fuji-Xerox started to develop theirown product, such as the Xerox 2200, suited to the Japanese market. Nowadays,
Fuji-Xerox is on a par with its parent company in its capacity to develop photocopier products, specially compact copiers, and in some areas the company has evensurpassed its American parent. In fact, not only are products developed by FujiXerox being exported to the U.S. and England, but the product development system,and the methods of production management and quakty control, are being transferred tothe parent company.6)

Now, Xerox is competing in the U.S. and European countries with Japanesecopier manufacturers. According to some observers, Xerox is able to cope with Japanesecompetition because of Fuji-Xerox's product development capabMties, and production
and quakty control systems. This view maintains that, assuming the U.S.'s Xerox was
not backed up by Fuji-Xerox, its competitive strength would be reduced.

Fuji-Xerox's case is important in two senses. First, it shows that technology
is not only transferred from the parent company to the foregin subsidiary, but also
from the foreign subsidiary to the parent in the country of origin. Second, it also
shows that even after the original technological superiority diminishes or disappears,

the foreign subsidiary, by developing its own strength, can grow and achieve good
performance.

3. The Sources of the Foreign Subsidiary's Superiority

Geographical Advantage
Foreign subsidiaries can, even if partiady, occupy a place of technological superiority
6) Foji-Xerox 20 IVen no Ayumi (Fuji-Xerox: 20 Years of History), Fuji-Xerox, D83, p. 203-205. Fuji-Xerox,

Nomura Management School, -83, p. 39.

20

HIDEKI YOSHIHARA

vis-a-vis their parent companies. Fuji-Xerox is one such example. What are the reasonsthat abow a foreign subsidiary to obtain a position of technological superiority overthe parent company?
The first is the geographical adwntage of the foreign subsidiary.

The first reason why Fuji-Xerox achieved technological superiority is that thecompany had to satisfy Japanese users. Japanese users, private individuals or
institutions (firms, public othces, etc.), when compared with their American or European

counterparts, are more discriminating, and moreover products must operate in more
severe conditiops.

In the early days of copying technology, duimg rainy days or very humid weather,

printing (copying) conditions were not good. Japanese users were unsatisfied withthis situation, and strongly demanded an improvement in the quality of the products.

Likewise, maintenance was not suthcient, and users demanded quick response fromthe service station in case trouble developed during usage. If the copier manufacturer
could not eliminate the source of the user's dissatisfaction, the user would shift tocompetitor's brands, because in Japan there was not just one supplier of copying
machnes, but several. This resulted in a strong competitive situation.

This severe competition is the second reason contributing to the development of
a competitive superiority on the part of Fuji-Xerox.

In the U.S. or Europe, Xerox's position is overwhelming, and the intensity of thecompetition is not as high as it is in Japan. Backed up by its technological superiority,

Xerox was able to achieve a position of quasimonopoly in those markets.
The third reason is the development of surrounding industries in Japan. Specially
importnnt is the development of the electronics industry. Copiers are making increasing use of electronic devices, and having operations in Japan, where the electronics

industry is well developed, is an important advantage for manufacturers of copying

machines.
I have been talking about the geographical advantage of being in a foreign country(in Japan, in the case of Fuji-Xerox), In fact, it is the geographical advantage that

American and European companies enjoy in their own countries that allows them todevelop original technology, and, based on this original technology, expand operations
into foreign markets.

The U.S. market dernanded goods for high-income consumers and artjcles that
could contribute to labor-saving aabor-ethcient technologies). American firms, inorder to meet these market needs, developed American style goods such as big
cars, electric home appliances, and machines for factory automation. These firms
subsequently expanded to the dfferent world markets, using their original products

FOREIGN SUBSIDIARIES AS CONTRIBU'IORS 21'IO PARENT COMPANIES

and technologies as competitive weapons, and became multinational enterprises.7)

The Japanese market had several features that contrasted with the American
market. The income level was relatively lower, and the country's area was smaler
and much more densely populated. In order to adapt to these Japanese conditions,motor vehicles, for example, had to be smaller, fuel-ethcient, and strong to endure roadconditions. If, as a further example, we take electrical home appliancessuch as color TV sets, refrigerators, and microwave ovens, the Japanese market
demanded appliances which were sturdy, compact and quiet. Since Japanese homes
are usuady small, refrigerators that make noise during the night are not accepted.

Nowadays, Japanese cars, color TVs, VCRs and office machines are
displaying great competitive strength in the worid markets. These products arefurther examples of the response given by the manufagturers to the special needs
that characterized the Japanese market.

As I pointed out earlier in this paper, one of the reasons why American andEuropean firms are expanding operations into Japan is their desire to acquire
superior technology from this country. If so, what kinds of technology are theyaiming at?

One of them is Japanese production technology. American semiconductor
manufacturers such as Texas Instruments and Motorola have factories in Japan. It issaid that the productivity of these Japanese factories is the highest in the company,

and at the same time the rate of defective items is prominently the lowest.8)

American semiconductor manufacturers take home the production technologyof Japanese factories, and introduce it in their home factories. Also, thesemanufacturers are makmg efforts to expand the application of Japanese production
technology to their other foreign plants as well.

The second is product development capabdity, in particular the abihty torepeatedly develop new products and launch them into the market. One of thecharacteristics of the Japanese market, compared with the American or European

markets, is that in Japan products have a short life cycle, and new products

are continuously being introduced. In consumer products such as color TVs,
VCRs and automobiles, or in OA machines such as word-processors or personal
computers, there are few cases of products that enjoy a ure longer than one year.

7) R. Vernon, op. cit., p. 77-81.

8) See ``Motorola no Keiei Rinen to Global Senryaku'' (Motorola's Managerial Philosophy andGlobal Strategy), Business Revieiv, Vol. 34, No. 2, p. 83.

22 HIDEKI YOSHIHARA
In Japan, having a new-product development capability sufficient to respondcompetitively to the rush of new products is a must if a company is to keep its

competitive strength. This new-product development system, which shortensdevelopment time, is one of the technologies that American and European firms
want to learn.

Electronics technology is the third technology that American and European
companies are trying to acquire in Japan. Japan is the most advanced country
with regard to electronic products (with the probable exception of electronics
for military use). The civilian Japanese electronics industry is the world leader

not only in color TVs, VCRs, personal computers, and wordprocessors, but also
in electronic parts and semiconductors.

This electronics technology is valuable not only for the electronics industry, butalso for firms in other industries. In industrial fields such as chemistry, machinery andoptics, the application of electronics technology, such as mechatronics,
chemical-electronics and opto-electronics, is becoming an important managerial
consideration. American and European companies compete to expand their operations
to Japan and strive to acquire electronics technology.

Entrepreneurship at Foreign Subsidiaries
As pointed out earlier, the geographical advantage was one of the reasons why
Fuji-Xerox could achieve a technological level superior in some areas to the level of

its parent firm. But we must not forget the importance of the efforts made by
Fuji-Xerox executives, managers, and engineers.

Fuji-Xerox is a 50-50 joint venture between England's Rank Xerox and Japan's
Fuji Film. From the establishment of the company, a policy of all-Japanese management
was adopted.9) All the full-time directors, including the presidents, have been Japanesenationals.iO)

The fact that from the time the compariy was established all executives wereJapanese, eager to develop their own technologies, is another important reason forthe high level of technological capabMty achieved by Fuji-Xerox. Fuji-Xerox was
originally a sales company. Manufacturing of copiers and expendables was performed
by Fuji Film (including its subsidiary).ii) But ever since its bimh as a sales company,

9) Fuji-Xerox 20 Nen no Ayumi, P. 36-sc.
10) thid., p. 46.

11) The integration of production and sales was materialized in Apnl, 197t and thereafter Fuji-Xerox had

production capabbities. FuJ'iXerox 20 Nen no Ayumi, p. tz4-rz6.

FOREIGN SUBSIDIARIES AS CONTRIBU'IDRS 23'IO PARENT COMPANIES

engineers and technicians were trained inhouse, accumulating independent technologicalcapabdities with which they tried to develop products. Behnd this development
stands the attitude of Japanese managers and engineers, who are aware of theimportance of possessing independent technological capabihty if the company is to
grow in the future, and, accordingly, try to persuade the parent company's management (Fuji Film, Rank Xerox and Xerox in the U.S.A.) regarding the need to enhancethese independent technological capabdities.rz)

Thus, there are two important factors that explain why Fuji-Xerox has now achieved
such a high technological level. The first factor is Japan's geographical advantage,

and the second is the initiative of Japanese managers and engineers, who strive todevelop an independent technology. The second factor could also be called ``entrepreneurship of the Japanese subsidiaries."

It is sometimes said that innovation emerges at the periphery rather than at thecenter. If this is so, the causes for this phenomenon to occur in the context we aretalking about are the geographical advantages of the foreign subsidiary and theinitiative (entrepreneurship) possessed by this subsidiary. In order to nurture foreignsubsidiaries able to contribute to the parent firm, efforts are necessary to takeadvantage of the geographical situation, and to promote entrepreneurship in the
management of subsidiaries.

4. Barriers of pride
het's assume that a foreign subsidiary makes the most out of its geographicaladvantage and surpasses the parent company in its technological capablity. For thistechnology developed at the foreign subsidiary to be transferred to the parent
company, the latter has tirst to recognize the value of the new technology, and makethe decision to adopt it. But this decision is not easily made.

The first product independently developed by Fuji-Xerox was the Xerox 2200,

a smah-sized copier.B) This machne, when compared with the desk-top machineon the market at that time (developed by the U.S.'s Xerox) was somewhat slower
in copying speed, but it had the capabMty to copy from books and magazines, its size

was substantiaby smaler foy 20 cm in depth and 11 cm in height), and it was also

lighter, by rs kg. Manufacturing cost was approximately one half of the cost of2) thid., p. 143-144.
B) The following description of the development of the Xerox 2200 is based on Fuji-Xemx 20 Nen no Ayumi,

p. 145, and Atsuo rmyamoto, "Shashi Sowa, Fuji-Xerox" (Fuji-Xerox: History and Episodes), 31,
Nihon Kogn Shimbun, Oct., 22, te82.

24 HIDEKI YOSHIHARA
imctionaby equivalent copiers,
Since Fuji-Xerox succeeded in its trial development of the machine, it informed its

parent companies (England's Rank-Xerox and U.S.'s Xerox) about this successand requested formal pemission to develop and manufacture. The answer was
negative. The head of the engineering department at the U.S.'s Xerox, Mr. W. Becker

is quoted as saying: "It is not likely that they can get so advanced functions
at such a low cost.''

At that point, the person responsibie for the development at Fuji-Xerox took

the prototype to Rank-Xerox in England and put it to work. Mr. Becker, who
was in England, saw the prototype himself and changed his mind: ``I was opposed
to independent developments, but I must admit that I have to rectify my opmion.''

After the smah-size copying machine developed by Fuji-Xerox was seen andits excellence recognized by both engineers and managers at the parent company,

the product was forrnaky approved and began to be exported to many countries
around the world. After that, the U.S.'s Xerox's R&D strategy was moddied, andthere was a tendency to gradually entmst to Fuji-Xerox the development ofsmal-size copiers.

From the point of view of the U.S,'s Xerox, it was very difficult to imagine
that Fuji-Xerox, a ``grandchild'' company, would be able to' develop a better product.

For this reason, reports from Fuji-Xerox on the new machine were not taken
seriously until people from the parent company actually saw the prototype.
However, after seeing the newly-developed product once, the parent company took
a fair and open attitude, recognized the value of the new machine, and not only
legitimized Fuji-Xerox's product development activities, but positively supported

them.
The transfer of superior technology from a foreign subsidiary to the parent
company does not take place when the parent does not recognize the value of thetechnology developed by the foreign subsidiary. In practice this recognition
is something very difiicult to achieve. The parent company usually has a sense of
pride and superiority. It is because of these feelmgs that the technical superiorityof the foreign subsidiary is not easily admitted. But if innovations are to beborn at a foreign subsidiary and then transferred to the parent compaay andused by it, the parent company must overcome these feelings of superiority andpride.

If the reverse tmsfer (from subsidiary to parent) of technology is to occur,

the foreign subsidiary should persuade the parent company. In doing so, it isnecessary to avoid damaging the parent company's pride or openly challenging

FOREIGN SUBSIDIAklES AS CONTRIBU'IORS 25
ro PARENT COMPANIES

the feelmgs of superiority of the parent company. As we saw in the case of Fuji-

Xerox, "the proof of the pudding is in the eating;' and actually demonstratingproducts incorporating superior technology is an effective method to gain recognition
from the parent firm.

5. Paradigm Change
Up until now, both executives of multinational firms and scholars workmg in thefield of international business have been sharing the following way of thinking.
First, the success of the foreign subsidiary, vis-a-vis competition from indigenous
firms, depends on whether or not the subsidiary is in a superior technological position.

Second, superior technology (in a broad sense which includes not only product andproduction technology but also marketing know-how and brand, managerial andadministrative systems and know-how, etc.) is tranferred from the parent to thesubsidiary. In the third place is the idea that the parent in the country of origin
controls the foreign subsidiary.

This way Of thinking may be called the "traditional paradigm of multinational
enterprises.'' This traditional paradigm has been applied to the study of foreigncompanies in Japan during the prewar years, as we saw at the beginning of this paper.

However, the behavior of foreign companies that came to Japan in the post-war years
has some features that challenge the traditional paradigm. Fuji'-Xerox is only one

example. When we look at the recent behavior of foreign firms in Japan, the needfor a new way of thinking about multinational companies becomes a necessity.

, paradigm of multinational enterprises which would complement the
The new
traditional paradigm has the following characteristics.

First, the foreign subsidiary is considered as a source of innovation. The foreignsubsidiary, based on its geographical advantage and entrepreneurship, develops new

products, and creates new production technologies or managerial systems. Foreignsubsidiaries have the potential to become a source of technology.

The second idea is that new technology born at the foreign subsidiary istransferred to the parent firm. Up to now it was thought that technology flows fromthe parent to the subsidiary, but in reakty there is also a flow of technology in the
opposite direction. So far, the foreign subsidiary has been considered the beneficiaryof the transfer of superior technology from the parent firm. According to the newparadigm, the reverse phenomenon also occurs, and the parent becomes the beneficiarythat adopts innovations originated in the foreign subsidiary. The foreign subsidiary26 HIDEKI YOSHIHARA
makes contributions to the parent firm.

In order for multinational companies to develop according to this new paradigm,
the following two conditions have to be met.

The first relates to the existence of management initiative or entrepreneurshipat the foreign subsidiary. According to the traditional paradigm, the foreign subsidiaryis controlled by the parent company. On the contrary, in the new paradigrn thesubsidiary is encouraged to pursue an independent style of management.
Concretely speaking, the following requirements have to be satisfied. The presidentof the foreign subsidiary should be a local national rather than a foreign expatriate.

The foreign subsidiary should not be considered by the parent simply as a branchfactory located abroad, but as an independent firm. It should be equipped witha whole range of functions, from development and production to marketing and sales.
Particularly important is the capabhity of the subsidiary to develop its products. 'Another condition is that the parent company should overcome feelmgs ofsuperiority over the foreign subsidiary, and humbly learn from it. The parent shouldbe able to recognize the immovations made at the subsidiary. Then, the parent company

should try to adopt superior innovations made at a foreign subsidiary and makeefforts so that synergetic effects emerge from the interaction of the foreign subsidiary's

resources and those at the parent company. Global synergy is one of the goals thatmultinational fums should pursue from now on.

Acknowledgement
This paper is based on the author's ongoing research project ``Foreign Companies
in Japan,'' which is funded by a research grant of the Inamori Foundation.

THE GAINS FROM FREE TRADE FOR A MONETARY ECONOMY i)

Murray C. KEMp2)

1. Introduction
The classical gains-from-trade proposition has been proved in a barter context only.
It has been taken for granted that the same proposition is valid for monetary economies.

In the present note it is shown that, for economies of a standard monetary type,free trade may be disadvantageous; the traditional production and consumption gains
may be swamped by a loss of satisfaction from holdmg cash when relative prices change.

2. Analysis
Consider a small country which produces, consumes and trades two commodities andwhich derives satisfaction from its holding of cash balances. To avoid inessential
complications, suppose that ak households are alike in preferences, endowments andfarnily composition. Let pi denote the domestic price of the ith commodity, ci thedomestic demand for the ith commodity, I(p,, p,) the maximum value of output at
Prices p, and p2, T(p,, p,) a suitable price index (positive, increasing, concave andhomogeneous of degree one), m the stock of money demanded, and m the given
stock of money. Then the community can be viewed as maximizing a utility function

U[Ci, C2, M/T(Pi, P2)] (1)subject to a budget constraint

PiCl+P2 C2 +M=I(Pl, P2)+M (2)The solution to the problem may be written
1) I acknowledge with gratitude the usefu1 suggestions of Ngo Van Long, Koji Shimomura and Kar-yiu
Wong. The present paper was written during my visit to the Research institute for Economics and Business

Admmistration at Kobe University, December 1989 to February 1990. I am gratefu1 to the mernbersof the Institute, especially the Director, Professor Hiromasa Yamamoto, for their generous and inendly
hospitality.
2) Research Professor, School of Economics, University of New South Wales, Kensington, Austraka.

28 MURR2e"r C. KEMPc,=c, (p,, p,, ni) i= 1,2 (3a)m= m(p,, p,, fii) (3b)In balance-of-payments equilibrium,

M(P,, P,, ni)=th (4)Moreover, since the country has no influence on the terms of international trade,

P, =XP, (X>O, constant) (5)Eqs (4) and (5) form a complete system in p, and p2. Let us assume that it
has a unique solution

pi=pi()t, iii) i- 1,2 (6)By varying the terms of trade parametrically, one can generate alternative feasible
output, consumption and export pairs. Presumably there is a critical value of X, say

X" , at which trade is erctinguished. Suppose that, mitially, X =X'.
The initial no-trade equMbrium is disturbed by a smab increase in X. What happens
to the wellbeing of the typical household? From (1),du=u,dc,+u,dc2+u.1.d(m/T) (7)where ui iii Ou/Oci and u./.!E au/a(mlT). However, from the first-order conditions
associated with (1) and (2),Ui /Uml."Pi /T (Pi, P2) (8)Hence'

7rduu.i. = (PidCi+P2dC2)- u;7 (Tidp,+T2dp,) (9)where Ti='OT/Opi. Finaky, from constraint (2) and equMbrium condition (4),p,dc,+p,dc,=O, (lo)implying thatm =-i(T,dp,+7r2dp,) (n)7rduu.l.

29
THE GAINS FROM FREE TRADE FOR A MONETARY ECONOMY

Evidently expression (11) may be of either sign. If (11) does not vanish, there canbe found a world terms of trade, say X, which is near but not equal to X* and suchthat trade is harmfu1, and there can be found a world terms of trade, say X suchthat trade is beneficial. If lX-X"l is suthciently large, trade is necessarily gainfu1.

It might be thought that the possibmaty of harmfu1 trade flows from a fai1ure to
make use of al relevant propenies of the price index T. ln particular, it might be thoughtthat the possibMty will go away if T is required to be a true cost of living index, so that

(7>O, constant)

Ti = 7Ci(2)

However it is easy to show that there is no escape along that route. Thus, availingourselves of (6), E Tidpi=O if and only ifdd(B)

x T(xp, (x, -m), p, (x, -m) ) ., oor, in view of (rz), if and only if(Xc, + c,)(dp,/dX) = -c,p,(14)

which may or may not be satisfied.
To remove the troublesome finding, it suffices to assume, in addition, that the income
velocity of circulation is a constant:(k>O, constant)I(Xp,, p,)/ni = k(15)

For thendp,- p2I1- P2X1

dX

XI +I

Xx +x

12

12

where xi is the output of the ith commodity. Since xi= ci in the initial equihbrium,
the righthand side of (16) reduces to -p,c,1(Xc,+ c,) and (14) is satisfied. Evidently(15) is a very strong and implausible assumption, since it rules out the possibMty that

consumption of one good requires 1arger cash balances, per unit of value, thanconsumption of the other good.
Suppose that X = X > X", as in Figure 1. What can the government do to cancel
or reverse the loss associated with X? Tinkering with the nominal stock of money will

be ineffective. Given any X, the homogeneity of T(p,, p,) ensures that real cash
balances (and therefore u) are independent of ni. On the other hand, the government(16)

MURRAY C.
KEMP

30

could kill al trade by imposing a suMciently heavy duty on imports (of the second
commodity). That would eliminate the loss but it would not corrvert the loss into a gain.

To achieve the latter objective it will be necessary, I suppose, to destroy the motive

for holdng cash. How that is to be done cannot be detemined without laying themonetary foundations much more carefully.

uu= U(A)

U(A*)

----

-----d--

!

l
'

' -

l
t

l

,

t

1

/
/

1

z

A* a
Figure 1(a)uu =tt (x)

N

N
Å~

N

N

Å~

u(x*)

-.Xe--"-'""'
N.

,
'
'

,

,

'

'

,

l

A* ft

A

Figure 1(b)3. Final remark
How seriously one takes the possibMty of harmfu1 trade depends on one's confidence
in the utility function (1). In the analysis of trade gains and losses one compares
altern,ative steady states. But in a context of uncertainty-free steady-state analysis thecase for (1) is at its weakest. In a more thorough analysis one would relate the demand

for money to uncertainty - uncertainty about the scope for barter trades and about
future household incomes.

ON THE OPTIMAL TIMING OF FOREIGN AID

Murray C. KEMp, Ngo Van LONG" and Kazuo SHIMOMURA

Abstract We offer a dynamic formulation of the aid process, in which questions of tirrimg
are centrnl. It is shown that in most cases it is optimal to give the aid partly in a lump,at the oubset, and partly as a flow, over tirne. However, if the donor and recipient cooperate,
stock and flow aid may be of opposite sign. It is shown also that when marginal utility is ofconstant elasticity, the rate of flow of aid increases (decreases) if and only if the initial worldstock of capital is less thari (greater than) its steady-state value.

1. Introduction
The available formal analysis of foreign aid is static, with no provision for the passage oftime. Its chief weakness is its inabMty to address questions of phasing or timing.
In particular, it has nothing to say about the optimal timm' g of aid, includmg its division

into stock and flow components.
A siMilar criticisrn can be directed to the analysis of reparations, indeed of ak forms

of unrequited transfer between governments. However we shad employ throughout
the concrete terminology of aid.

Here we offer a dynamic formulation in which questions of timing are central.
The formulation has the virtue and defect of being very simple. Thus, for the mostpart, we recognize just two counuies, each producing a single commodity (the samein each country) by means of homogeneous capital and labour, and differing onlyin their initial factor endowments. Of course, in such a world there is no scope forconventional trade; in the absence of private international investment and of transfers

between govemments, each economy would be isolated. However, at the end, we
do broaden our analysis by introducing a second traded commodity.

The country offering aid will be referred to as the donor, the other country
as the recipient. The donor seeks that combination of initial stock transfer n andcontinuous flow transfer <ul(t)> which achieves a given improvement in therecipient's welfare at least welfare cost to the donor. In its search for the optimal

pair (9, <ol(t)>) the donor may or may not enjoy the cooperation of the recipient.
If the recipient cooperates, 9 and w(t) are unrestricted in sign; in the absence ofcooperation, 9 and o(t) are constrained to be non-negative. The optimal pair wil1
' Professor of Economics, Australian National University.

32

MURRAY C. KEMP, NGO VAN LONG AND KAZUO SHIMOMURA

prove to be sensitive to changes in assumptions about cooperation and to changes in theassumed degree of capital mobvaty.
It is shown that in most cases it is optimal to combine stock and flow aid, that is,
to give the aid partJy in a lump, at the outset, and partly as a fiow, over time. However,if the two countries cooperate, stock and flow aid may be of opposite sign. It isshown also that when marginal utility is of constant elasticity, the rate of flow of aid

increases (decreases) if and only if the initial world stock of capital is less than(greater than) its steady-state value.

2. Private Capital Immobile Between Countries
In many real-world situations the case for foreign aid rests in part on the reluctanceof private capital to migrate. Indeed, "for most of the least developed countries,

foreign aid has become rnore important than borrowing as a source of funds fromabroad'' (Levy (ro88), p.ts2). We therefore begin our analysis under the assumptionthat private capital is internationaky immobile.

WTithout loss, it is assumed that the labour force in each country is initiaby equal

to one. The following standard notation will be employed.

Q the rate of time preference in each country
n the rate of growth of the labour force in each country
ki the capital: labour ratio and capital stock in the i th country, i=1, 2

f(ki) the common production function, assumed to be increasing, strictly concave andto satisfy the Inada conditions

ci the level of consumption per capita in theith countryu(ci) the common individual uthity function, assumed to be increasing, strictly

concave and such that lim u'(ci) = coci.oIn a state of isolation, the i th country solves the problem(P•i) n2fiix foco u(ci)exp(-6t)dt (6 =- Q-n>o)s.t. kj. =f(ki) - nkj •- ciki (O) = kio, given
Let the maximum value of the integral be denoted by v(kio).

ON THE OPTIMAL TIMING OF FOREIGN AID

33

The first country (the donor) wants to (or is required to) increasev(k2o) tov(k2o) + A, A> O. The problem facing the donor then is to findthe least

utility-cost way of doing this. Forrnaly, the donor's problem is to find
(P.2)

c1, g12il{.ico ,g fo u (c1) exp (- 6t) dt

s.t. kl =f(kl) - nk1 - cl -w. = f(k2) - nk2 - c2 +ok2ki(O) + 9 = kio, given
k2 (O) - 9 = k,o, given

foco U(C2)eXP(-6t)dt l v(k,o) + A

formulation
is as follows: for any 9 and <w(t)'> there is
The reasoning behnd
this
an optimal consumption path {<c2(t)>:9, <to(t)>} which the recipient would
choose; however the donor would select the same path if, as we have assumed, the< c2 (t) > , for it is in the donor's interest that any aid be used ethciently.
donor controls

Nternatively,the donor's task is that of findng, for some X>O,Max [Soco u(cl)exp(-pt) dt + XSoco u(c2)exp(-pt)dt](P.2,)

C1,c2,w,k1(O),k2(O).
s.t.
kl=f(ki) - nk, -c, -o (1)k2=f(k,)-nk, -- c2+w (2)ki (O) + k2 (O) s kio + k2o, given (3)Evidently X l 1 if and only if, in the optimum,

foco u(ci)exp(-6t)dt gJoco u(c2)exp(-6t)dt

In (P.2) and (P.2') the controls w and 9 are unrestricted in sign. This implies

a high degree of cooperativeness between donor and recipient. In some situations
it may be more reakstic to require both tu and 9 to be non-negative, so that to theconstraints of (P.2') are addedMURRAY C. KEMP, NGO VAN LONG AND KAZUO SHIMOMURAsuk2 (O)lk2o (5)In the analysis to follow we shak consider both the case in which (4) and (5) are

imposed (the non-cooperative case) and the case in which they are not imposed(the cooperative case).

The current-value Hamltonian associated with (P.2 ') is

H= u(cl) + Xu(c2) + Wl [f(kl)-nki•-Ci-w](6)+ W2 [f (k2)-nk2 -- c2 + w]
and, if the ful1 complement of constraints (1)-(5) is recognized, we have as necessary
conditions

oH/ac,=u' (ci)-cbi =o (nOHIOc,=Xu' (c,)-W, =o (8)OHIOo=-W,+ W, s O, w >= O, w(- ip,+ W2) ==O (9).

Wi =6W,-Wi [f' (k,)-n] (lo)l2 =6ut2'V2 [f' (k,)-n] (11)It follows from (9) that

Wi (O)IW2 (O) (2)Suppose, reaksticaly in the case of foreign aid, that, before and after aid, thedonor is the wealthier of the two countries so that X < 1. In the absence of aid,ki(t)>k2(t) for al t)-O and the marginal product of capital is always greaterin the second country. The same is tme if ak aid is given in a lump, att=O. It is
intuitively clear, then, that ak aid should be given in a lump and that the optimal

ca(t) is identicady zero. More formaby, suppose that there is a non-degenerateinterval [ti, t2] on which tu (t)>O. Then, from (9),Wi(t) == W2(t) fOr tE [ti, t2] (13)so that, bearing in mind (D and (8),u'(c,) -- Xu'(c2) (14)

ON THE OPTIMAL TIMING OF FOREIGN AID 35
Since X<1, u'(c,(t)) <u'(c, (t)) andc, (t)>c, (t) for tE [tvt2] (rs)From (9)-(11), on the other hand, if w(t)>O then k,(t) = k2(t) and Ri(t) =k2(t) so that, from (1) and (2), ci + w = c2-o orCl(t) = c2 (t) -2ct) (t)<c, (t) for tE {t,, t21 (16)Evidently (va) and (16) cannot both be true. Hence o(t) cannot be positive ona non-degenerate interval.

Thus our intuitive conclusion, that the whole of the aid should be given ina lump, is justified. However in arriving at that conclusion it was assumed that
constraints (4) and (5) are satisfied. If those constraints are not imposed then,instead of (9), we have V,(t) = W2(t) for ad t. It then follows from (10) and (11)that k,(t) = k,(t) for al t.

Hence

9=5 (k io-k2o) (in'and, since the donor remains the wealthier country, w(t) must be negative onsome interval. In fact the optimal w(t) is •negative always. For suppose that w(t) =O at t = ti, so that ci(ti) = c2 (ti). From (7) and (10),a(Ci(ti)) (Ci(ti))/C, (t)) = f' (k,(t,)) --- 6 . (ts)where''or (C) i! -U" (C) C/U' (C) > O
is the elasticity of marginal utility. Simlarly, from (8) and (13),or .C2 (ti) C2 (ti)/C2 (ti) = f' (k2 (ti)) -6 (te)Hence

6i (t,)/c, (ti)= 6, (t,)/c2 (t,) (2o)It follows that ci(t) = c2(t) for ad tlti; and, running time backwards, that
Ci(t) = c2(t) for ak tE[O, ti]. This in turn implies that the two countries enjoy
the same level of wellbeing, a contradiction.

If marginal utility is of constant elasticity these results can be considerably
sharpened. Thus if or(c) == bl, (rs) and (te) imply that ci and c2 change at the same

36 MURRAY C. KEMP, NGO VAN LONG AND KAZUO SHIMOMURA
proponional rate, increasing (decreasing) if and only if the initial world capital stockis smader than (greater than) its steady-state value, that is, if and only if -li- (kio + k2o)

is less than (greater than) R, where R is defined by f' (R) = 6; it then follows thatw (t) steadily rises (falls) under the same necessary and sufficient condition.

Let us summarize our conclusions to this point. Suppose that, before and after
aid, the donor is the wealthier of the two countries. In the non-cooperative solution

to (P.2'), al aid is offered at the outset. In the cooperative solution there isan "excessive" initial pulse of aid equal to t (kio-k2o), followed by a flow of aid
which is always negative; if marginal utility is of constant elasticity then consumptionin each country, as well as --w(t), rises (faks) if and only if the initial world capita1
stock is less than (greater than) its steady-state value.

Other cases can now be treated relatively briefiy. Thus suppose that before aid
the donor is the wealthier country but that after aid the recipient is wealthier, sothat X>1. Then, whether or not the recipient is cooperative, it is optimal to set
9 = -ii- (kio-k2o) > O and to supplement this lump of aid with a fiow which is always
positive. If marginal utility is of constant elasticity then optimal consumption changes
at the same proponional rate in each country; if and only if -} (kio+ k2o) is less than(greater than) k then ci(t), c2(t) and co(t) are increasing (decreasing), and if andonly if t (kio + k2o) = 2 then ab three variables are positive and constant.
Suppose, finaly, that, before and after aid, the recipient is the wealthier country,
as it might be in the event of post-war reparations. In the non-cooperative (cooperative)

case, 9=O (9=t(kio-k2o)<O) and w(t) is positive for all tlO. If theelasticity of marginal utility is constant then optirnal consumption changes at the same

proportional rate in each country, with ci(t), c2(t) and w(t) increasjng (decreasing,constant) if and only if -li' (kio + k2o) is less than (greater than, equal to) R.

3. Private Capital Mobile Between Countries
If capital is completely mobile between countries, so that the marginal product of
capital is always and everywhere the same, then it is a matter of indifference to thedonor whether aid is given in a lump or as a flow or as a mixture of both; moreover,
if some or ak of the aid is given as a flow, it is of no importance to the donor whether

it is increasing or decreasing, positive or negative, for the difference between one
aid profle and another will be condnuously offset by an equal and opposite difference
between the associated profles of capital flow. Nevenheless the many optimal patternsof aid harTe one thing in common - they are ab associated with the same pair of

ON THE OPTIMAL TIMING OF FOREIGN AID 37
optimal consumption paths <cl(t), c2(t)>•If marginal utility is of constant elasticity then ci(t) and s(t) change at the same

proponional rate, increasing or decreasing according as S (kio+ k2o) is smaller orgreater than R.

These conclusions hold whether or not the donor and recipient cooperate;
however the extent of the indeterminacy is less in the absence of cooperation, forthen 9 and w(t) are constrained to be non-negative.

4. Final Remarks
Our analysis can be extended in several directions. Thus the donor and recipient
might be abowed to differ not only in initial endowments but also in technology andrate of time preferenge; and they might be alowed to produce more than one good,so that trade and aid could be seen to interact. Finaky one might recognize that theabsorption of aid is costly, with the cost increasing with the rate of absorption; thenthe sharp distinction between stock and flow would disappear. •Here we briefly indicate how the analysis must be modified to accommodate thepossibMty that the donor is more productive tlian the recipient and the possibikty

that there are two commodities, one a pure consumption good, the other a pureinvestment good. In addition we record a fact which will come as no surprise to theattentive reader of Sections 2 and 3. Problem (P.2) contains the a priori restrictionthat a stock transfer can occur only at t=O. If the problem is formulated more
fiexibly, with ki and k2 as control variables, it can be shown that t=O is the only
date at which a stock transfer would occur in an optimal plan.
The donor more productive than the recipient. We confine our attention to the casein which kie>k2o and private capital is immobile.

Let the donor's production function be denoted by f(ki) and the recipient's by
x3f(k2), with O<x3<1. In isolation ki approaches ili, defined by f' (Ri) = Q, and k2

approaches R2, detined by l3f' (R2) = Q. Since Q/B> e, Ri>R2. The donor seeks
the solution to (P.2'), with Bf(k2) replacing f(k2) in constraint (2); and the newnecessary conditions consist of (" -- (11), with (11) replaced by.

'

IP2 =Qyb2-lb, l3f' (k2) (11 ,)If the constraints olO, 9 l O are ignored (the cooperative case), the solution ischaracterized by

MURRAY C. KEMP, NGO VAN LONG AND KAZUO SHIMOMURA

38u'(cl (t)) < u' (c2 (t)), hence cl (t) > c2 (t) for al tf'aci(t)) = Bf'(k,(t)) for akt

lim k,(t) = R,t-co
lim k,(t) == R,t-co
It follows that if f'(kio)>Bf'(k2o) then it is optimal to set 9< O and cD(t) > O for allt, that is, it is optimal to shift capital to the more productive donor country; and that if

f'(kio)<6f'(k2o) then it is optimal to set 9 equal to the tpositive) solution to the.
equationf'(kie-9)d6f'(k2o+ 9) = O
and to then set cd(t)> O for altor w(t) < O for all t, dependmg on the values of
B and X.
If the constraints wlO, 9).O are recognized (the non-cooperative case), capitalcannot be shifted to the donor country. It follows that if f'(kio)>Bf'(k2o) then it is

optimal to set 9 = O and o(t) always positive but smaker than in the cooperativecase.

A second commodity when a second commodity is recognized, we have theadditional complication of variabie terms of trade. However, if the two countries cooperate,

so that ki(t) = k2(t) for ab t, the relevant analysis remains straightforward andyields conclusions not unlike those of Section 2. The appendix contains a complete
examination of the case in which private capital is internationaky immobile. Here we
merely list the main conclusions.
(i) Except when the mitial world capital: labour ratio greatly exceeds its steady-statevalue, production is alvvays and everywhere incompletely specialized.
(li) Suppose that production is incompletely specialized in each country.
Then ci(t) '•dc c2(t) and to SO if and only if X g 1. If the consumption good isrelatively capital-intensive, ci monotonely increases (decreases) if the world
capital: labour ratio is less than (greater than) its steady-state value. If in addition

the elasticity of marginal utility is constant then 1 o1 monotonely increases.

ON THE OPTIMAL TIMING OF FOREIGN AID 39
APPENDIX
In this appendix we extend•the analysis of Section 2 to accommodate a second

commodity. One of the two commodities is a pure consumption good, the othera pure investment good. Both can be traded internationaly. wrth each commodity thereis associated a production function with the same propenies as f; however the two
commodities dffer uniformly in their relative factor intensities. As in earlier sections,the two countries are distinguished only by their initial wealth.

The following additional notation is needed.

p the relative price of the consumption good in terms of the investment goodg(p, K) the per capita revenue or GNP function of the ith country, in terms of theinvestment good
The flow of aid is recorded in terms of the consumption good.

Throughout the appendix it is assumed that private capital is intemationallyimmobile but, of course, intersectorally mobile. Moreover it is assumed that the donor

and recipient cooperate, so that both fiow aid and stock aid may be of either sign.

Then, for some X> O, the two countries seek(P'3) ci,kirEo}si,c.,p j';O[u(ci) + xu(c,)] exp(-6t)dt

s.t. ki. = g(p, ki) - nki - pci - pal
k2 = g(p, k2) - nk2 - pc2 + pw
gp (p, ki) + gp (p, k2) 2 Ci+ c2

ki (O) + k2(O) s kio+k2o, given
where, from the familiar propenies of the revenue function when commodities differ
unifomiy in factor intensity, gp(p, ki) is the per capita output of the consumption

good in the ith country. Defining -ci !iE ci+cD and -c2 =-= c2-cD, (P.3) can bereforrnulated as

40 MURRAY C. KEMP, NGO VAN LONG AND KAZUO SHIMOMURA(P'3') -,i,kin?ti)yf,.,pJoco[u(-ci-co) + xu(-c2+co)]exp(-6t)dt

s.t. ki .= g(p, ki) - nki -- pMci(21)

. g(p, k2) - nk2 - p-c2
4 ==

(22)

gp (p, ki) + gp (p, k2) = -ci + -(2(23)

ki (O) + k2(O) s kio+4o, given(24)

The current-value Hamltonian associated with (P.3') is

H = u(-c,-cz))+Xu(-c2+w)+i Wi[g(p, ki)-nki-p-ci]
and the Lagrangean is

L=H + W[gp (p, ki) + gp (p, k2) - -Ci - -C2]
so that we harTe, as necessary conditions,

OLIO-c, = u' (-c,-tu) - pWi- W = O(25)

oL/a'c2 = xu'(-c2+o) - pW2 -V = O(26)

OL/O cD = -U' (-Cl •- o) + XU' (-C2 + W) = O(2D

aLlap = lbi [gp (p, ki) - -ci] + le2 [gp (P, k2) - -C2]

+ V[gpp (p, ki) + gpp (p, k2 )] = O(28)

Wi. = 6Wi - 6L/6ki = 6thi -- Wi[gk (p,ki) - n] - ipgpk(p, ki)(29). = 6 ip2 - 6L/6k2 = 6ip2 - W2[gk (p,k2) - n] - Wgpk(p, k2)
W2

(30)

ON THE OPI'IMAL TIMINGOF FOREIGN AID

We begin our study of these conditions by establishng a usefu1 prelirninary
proposltion.

LEMrm: On the optimal path, p > O.
Proof Suppose that p(t) =O for some t, say t'. From the assumed propeniesof the production funodons, gp (O, ki) = O. Hence, from (23), Ei + E2 = O. From
this result, and the non-negativity of ci, ci =c2 = O, contradicting the assumed

propenies of the utility function. m
From (25)-(27), with p > O,

Wi=ip2 EE ipo (31)which, with (29) and (30), implies that

Wogk(p,ki) + Wgpk(p,ki) = Wogk(p, k2) + Vg,k(p, k2) (32)
It is corivenient to consider separately the two cases, W > O and W = O.

Case A: W > O In this case,gp(p, kl) + g,(p, k2) - 6i - 62 =O (33)Together with (28) and (31), this implies thatg,,(p, ki)+g,,(p, k2) =O (34)which, since gpp(p, ki) ) O, implies thatg,,(p, ki) =O i= 1,2 (35)Thus production must be completely specialized in each country.

Given the restrictions imposed on the udity function, it is impossible thatboth countries produce only the irrvestment good. And since capital can becooperatively shifted internationaly and the same production functions prevail
everywhere, it is inethcient for the countries to specialize in producing different
goods.

Thus we are left with just one possibdity: both countries produce theconsumption good only. Thenandfe(ki)'Ei i= 1,2 (37)41

42 MURRAY C. KEMP, NGO VAN LONG AND KAZUO SHIMOMURA
where f, is the per capita production function for the consumption good. Eq.
(32) therefore reduces to''(pW, + W) fE(k,) = (pWo + W)fE (k,) (3s)which, since pWo+W>O, implies that ki=k2iik. From (37), therefore, ei=
62!a6. In the absence of a switch of regime, 6 and k, and therefore ci=
ei ' tu and c2 = 62 + w, corrverge monotonely to zero.

Case B: W = O From (25) and (26), Wo > O. Hence, from (28),gp(p, ki) - ii + g,(p, k2) - 62 =O (3g)
Bearing in mind (29) and (30), with Vo > O, (32) can be seen to reduce togk(p, ki)=gk(p, k2) (4o)As we have noted, it would be inethcient for the two countries to specialize inproducing different commodities. We therefore focus on the remaining possibMties:

that each country produces only the consumption good and that each country
produces both commodities.

(Bi) Suppose that each country specializes in producing the consumption good.
Then (40) reduces topfE(k,)=pfE(k,) (41)
Since p is positive, (41) implies that

'

'

Thus

Ei "= 62 E6' fc(k) (43).
where k follows
k = -nk. Evidently the trajectory is the same as in Case A.
(Bii) li neither country specializes, we can writeg(p,ki) == r(p)ki+w(p) (44)AID
ON THEOPTIMALTIMING OFFOREIGN

where r(p) and w(p) are the price-dependent rental rate and wage

43

rate,

respectively. From (21) and (22), defining k =' ki + k2,

k= r(p)k + 2w(p) - nk - p(6i + 62)(45)

Furthermore, from (39),r'(p)k + 2w'(p) == 6i + 62

(46)

On the other hand, from (25) and (26),
6i + E2 = di(pyCt,) + Åë(pyet,1>L)(4nHence, from (46) and (4",r'(p)k + 2w'(p) == di(pVo) + ofpWolX)(48)

which can be viewed as determining p as a function of k and cbo:p=p(k, Wo)'

Thus (45) can be rewritten as
k - [r (p (k, ipo)) - p(k, Wo) r' (p ik, Vo))]k+ 2[w(p(k,Wo)) - p(k, Wo)w'(p(k,Wo))] '- nk(49)

On the other hand, from (29) and (30),sbo = 3Po[Q - r(p(k, sbo))](50)

Investment

good
A

P
F'

F

F,
1
,

l
1
1
l

1
s
t

1

F, B
OF,
OF,

[n(p)-pr'(p)] R+2r'(p)R+2w'(p)Figure 1ppConsumption

good[w(p)-pw'(p)]"

MURRAY C. KEMP, NGO VAN roNG AND KAZUO SHIMOMURA
We now have ad the pieces needed for the construction of the phase diagram

associated with (P.3'). Let us begin with Case (Bil). In Figure 1, AFB is theworld per capita production possibhity curve for a given value of k. Given ipo
and R, (48) deterrnines the price ratio p and therefore the production point
F. Dfierentiadng (48) with respect to p and Wo, we obtain

dp . p[di,(pW,) + (1/X)Åë'(pWoA)] <o (sl)dWo r"(p)k + 2w"(p) - [th'(pWo) + (1/X)Åë'(pWo/X)]Wo
Now, from (44), r(p)k + 2w(p) :g(p,k). Hencer"(p)k+2w"(p)=g,,(p,k) (52)which, given the incomplete specialization of production, is positive. It follows

that the denorninator of (51), and therefore dp/dWo, are negative. Thus, as ipo
increases, p declines and the production point moves to the north-west from F.

However there is no finite value of Wo• such that production occurs at A, forthere is no finite value of Vo such thatO = Åë(pWo) + th(pWo/X)

where p is defined by Fjgure 1. 0n the other hand, when ipo takes on asuthciently small positive value, the production point reaches B. At that point,
p = P and we have the pair of equationsr(p)k + 2w (p) =p[r' (p)k + 2w'(p)] (53)r'(p)k+2w'(p) -- Åë(pW,)+di(pW,IX) (54)
tho

tho

R

Figure 2(a) : r'(p)>okFigure 2(b) : r'(p) <oON THE OPTIMAL TIMING OF FOREIGN AID
so that,djfferentiating with respect to P, sbo and R, and elimhating dP,

dWor (p) [r " (p)k + 2w " (p)] --- [th ' (p ip,) + (1/X) Åë ' (p W, /X)] [r (p) - pr ' (p)](55)
dli = p[di'(pw,) + (11X) Åë'(pW,/X)][r"(p)k+ 2w"(p)]If the consumption good is relatively capital-intensive, so that r'>O, thendipo/dk < O; otherwise, the sign of (55) is ambiguous. Thus we arrive at Figure 2;

above HJ both commodities are produced, below HJ only the consumption goodis produced.

Returning to (50) and (51), we seek the loci kI(so) =O and Wo1(si) = O• Dfferentiating (49) with respect to p, k and ipo, we obtaindp - -(1/A)r'(p)dk + (p/A)[Åë'(pW,) + (1/X)di'(pW,/X)]dWo (56)
where
A iii r"k + 2w" - [di'(pipo) + (1/X)th'(pVo/X)]Wo > O
Dfierentiating (50) with respect to p and k, we obtaindk = -p[r"(p)k + 2w"(p)]dp + [r(p) - pr'(p) - n]dk (57)And, finaky, differentiating (51) with respect to p and ipo, with p satisfying
Q == pr(p), we obtain.

dWo =-Wor'(p) dp (s8)Substituting from (56) into (5D and (58),dk =(PX' (r"R + 2w") + (r - pr'-n))diE-(1/A)p2[Åë'(pW,) + (1/X)th'(pW,/X)][r"R + 2w"]dW, (59)anddip, = -W,r'{-(11A)r'dk + (1/A)p(th'(pW,)+(1/X)di'(pW,/X)]dW,} (60)Now consider the function

h(X) =' det [-Xwolr")2/A ipor,BpiA] (6i)where

' (r"R+2w")+(r - pr' - n)
A - PrA

and 2

B . 'lliL [Åë'(pipo)+di'(pwo/x)/)t] [r"R+2w"]

45

46 MURRAY C. KEMP, NGO VAN roNG AND KAZUO SHIMOMURA

It can be verified thath(O) - -(pW,r'/A)[th'(pW,) + Åë'(pV,/X)/X] [r-pr'-- n] (62)is negative if n is suficiently close to zero. It follows that, for sufficiently smadn, the stationary state of the system [(50), (51)] is a saddlepoint: If the mitial(Wo,k) is chosen on one of the stable arms of the saddle, (Vo,k) converges tothe stationary state.

IPeoA

rax x

c Xx L
Å~

E•
R-o
N
Å~

HX x c'

B xb
IX
.
i
Xb, J
cbro=O t
t B'

k

Rb
Figure 3

: r'

(p)>o

Vo

r

ax

A

Å~ uto=o
x

t

C'

Å~

xE
x

C

H

x

B

Å~

x b
1

.

tho=O

t

B'

t

o

Rb

Figure4 :

r'

(p)<o

xb'
XJ

R

ON THE OPTIMAL TIMING OF FOREIGN AID 47
Figures 3 and 4 are the phase diagrams associated with (P.3') when n issuficiently smal but positive. In each figure the optimal trajectory is represented

by the dotted locus aEbb'. On bb' only the consumption good is produced;

on aEb both goods are produced in each country. Moreover, ki=k2 on bb',
implying that, if kio + k2o > Rb, there is an initial stock transfer such that ki(O) =k2 (o) = S (k,o + k,o)•' While the phase diagram makes clear the existence and saddlepoint stabdity
of a steady state, it contains no information about the manner in which aid andconsumption behave through time. However, we know from our earlier discussionof Case A, that, when both countries produce only the consumption good, therate of flow of aid and the two rates of consumption go monotonely to zero.

If X<1 then ci>c2 for ak t, and w<O for ad t. It remains to study the
behaviour of aid and consumption above HJ, where each country produces bothcommodities.

From (27) we know that, if and only if Xsl, cilc2 for ad t. What more
can be said? Dfferentiadng (59) with respect to time, we find that'.
{(1/Vo)(r"R+2w") - [th'(pWo) + (1/X)Åë'(pWolX)]}pVo(63).L= (p/Wo)(r"k +- 2w")Wo- r'k'. the coethcient of Vo are positive.
where both the left side of the equation andOn the other hand, the stable arms of Figures 3 and 4 are negatively sloped,--

implying that lo and k are of opposite sign, with lo<o, R>o on Ea and
Wo >O, k <O on Eb. Together with (63), these facts imply that, if the consumption good is relatively capital-intensive, so that r'(p) > O, then d(pWo)/dt isnegative on Ea and positive on Eb. Since u'(ci)=pWo and u'(c2) == pWo/X, we
can infer that, if the consumption good is relatively capital-intensive, ci monotonely

increases on Ea and monotonely decreases on Eb. Thus we have shown that
if the consumption good is relatively capital-intensive then ci increases everywhereon the left stable arm of the saddle and decreases everywhere on the right stable arm.

Let us now consider the behaviour of aid above HJ. Suppose that R(O) > Rb
and X< 1, so that ci (t) > c2 (t) for ad t. When R reaches Rb at t= {, ki = k2

and w<O. At {, each country produces the same amount of the consumption
good, and cl exceeds c2 by tu, the amount of the transfer. After l, each country

moRRAIY C. KEMP, NGO VAN LONGSHIMOMURA
ANDKAZUO

48

produces both goods. Hcvwever the transfer will continue to be effected by a net
shipment of the consumption good only; if the recipient were to ship both goods,

the donor would simply sell back al irrvestment goods received. Since ci(t)>c2(t) for ad t, the flow of aid is negative for ak t. Moreover, from the equationsof accumulation.

ki = r(p)ki + w(p) -• nki -p[di(pWo) - w] (64a).k2 n r(p)k2 + w(p) - nk2 - p[th(pWo /X) + ol] (64b)and the equaity of ki and k2, we deduce thatth(PWo) - CD == th(Vo/X) + W
so thatW- -il- [di (P Wo) - di (P Wo /X)] (65)
Dfierentiating (65) with respect to time,di = S [Åë'(pwo) -- a/x)Åë'(pwoix)]8t(pwo)-S[di(pw,) PV;?p'iP,)Wo) -- th(pw,/x) (PipoiX(iÅëw,'(/Px4o/X)]d(PpWi,)/dt (66)

If the elasticity of marginal utility is constant, (66) reduces to

di = ';T. [th(pwo/x) - di(pwo)] d(PpVi,)/dt

Since di is a decreasing function,

sign [gb(piet,/X) - th(pib,)] F sign (X-1)

Thus, if r' >O then on Ea w monotonely increases (decreases) and on Eb w
monotonely decreases (increases) if X<1(X>1). In short, if the consumption
good is relatively capital-intensive we reach conclusions very similar to thosereached in the one-good case.

ON THE OIrl'IMAL TIMING OF FOREIGN AID 49
It remains to consider the possib-ty that the population is declining or stationary.

If the population is declining, there is only the steady state with k=O. li thepopulation is stationary we have a more interesting case. For the locus k =O
is determined by (49) and (50); and the locus HJ is determined by (53) and (M).

Comparing the two pairs of equations, one sees that, if n=O, the locus k=O
coincides with HJ. Moreover, differentiadng (49) and (50) with respect to p,
Wo and n, we find thatdWo r"R + 2w" - [Åë '(p W,) + (b '(p V, lx)lx] [r "R + 2w "] -i R>odn - [Åë'(pWo)+Åë'(pcbolX)/X]p
thus confirming that the locus.k=O lies above EU if n > O.

Referencesp] levy, v.

(te88), Does concessionary aid lead to higher imrestment
Review of Economics and Statistics 69, rs2-156.

rates

in low-income

countries?

A SIMPLE UNION-RIDDEN GENERAL EQUILIBRIUM MODEL
Kazuo SHIMOMURA

1. Introduction
In this paper we present an equilibrium model involving a maxirnizing labour union.

It is not the main purpose of this paper to construct an union-ridden model whichis realistic in such a sense that it can weil explain some important facts in labour

markets. Instead, we shad constmct a simple, abstract and yet general equilibrium

model from which more complicated union-ridden general equilibrium models could
develope.

Before starting formal analysis, the following points may be worth mentioning.

First, with respect to the labour union objectives, we shak basicaly follow
a traditional approach: A labour union maximizes the expected utility of a union

member under the assumptions that ad member are identical and that employed

members are randomly chosent See McDonald and Solow (1981), Oswald (1982,
1985), Sampson (1983) and Farber (1986). Although that approach generaky does
not consider the possibmaty of redistribution of wage income and workmg hours
over ad union members, there may be no reason, at least from a theoretical pointof view, to exclude that possibdity from our analysis, if such redistribution canmake any member better-off. To our knowledge, the redistribution activities werefirst discussed by Pencavel (1985). He virtuaky showed that if al mion members
pool their income and the labour union redistributes this total income over ad

members in such a way as to maximize the expected utility of each member thenmaximizing the expected utility of each member is equivalent to maximizing therents from unionization. Although he argued that the income redistribution within

the union has some relevancy to unionism in the real world, he did not exarnine
the theoretical implication of the maximization of the rents from unionization

for union-ridden equdibria. That attempt was made by Kemp, Long and Shimomura(1990) which investigated how the pure theory of international trade andinvestment may be affected by introducing maximizing labour unions. However,they did not take into account the redistribution of workmg hours; they assumed
that each worker can inelastically provide a fixed amount of workmg hours. Formulating the objective function for a labour union later in this paper, we shak take into

52 KAZUO SHIMOMURA
account the intra-union redistribution of both wage income and working hours.

Second, we shak make the production-side of our model consistent with thestandard theory of production. Thus, it will be assumed that there are many competitive firms which, taking factor and commodity prices as fixed, determine thedemands for capital services and workmg hours and the supply of their commodity
in such a way as to maximize their profit. Entry into and exit from the market for

their commodity are free for them. Hence, the commodity price always tends tobe equal to its mit cost.

Third, just as workers can form a labour union, so may capitalists be able toform their union, say capitalists' club, which appears in the market for capital service

as a monopolist. This possibMty will be also taken into account in this paper.

The stmcture of this paper is as follows. In Section 2 our model is presented.

In Section 3 the pre-union equilibrium of our'model is examined. In Section 4
the reaction functions of workers and capitalists are derived. In Section 5 and 6
several types of equmabrium solutions are obtained and the relationship among themis visualy shown.

2. The Assumptions
Let us state the main formal assumptions underlying our model.

A.1 There are N households who earn their income only from providing labour
services measured by time, say hours. Let us cal the households workers. Eachworker has a system of preference ordering over consumption and leisure whichis common among workers and represented by the utility functionu=u(c., 1- I) a)
where cw is the amount of a worker's consumption and 1 is workng hours.
The maximum workmg hours are assumed to be unity for ary worker. The utility
function is strictly qusi-concatTe and has the following propenies; for any (c., h) > Ou, (c., h) iii a u(c., h) > O
Ocw

uh(c., h) Ei! O u(c., h) >o <2)
Oh

02
Ucc(Cw, h) iE ec.2 U(Cw, h) < O

ss
A SIMPLE UNION-RIDDEN GENERAL EQUILIBRIUM MODEL

02

Uch(Cw, h) iii

OCw Ohu(c., h) > O(2)uhh(cw, h) i!!! 2Ilh2, u(cw, h) <o

A.2 There are K households who earn their income only from renting capital
equipments which they possess. Let us cad the households capitalists. It is assumed

that each capitalist possesses just one unit of capital equipment and that the
maximum renting hours for each equipment are equal to be unity. The utility ofeach capitalist depends only on his/her consumption.

v = v(Cr)The shape of the function v(.) is(3)

common among capitalists. v(cr)has thefollovving propenies; for aqy cr>Ov'(cr) - d v(cr) >odCr(4)v"(cr) =i ddc2,2 v(cr) < o

A.3 There are no "middle class" people who earn their income from providing
both capital and labour services.

A.4 There is a single consumption good which is produced by competitive tirms.
The production function is denoted by

Y = F(X, L)
where X and L are the rendng hours of capital and the workmg hours of labour,

respectively. From A.1 and A.2 XSK and L:N. The production function isstrictly quasi-concave, homogeneous of degree on in X and L, and satisfies Imada
condition. The marginal productivities of X and L are decreasing and both of thefactors of production are indispensable.

Denodng by w, r and c(w, r) the wage rate per workmg hour, the rental rate per
rendng hour and the unit-cost function of the consumption good corresponding to(5), each firm maximizes, for given w and r, its profit

(5)

M

SHIMOMURAKAZUOTE (1-c(w, r))y (6)where y is the output of the firm and the price of the commodity serves asnumerare.

A.5 Workers can form a labour union which appears as a monopolist in labour

market. The union sets the minimum wage rate, say wm, leaving competitive
firms to determine the volume of output and, therefore, the volume of employment.

The wage rate w, which possibly ditiers from w., is determined through market
mechanism. Suppose that as a result of choosing a certain wm the labour union

obtains a pair of the wage rate and the volume of employment (w, L) where
L=<N. As stated at the previous section, the union offers a scheme of theredistribution'of wage income and workmg hollrs, (c.(T), 1(T)), O S- T--< N, randomiy

to ak union members in such a way as to maximize the expected utility of eachmember. That is, the mion seeks to maximize

UE ,m.op, kf,"u (cw(7)• i-i(T) d7 (nsub to wL -fXcw(r)dTlOfl]I I(.)d. - L l O

w, L, N given and L 5 N
Associated with (D is the Lagrangean

J - -Sl- u(c.(7), 1 - 1(T)) - X,c.(T) + XII(7)and the necessary conditions for optimakty are

OJ1oc.(.) = iC- Uc(Cw(7),1-1(7)) - x, .. oOJ 1oi(.) = '' iG- Uh (Cw(7), 1-1(T)) + Xi = oA SIMPLE UNION-RIDDEN GENERAL EQUILIBRIUM MODEL 55

xcio, xc' [wL-fNc.(7)dT] =o (s)Joxl l o, xl • [fNI(.)d. ... L] = olo
and Xc and Xl are independent of T.1) One may easily verifY from (8) that the
optimal solution to (" iswL

L

cw(r) = N and l(7)= -N- for any TE[O, N] (9)Substituting (9) to (", we see

U= u(wl, 1-1) (10)It may be natural to assume that (10) is the objective function of the labour
union.

A.6 If workers can forrn a labour union, there may be no reason to assume awaythat capitalists can form a union, say capitalists' club. By a parallel argument to
A.5, we can obtain the objective function of the capital union as follows.

V= v(r6) (11)X
where 6 = - i(-, which may be cabed the rate of capital utilization.

A.7 Workers and capitalists decide to unionize themselves respectively, only if it isto their interest to do so. Thus, the unionization of workers takes,place, only if U

is greater than the level of utility which may be obtained by each worker ifworkers give up forming a labour union and behave as price takers in labour
market.

3. A Pre liminary

AnalysisFirst of all, let us

consider pre-union equilibria. The convex curve AEA' in

Figure 1 depicts 1= c(r, w), which is supposed to hold through market

mechanism. The point E represents a pre-union equdibrium, i.e., (r* , w*) satisfies
1) See Long and Vousden (lg77, p.

ts).

56 KAZUO SHIMOMURA

1= c(w, r) (rz)and the factor market clearing condition

Nl(.). cw(w, r) (B)

K

Cr(w,
r)

Oc(w,
where 1(w) i arg max {u(wl, 1--1) sub. to 1--1l O},r)c.(w, r) ='ow

and c,(w, r) =---a c(w, r). In what follows it is assumed that the function 1(w) canar
be defined for any w>O and that 1'(w) fE d 1(w) is always pbsitive. It follows

dwthat for any w>O we harre

wuc(wl(w), 1-1(w)) - uh(wl(w), 1•-1(w)) =O (14)andu,(wi(w), 1-1(w)) + 1(w) {wu ,,(wl(w), (15)1-l(w)) -uh,(wl(w), 1-1(w))}>O
The latter inequakty is established if, for example, u(cw, h) is homogeneous ofdegree one in c. and h. As is well known, (B) at (w*, r*) is equal to the slopeof BEB'.

r

A

B

x

x

Nx
NL N

NE

r-

l
'
1
'
1
s

o

N

x

N

N

N

* B'

W

Figure 1 factor price flontier

A'w

EQUILIBRIUM MODEL
A SIMPLEUNION-RIDDEN
GENERAL
For the corrvenience of later argument, let us obtain a sort of the supply curveof the output. From (12) r can be regarded as a decreasing and corrvex functionof w. Let us denote it by n (w). Then the imctions of w

K

YK(W) iii
Cr(W, n(W))and

YN(w) si Nl(w)cw(w, n(w))

ercpress the volumes of the output for given w in the case that the volumes of capitaland labour become fuidng respectively. Since

EltlT YK(W) = - EiTt (CrCrw - CwCrr) < O
andtiltT YN(w) = El:T, {1'cwcr '- 1'(crcww - cwcwr)}> o, the graphs of YK(w) and YN(w) are like in Figure 2, which tells that for w < w*
labour is findmg while for w > w* capital is finding. Therefore, the kinky curve AEB

expresses the supply curve of the output and if w is smaber (resp. greater) than w*
then r declines (resp. rises) and w rises (resp. declmes) undi w coincides with w*.

Yn

Yk
1

l
l

t

E

1

1

l

l

l

1

l-.-

A

1
l
l
1

1
1

1

'
t
1

,
,
l
'
t

`t

1
1
1

w4
Figure2

supply curve AE B

B

W

57

58 KAZUO SHIMOMURA
4. Deriving the Reaction "functions"
At this section we shad derive the reaction "functions",-w(r.) iiE arg maxUfor given rm (16)
Wrn

!(w.)
ii arg maxVfor given w. (17)rm
The double quotation marks are used above because w(rm) and !(wm) are, as wil1
be sh(wn, correspondences for some rm and w., respectively.
The derivation of -w(rm)First, Suppose that r. is set r*. if w. is set above di(r.) where Åë !s n-i, thenfor any (r, w) l (rm, w.) 1 < c (r, w), which implies that no firm produces theoutput. Therofore U = u(O, 1). ff w. is set below Åë(rm), then (r, w) becomes equalto (rm, Åë(rm)). For, at any other point oti QR in Figure 3A r must declme to r.,
since on QR labour is tindng, as vvas shown at the previous section. Therefore, forarry wm E Åë(rm)'Ulas) i:i u(di(rm)1(Åë(r.)),1--l(Åë(r.))) (rs)See Figure 3B, which depicts the graph of U for r. > r*. From this figure it may

be clean that when rm => r*-w(r.) = {wmlO -<- wm s-Åë(rm)} (te)
r

1
t
1

U

Q

UI(ls)11'''

u(O.1)

l
,
t
l
1

:
:

R

rm

-FT

r-

- -"t

t
,

--,

1
,
l 1
l
l t,
t 1
l
wmÅë(rm)w-l lo

Mgure 3A

y<w)

w
nm)n'

--tt

Wm

aS (rm)Figure 3B

A SIMPLE UNION-RIDDEN GENERAL EQUILIBRIUM MODEL 59
Second, let us examine the case in which rm is set below r*. Before startjng
our rnain analysis on this case, let us consider the function of w
O(w) =' u( W,C,\;;l!I7(LllllN)K , 1 - ,C,W((.W,',"((.W)))KN ), which is equivalent toti(w)=u( WLN(W) ,i- LkW)) (2o)aOLwhere L(w) is the solution to the equation w = FL(L, K) = -F(L, K). In what
follows, we assume that (20) has a positive, unique and global maximum solution,
say W, and that there exists no local maximum solution. These conditions are certainly
satisfied if, for example, both the utility imction and the unit-cost function are of

Cobb-Douglas type. Dfferentiating (20) with w, we seeO'(w) fE -d!3iti)\)- = -!`i}!il!N u, + -!`-liS!i)- (ucw-uh) (2i)

Therefore, from a4) O'(w*)= L(W N') u,( WLkW*) ,1- L(WN"))>o,

which implies that w* < SXr . Figure 4 is a possible graph of U(w), where wO is thesolution to N= L(w). '
-.

u(w)

u(O.1)

---

--

--t1

ow

Wo

W*

Figure4 the graph ob ti(w)

1,

-v

W

- --

KAZUO SHIMOMURA

60

Now let us return our main business. Suppose that rm is set between r* and n("Cr).

li wm is set above di(rm), then for any (r, w) l (rm, wm)1 < c(r, w), which implies
that U = u(O, 1). If wm is set between w* and di (rm) , then w must decline to wm along

the locus of n(w), since capital is findmg for w>w*. Then U = U(w.).
li wm is set be1(rw w*,then the area{(w, r)/(w, r) l (w., rm)} contains (w*,r*).

Therefore (w, r) must be equal to (w*, r*), and U = U(w*) for any wm ! w*.
We now obtain Figure 5B, from which it may be clear that when r* > rmln("Cr)w(rm) = di(rm)

(22)

r

U
,

1
t

1
1
t

r*

1

t

rrn
ij (W)

1

U(di)

----L
lt -

ltl

tt

..--1-4ll t
lt 1
1lll•11--- -- --e-

t
1
l

n(w)

lll.-:Nt I Nxi i Nu(w)

ll
t

t

e

,

1

,

w"di (r.)ww

w 'di (r. ) w

l l•

Figure 5A r' >rm l ij (W)Fibure 5B

What remains is the case in which rm is

set below n(W). By making a simlar

argument to above, we can obtain the graphof U as in Figure 6, from which we

see that when n(W) > rm

U

el
11
ltt ll

tl 11
tl
l' lt

ii l {so(.).---.L---F--1
l llll1w* ll W di (rm>Figure 6

n (S)V) > r.

Wm

Wm

A SIMPLE UNION-RIDDEN GENERAL EQUILIBRIUM MODEL61-w(r.) = W(23)

Talcing (te), (22) and (23) together,.we obtain thegraph of w(rm) as depicted

l r*

in Figure 7. Note that .w(rm) is a correspondence for rm. Moreover, we caneasily verify that

rm

r*
1
1
'

1
'

NN N

NNN ij(W),w" W Wm

N

Figure7 Yg(r.)(rm, di(r.)) for r. ). n(riXr)(r, w) ={(n(W), "r) for r.< n(W)} (24)The derivation of -r (w.)
A similar argument to what we have rnade brings Figures 8A and 8B. The diiference

between these figures comes ffom whether the counterpart of U(w),V(r) i rCr(th(r), r)Nl(di(r))

cw(di(r), r),hasapeak at some r, say f, which is greater thanr*. For example, if the rate of factor
substitution is not smaker than one, then V(r) is decreasing. When V(r) is decreasing,

we have, from Figure 8A,

62

KAZUO SHIMOMURA

rmt ny (m)
1

N
N

N

N

N
N

N

x

N
x

r*

W*
Figure 8A

Wm
V(r)is decreasing{rmiOE rm S- n(wm)} for rm>r*-r (wm) = (

r*

(25)

for rm S- r*

rmi a(w)

1

N
N
N
N
N
f
r*

W*

Wm

Figure 8B V (r) has a peakMoreover we can easily see that(r,w)-I((,".(W,m.)i)Wm)ff,O,'.W.m.i.W,"(26)

A SIMPLE UNION-RIDDEN GENERAL EQUILIBRIUM MODEL

63

5. Unionridden Equilibria
Now take a look at Figure 9 which is obtained by putting Figures 7 and8 together.

Inspecting Figure 9, we find the following things.

rm

A

y(w)

F

7

r*

E

C

l
t 11t

l 111111 Illllt itlll
1 IIIII
1 111IlB,
tll
lltlll A'
Disititiiew" diV ij (w)Figure 9 union-ridden equilibria(i) The Nash noncooperative equdibria exist infinitely. For example, in the casewhere the graph of -r (w.) is like Figure 8A, any point on CEBD represents a Nashequdibrium. However, (r, w) to be reakzed through market mechanism is common
among (r., wm) expressed by the points on CE and BD, respectively: If (r., w.)
is on CE (resp. BD), then (r, w) = (r*,w") (resp. (n(W), W)). Thus, if (rm, wm)
is on CE, unionization does not bring any substantial profit to either capitalists

or workers.
(li) The points on BD represent the Stackelberg equilibria with the labour union
acdng as the leader. As we discussed at the previous section, the equihbrium wage
rate Sir is determined by the following system of equations.

Q Ei [FL(x, 1) + xFLL(x, 1)] Uc(-!S xFL(x, 1),1--!S x) (27)NN

-Uh (-!S xFL(x, 1), 1-l!g x) = o

NN

W- FL (x, 1) (28)64 KAZUO SHIMOMURA
where x !E ! = IN . Dfferentiating (27) with x and K/N, we

KKSee( OoQx )d. + xN.llih (u.FL-uch)- (uh,FL-uhh)} d(KIN) = O

OQ
Ox

where) (is negative. Therefore,dx x Uhd(K/N) = - (OaQx ){ u, (UocFL -" UCh) -- (UhcFL 'uhh)} < o

It follows from (28) that the increase in K/N lowers W: We obtain the following
statements:

Capital accumulation andlor decrease in membership lower the working hours
per unit of capital and the vvage rate, and raise the rental rate. Capitalists are
better-off, while workers worse-off.

The last statement may need a proof. Considering (27), we see

du Ou dx

d(K/N) = a(K/N) = X'[UcFL-Uh] d(K/N)=-x2FLv dX <od(K/N)

6. A Pareto-optimum Locus
In this section we shak obtain a Pareto-optimum locus on the (r, w)-plane. Consider

the maximum problem,

max U = u (wl, 1-1)

Sub to F(IN, 6K) l wlN + r6K
v(r6) )- V

1-llO llO
1 -- 640 610
V given

A SIMPLE UNION-RIDDEN GENERAL EQUILIBRIUM MODEL65

It may be intutively olwious that 6 is equal to 1. Resorting to the theorem on Kuhn-Tucker

conditions2), we have the system of equations

F(IN, K) = wlN + rKu, (wl, 1--1)FL (IN, K) = uh (wl, 1-I) (28)v(r) = V, which determines 1, w and r.
Recak (14). We can easily verifY that the pre-union equilibrium point satisfies (28)

if r = r*. Now, differentiating (28) with 1, w, r and V, we haveddr. =- IKN [+ o[,FL-W] [UccFL-uhc] ] (2g)
'Ziti'i2 u(wl, 1 -1)+NucFLL
Since FL- w = O at the pre-union equilibrium point, we seed, IN c. dr (30)dw (2g) K cr dw l=c(w, r)

at the pre-union equilibrium. Moreover, differentiadng (30) with w and initiaby evaluating

it at the pre-union equmabrium,dl

dd.2,r (2g)- dd.2r, i.,(.,,)-(- iKN) [NFLL[doow;:-l] iil:ciFFiL']"hc] (3i)

, whereo2u
2 + NFLL [Uc+1{uccFL'Uhc }]dlNFLL• -1--al>o+ ucNFLL
OI2

dw o2uFor, from (15), uc + 1 (uccFL --uhc) > O. Hence, (31) must be negative. We now obtaina Pareto-optimum locus PEP"P' as is depicted in Figure 10. Moving toward the point
P' along the Pareto-optimum locus, V declmes and U rises.

2) See, for exarnple, intriligator (1981, pp. 66-69).

KAZUO SHIMOMURA

66

rrn

A
P

r-

C Ei t P"
tlII
11
1

1

l

B
A'

,

w' wp W Wm

P'

D

Figure 10 several types of union-ridden equilibria

AEA' : 1=c(w,r)
PEP"P' : thepareto-optimumlocus

E : thepre-unionequibigium
BD : the Stackelberg eguilibia with the leboun
union acting as the leader
CE : the Stackelbeng equilibia with the capitalists'club acting as the leader

CEBD : theNashincouperativeequilibia
EP" : the candidetes for the Nash cooperative

epuilibia
Figure 10 is the final product in this paper, where several types of union-ridden

equlibriu as well as the pre-union equilibrium are shown together. Note that only

a ponion of the Pareto-optimum locus, P"E, represents the condidates for thecooperative equilibria: Arry point on either portion of the locus, PE or P"P', cannot
be a cooperative equdibrium. For, at any point on PE (resp. P"P') except E (resp. P")
capitalists (resp. workers) wouid give up forming a capital (resp. Iabour) union.

7. A Concludin g Remark
How can we single out a cooperative equilibrium point on EP" in Figure 10? Following

the literature on cooperative game, one can apply a Cobb-Douglas function definedover pay-off space and obtain the cooperative equilibrium point as the maximizerof the function on the pay-off frontier like PEP"P' in Figure 10: The constant elasticitiesof the function represent the degree of the differentials in bargaining skills between

A SIMPLE UNION-RIDDEN GENERAL EQUILIBRIUM MODEL67

two players. See, for example, Ohyama (te90). Using his terrn, the greater the measure3)-g!tL!}grgaj!llng"sbof thekilllabour union (resp. the capitalists' club) relative to that of thecapitalisbs' club (resp. Iabour union) the closer to the point P" (resp. E) in Figure 10
the Nash cooperative equilibrium is. In fact, if the measure of bargaining ski11 of thelabour union (resp. the capitalists' club) is sufuciently great, capitalists (resp. workers)

give up unionizing themselves and the Stackelberg equilibrium with the labour union(resp. the capitalists' club) acdng as the leader is established: The difference in bargaining

power between the two groups determines whether our model is the monopoly4)the pre-union model.
model, the ethcient bargain model orReferences
P] Farber, H. S. (te86) ``The Analysis of Union Behavior:' in: O. Ashenfelter and R. Layard, eds.,
Handbook of Labor Economics, Vol. II, North-Holland.
[2] Intriligator, M. D. (te81) ``Mathematical Programming with Applications to Economics," in: K. J. Arrow
and M. D. Intriligator, eds., Handbook of Mathematr'cal Economi'cs, Vol. I, Nomh-Holland.

[3] Kemp, M. C., N. V. Long and K. Shimomum (1990) Labour Unions and the Theory oflnternational Trade,Nonh-Holland.
[4] Long, N. V. and N. Vousden (lg77) ``Optirnal Control Theorems," in: J. D. Htcnford and S. J. Turnovsky,eds., Appfications of Control Theory to Econonp'c Analysis, North-Holland.
[5] Mc Donald, I. M. and R. M. Solow a981) ""lage Bargaining and Ernplcyrnent," American liconomic Review,Vol. n. 896-908.
[6] Ohyama, M. (1990) "Bargaining with Dfierential Skills," Keio University.

[n Oswald, A. J (D82) "The Microeconomic Theory of the Trade Union;' Economic Jounial, Vol. 92,

576-596.
[8] Oswald, A. J. (1985) "The Economic Theory of Trade Unions: An Introductory Survey," Scandinavian

Joumal ofEconomics, Vol. g7, 160-N3.

[9] Pencavel, J. (D85) "Wage and Employment under Trade Unionizm: Microeconomic Models andMacroeconomic applications," Scanclinavian Journal of Economics, Vol. 87, 197-225.

[10] Sampson, A. A. (re83) "Emplqyment Policy in a Model with a Rational Trade Union," EbonomicJouinal,Vol. 93, 2on-3ll.

3) Ohyarna a990, p. 3).
4) The first two terms are from Oswald (D85, p. 166).

INDUSTRIAL POLICY UNDER INTERNATIONAL OLIGOPOLY
Kenji KoilMA

Abstract
This paper considers the industrial policy such as product development subsidy ininternational oligopolistic market. A three-stage game in which the government is
the first mover to influence equdibrium outcomes of oligopolistic firms is constructed.

It is found that subsidization of the government cruciaky depends on the slopes ofreaction curves in outputs and product development. It is also shown that the
government with the multinational firm could bring the asymmetric equjlibrium outcomes.

1. Introduction
Governments in a number of countries subsidize research and development activitiesof their domestic firms which are in competition with other countries' firrns ininternational markets.i) This paper presents a theory to explain industrial policies in

the international oligopolistic market where the product development rivalry between
firms plays an important role.

We focus on subsidization of product development such as, for example, Japaneseand the U.S.A. subsidization of semiconductors. Product development is assumed to
be undertaken before the output is produced, with firms anticipating the effect of productdevelopment on their demands. The government is assumed to cormnit credibly itself
to product development subsidies before the product development decisions are madeby the oligopolistic firms. The govemment becomes the first mover in multi-stage gameand can infiuence the equthbrium outcome of the game played by private firms bychanging the set of credible actions taken by them.
The model of firm behavior is based on a two-stage game played by two competingfirms, one is multinational firm, the other domestic firm. The multinational firm produces

for two national markets. They are assumed to be registered in durerent countries.
In the first stage tirms choose product development levels, and in the second stage,
output levels. The second stage equilibrium is a Nash equilibrium in outputs, taking
1) Trade and industrial policy under oligopoly has recentiy studied by the followings; Dixit (1984), Eaton

and Grossman (1986), Spencer and Brander (1983), and others.

70 KENJI KOJIMA
product development levels as given by the preceding stage. This gives rise to a subgame

perfect equilibrium in the two-stage game.

This two-stage game is extended in the following ways. The both governments
are adowed to simultaneously set such product development subsidies. In the extended

game, we examine the subgame perfect equilibrium.
The main results are as follows. The government with multinational firm willsubsidize if increase in other firm's output iowers the marghal profitabdity of its own

country's firm. On the other hand, the government with domestic firm wil1 subsidize
if increase in other firm's output raises the marginal profitabihty of its own country's

firm. Thus subsidization of the govemment cruciaily depends on the slopes of reaction

curves in outputs and product development. The government with the multinationalfirm could bring the asymmetric equMbrium outcomes.
Section 2 contains the model, the government is introduce and the main results
are developed in Section 3, and Section 4 contains the concludmg remarks.

2. The Model
We begin by analyzing the last stage in the firms' rivary. Each firmiproduces
output yi at variable cost ci, which includes ad cost except product development

and earns revenue Ri. The product development level of firm i is denoted xi andcosts ri per unit. A subsidy per unit of product development is denoted si. It is
assumed that each variable belongs to the real line and Ri and ci are twice continuously differentiable in their arguements. Profit of multinational iirm m and domestic

tirm d are then7rM (yMi, yrn2, yd; xrn, si) = RMi (yMi ;xM) +(1.a)

RM2 (yM2, yd ; xM)-crn (yrni, yM2) -- (rM-si) xM,'
7rd (yM2, yd; xd, s2) = Rd2 (yM2, yd; xd)-cd (yd) -- (rd-s2) xd, (1.b)
where the subscript denotes the market j=1, 2.
Each profit imction is also assumed to be strictly concave in its arguements everywhere.

Outputs yM2 and yd are substitutes. Using subscripts to denote derivatives,
this implies

7rM3<O, Tdl<O. (2)The effect of an increase in product development level is to induce Ri given yi, andthe rate of increase declines as xi increases:

INDUSTRIALPOLICY UNDER INTERNATIONAL OLIGOPOLY n

Rix>O; R'xx<O• (3)The Nash equMbrium in output is characterized by tirst order conditions

7rMi = ORMI /OyMl -- OcM/ayMl = O, (4.a)

TM, =ORM2 10yM2 -OcMIOyM, = o, (4.b)

Td, == ORd2/ayd-ocdlOyd=o, (4.c)
and second order conditions

Tmll = o2RMIIayMlayMl --o2cm/oyrnloyml < o, (5.a)

irM22 = 02RM2/OyM20yM2-02cMIOyM20ym2 < O, (5.b)

Td22 == 02Rd210ydoyd-o2cd/oydayd < O. (s.c)
We also assume that own effects of output on marginal profit dominate cross effects,
giving rise to following condition:

A= 7rMii7rd22-TMBTdrz>O, (6.a)
B= 7rM22 7rd22 -TM23Tdrz > O, (6.b)
C == 7rMll 7r M22-TM21 7r M12 > O, (6.c)
D = 7rMn(7rM22Td22-TM237rd2i)-TM2i(TMi2Td22-TMB7rd2i) < O. (6.d)
These conditions ensure uniqueness and locaky strict stabmaty of equdibrium.

The solutions yMi yM2", and yd' to (4) depend on xM, xd and can be written as

yMi" = qMi(xM, xd); yM2" = qM2(xM, xd); yd* = qd(xm, xd). (7)The reaction functions GM j(yd), Gd(yM2),j = 1, 2 is characterized:

7rMi (GMi (yd), yd)=O, (8.a)
7rM2 (GM2 (yd), yd)=O, (8.b)
Td, (Gd (ym,), ym,)=O. (8.c)

72 KEr,UI KOJIMAThe slope is obtained by differentiadng (8):Grni'(yd) =-7rMi3 (GMi(yd), yd)/7rMn (GMi(yd), yd), (9.a)
GM2'(yd) =-TM23 (GM2 (yd), yd)/TM22 (GM2 (yd), yd), (g,b)
Gd'(yrn2) : -Tdi2 (Gd (yrn2), yrn2)/Td22 (Gd (ym2), ym2). (9.c)
We thus have sign (GMi') == sign (TMi3); sign (GM2') = sign(7rM23); sign (Gd') ==sign (Tdi2).

The reaction curve is upward sloping if TMi3; TM23; Tdi2 > O and downward
sloping if TMi3; TM23; Tdi2 < O. Fo"owing Bulow, Geanakoplos,i and Klemperer(1985), we will also consider the output of the two firrns to be strategic complements if

TM13; lrrn23; Td12 > O and strategic substitutes if TM13; TM23; Td12 < O.
We totady differentiate the first order conditions:

7rMn TM12 TM13 dYrn1 TM14 dXM

TM21 7rrn22 TM23 dYM2 =- Trn24 dxM (10)O Td21 Td22 dyd Td23 dxd
We assume that there are joint economies across markets, that is TMi2 > O
and demands in the two markets are unrelated, that is TMi3 = O. Condition (3)implies that TMi4; TM24; Td23 > O. Then we obtain thatdyMi/dxM = { -TMi4 B+TM24 TMi2 7rd22-Td23 TMi2 Trn23 dxdldxM}/D > O

if sign (7rM23) = sign (dxd/dxrn), (11.a)dyM21dxM = {(-7rMn TM24+TMi4 7rM2i) 7rd22--TM23 7rd23 dxd/dxM}/D > O

if sign (TM23) = sign (dxd/clxM), (11.b)
dyd/dxM = {-C7rd23 dxd/dxrn+(7rMnTM24-TMi4 TM2i) Td2i}/D > O
if sign (Td2i) = sign (dxd/dxm) > o,dyd/dxM < O

if sign (Td2i) = sign (dxd/dxM) < O, (11.c)dyMi/dxd = {-(7rMi4 B-7rM24 7rMi2 rd22) dxM/dxd-Td23 TMi2 TM23}/D > O
if Sign (TM23) = sign (dxrnldxd) > o,dyM,/dxd < O

if sign (rM23) = sign (dxM/dxd) < O, (11.d)

INDUSTRIALPOLICYUNDER,INTERNATIONAL
OLIGOPOLY
dyM2/dxd = {-(7rMn 7rM24-TM21 TMi4)Td22 dxM/dxd+TMn TM23 Td23}1D>O
if Sign (7rM23) == sign (dxM/dxd) > o,dyM,ldxd < O

if sign (7rM23) = sign (dxMldxd)<O, (11.e)dyd/dxd = ( -- Td23 + (TMn TM24 "-'TM2i 7rMi4)Td2i dxM2i dxd}ID>O

if sign (Td2i) = sign (dxMldxd)• (11.f)
The comparative static results show that a firm's equlibrium level of output is increasing

in own product development level if the $lopes of reaction curves of the productdevelopment and outputs are the same. It is decreasing in the other firm's productdevelopment if the slopes of reaction curves of the product development and outputs
are downward sloping, that is, strategic substitutes and increasing if they are strategic

complements.
We now proceed to the first stage, in which firms choose prodqct development levels.

Firms are aware of the dependence of output on product development levels. Thus,
profit can be written as functions of xM, xd, (bi represent the profit function for firm i.

diM (xM, xd;sl) - TM (qMl (xM, xd), qM2 (xM, xd),

qd (xm, xd);xM, si)(rz.a)

Åëd (xM, xd;s2) ii! 7rd (qM2 (xM, xd), qd (xM, xd);xd, s2) (12.b)
The Nash equMbrium in product development levels is characterized by the first orderconditions for each firm using (1), (4), (12).

ÅëM, = aRM,/aqd'Oqd/OxM-(rM-si) = O, (B.a)Åëd2 = ORd2/OqM2'aqM210xd-(rd-s2) = O, (B.b)
and second order conditions

ÅëMn<O, (14.a)
did,,<O. (14.b)
We also assume the condition

E= dimn Åëd22-(bM. did2i > O. (us)rs

74 KENJI KO"MA
The reaction functions Hrn (xd), Hd (xrn) is characterized:(t)m, (HM (xd), xd)=O, (16.a)
did, (Hd (xM), xM)=O. (16.b)
The slope is obtained by differentiating (16):

Hm' (xd) =-ÅëMre1diMii, (17.a)Hd' (xM) =-did,,/did,,. (17.b)
We thus have sign (HM') = sign (q5Mrz);sign (Hd') = sign (Åëd2i).
The reaction curve is upward sloping if ÅëMra > O ; did2, > O and downward sloping if

diMtz ; did2i < O. We will also consider product development level of the two firms

to be strategic complements if ipMrz > O; ipd2i > O and strategic substitutes if
Åëm. < o ; Åëd2, < O.
We totally differentiate the first order conditions:[$M,,1i $M,,][gi,M]-[:g!,i] E,lgg',
diMii, Åëd22 < O is implied by condition (3). Then we obtain thatdxMlds, >O if sign (ds2/dsi) = sign (diMi2), (ro•a)
dxd/ds, > O if sign (ds2/dsi) = sign (Åëd2i) > O,

dxd/ds, <O if sign (ds21ds,) = sign (thd2i) < O, (te.b)dxM/ds, > O if sign (ds2/dsi) = sign (ÅëMi2) > O,dxM/ds, < O if sign (ds21dsi) = sign ((bMi2) < O, (te•C)

dxd/ds2 >Oif sign (ds,/ds,) = sign (Åëd,,). (19.d)
This results show that a firrn's equdibrium level of product development levelis increasing in the subsidy of its own national government if the slope ofreaction curves of subsidy and product development are the same. It is increasingin the other country's subsidy if the slopes of those reaction curves are upward sloping,that is, strategic complements and decreasing if they are strategic substltutes.

INDUSTRIAL POLICY UNDER INTERNATIONAL OLIGOPOLY 75
3. Industrial Policy
We characterize the subsidies that would maximize the national welfare. The optimal
subsidy is found by maximizing net national welfatre Wi, which is consumer surplus Ui

and the profit of the firrn less the cost of the subsidy. W' and and U' are assumed
to be twice continuous!y dfierentiable in their arguements and stricly concave in its
arguements everywhere. Each country subsidizes product development of its registeredfirm independently given the subsidy imposed by the other. The national welfare ofeach country is

Wi (si, s2) = {Ui (yMi)-RMi}+7rM-sixM, (20.a)W2 (s,, s,) = {U2 (y2)-RM,- Rd,}+Td-s, xd, (2o.b)'
where U'(yMi)=fYMi p'' (u)du;dU'/dyMi=pi(yMi);U2 (y2)=fY2 p2(v)dv,
where y, = yM , + yd ; dU2/dy2 = P2 (y,)

ooearned by each country when both subsidize product development.

We assume that demand curves are downward sloping, that is, pi'(yMi) < O;
Pi2 (y,) < O.
The Nash equdibrium gives rise to where the first order conditions

W'i (si, s2) == O, (21.a)W2, (s,, s,)=O. (21.b)

Optimal subsidy is

Sl >O
if sign (7rd2i) = sign (TM23) = sign (dxM/dxd) < O, (22.a)
S2 > O,if sign (Td2i)= sign (dxrn/dxd)>02). (22.b)
Positive subsidies of country 1 are called for if both output and product develop-

ment level are strategic substitutes. On the other hand, country 2 is required tosubsidize if they are strategic complements,
The comparative static results of the two-stage game played by the competing firrns

and the optimal subsidy imply how the subsidy of the government influences
the equilibrium outcome of the game. The increase of subsidy provided by thegovernment with the multinational firm increases product development level of its own,
2) The detail proof is available from the author.

76 KENJI KonMA
and reduces that of the domestic firm. If the product development of the multinationalfirrn raises, the output of its own increases and that of the other decreases. If the

product development level of the domestic fum lowers, the output of the otherincreases and that of its own decreases. The optmal product development subsidyof the government with the multinational firm maximizes its national welfare by
influencing its own firm to gain more market share. On the other hand, the increaseof subsidy by the govemment with the domestic firm increases product developmentlevel of both firms. If the product development of both firms raises, the output of

the both increases. The optimal product development subsidy of the government
with the domestic firm maximizes its national weifare by bringing neutra1 effect tothe both firms.

4. Concluding remarks
Governments play an important role in certain international industries. Such industries

consist of a few firms which are irrvolved in a strategic game. This paper considers
the optimal industrial policy maximizing the national weifare under the international

oligopolistic setting. We have found that subsidization of the govemment cruciaky

depends on the slopes of reaction curves in outputs and product development.
The optimal product development subsidy of the government with the multinationalfirrn maxirnizes its national welfare by influencing its own firm to gain more market share.

On the other hand, the optimal product development subsidy of the government withthe domestic firrn brings neutral effect to the both firms.

References[1] Bulow, J.I., J.D. Geanakoplos, P.D. Klernperer, (985), "Multimarket Oligopoly: Strategic Substitutes

and Complements," Joutnal of Political Econonry, 93, 488-511.
[2] Dndt, A,, (1984) "lnternational Trade Policy for Oligopolistic Industries," Etonomic Joumal, supplement,

94, 1-16.
[3] Eaton, J. and G.M. Grossman, (1986), "Optimal Trade and Industrial Policy Under Oligopoly;'
Quarterly Journal of Economi'cs, 101, 383-406.

[4] Spencer, BJ. and J.A. Brander, (te83), "International R & D Mvaly and Industrial Strategy,"
Review of Economic Studies, 50, 7or-M2.

REALTIME DISTRIBUTED CONTROL OF WORLD LINK MODELSIN THE INTERNATIONAL COMPUTER NETWORKS
Ko MrvAzAKI

1. Introductions
In recent years, the technology of international data communications has madea remarkable progress, so that we can now make computer-to-computer cals at
anytime from any p!ace in the worid. This trend has been accelerated further by thefact that powerfu1 portable personal computers have come into wider use as

intehigent terminals. •For example, Toshiba's laptop personal computer, J-3100SGT/101 weighng only

6.8 kilograms, is a 32-bits MPU (intel 80386/20MHz) machine with co-processor (intel

80387120MHz), 4MB RAM and 100MB hard disk. This laptop computer has provento be capable of solving and simulating large-scale econometric models. More impor-tant, this very portablity of laptops makes it possible to carry out econometricmodel simulations in the audience's presence at a conference held in any country.
It might be no wonder that just one laptop may not be able to solve such a hugeeconometric model as the PROJECT-LINK Modeli) with 70 countries involved, but
a combination of two or more laptops together could make it well. This can be donein reality by building a kmd of parallel processing system on a local area network(LAN) of laptops. In addition, if international data communication functions areequipped with in this system, econometricians can get the most up-to-date models ordata easily and directly from various econometric database centers around the world.
With this system, realtime model simulation could be realized at any place at any

time-at the conference room of ``PROJECT-LINK'', ``G7" or "Summit'', forexample. The aim of this paper2) is to present the concept of a realtime econometricmodel simulation system3).

1) This is the world link model consisting of more than 20,Ooo equations developed by Professor Lawrence

R.Klein.
2) I would 1ike to thank Professor Hiroshi Sadamichi (Kobe University), Professor Ippei Sugiura (Osaka

Sangyo University), Professor Hikoji Katano (Kobe University), Professor Tetsuji Shimojo (Konan
University) and Professor YZisuo Nunokami (Konan University) for helpfu1 comments and suggestions.
3) This study is fuiancially supported by a grant under the Monbusho International Scientific Research
Program (Project No.63044rs2 headed by Professor Hikoji Katano).

78 KO MIYAZAKI
2. The concept of a ECONET``ECONET" stands for ``ECOnomic model simulation NETwork system.'' It is

an international information network system to enable econometricians to carry out

realtime econometric model simulations on personal computers at ary place in the

The essence of ECONET is as follows:
1) Distributed processing system to solve large-scale econometric models by
combining several laptops together.

2) Econometric database system to provide econometric models and macro
economic data.
3) International data communication system to connect those systems mentioned

above.
The concept of ``ECONET'' js shown in Fjgilre 1.

WEDS
ASIA

DBMS
modelsdata

WEDSAMERICAWEDS EUROPE

DBMS

DBMS
modelsdata(

medelsdata..s=::t.y/-/Figure 1 The concept of "ECONET',REALTIME DISTRIBUTED CONTROL OF WORLD LINK MODELS ro
IN THE INTERNATIONAL COMPUTER NETWORKS

1) Distributed processing system: .
This system is at the core of ECONET. It makes it much easier for econometriciansof each country to control their country's models and data during simulation of theWORLD LINK MODEL, because, unlike the centralized processing where theequations of ak countries are treated as those of one big country, the models of eachcountry are processed in parallel and independentiy of those of the other.
The advantage of this distributed model simulation lies not only on controllabthty

of models but also on costs. Running costs and communication costs are muchcheaper in this distributed processing method on laptops than in the centralized
processing way on a very 1arge scale computer.

2) Econometric database system:
This is a database service system to provide economeuicians with models anddata whenever the need arises. This system should be equipped with a function oftransferring text Mes or binary fles stored in the database directly into the disk
storage of terminals.

It is also desirable that every country or area have a database system centeimg

on econometric models as well as economic data of its own country or area.
3) International data communication system:

This system may be part of the econometric database system mentioned above.
The data stored in the database system should be easily accessible from terminals of

the distributed processing system through telecommunication lines such as public
telephones or public data communication networks.

3. Distributed Link Model Simulation System
The distributed link simulation method was proposed by Professor Ippei Sugiura(Osaka Sangyo University)4) and the system has been developed by him together withProfessors Mamoru Shibayama (Osaka International University) and Yasuo Nunokami(Konan University).

This system was originady designed for the purpose of tnmsplariting the
PROJECT-LINK model simulation programs developed for large-scale computers tomuch less expensive smaller machnes. '4) Ippei Sugiura, Distributed Control of Econometric Data Bases and Models, in Duncan Ironmonger et al.(ed.),National Income and Economic Progress, Macrnillan Press, GBR, te88

KO MrvAZAKI

80

The concept of the Distributed Link Model Simulation System is shown in
Figure 2.

l(llli:1

LAN or(;lWAN
l4iiii)l(lll::ziPersonal Computeror Work-Station
Figure 2 The concept of the Distributed Link Model Simulation Systern
The system is composed of two or more personal computers (or work-stations),

combined with one another to form a LAN (Local Area Network) system. The
distributed link simulation method is to allocate one or more models to each personal

computer and to run the world link model on the LAN of several personal computersin the way of parallel processing. The personal computer assigned the trade matrix
model plays a supervisory role and controls the flow of the simulation process.

4. World Economic Database System This Distributed Link Model Simulation System made up of several personal laptop
computers, easy to take along with, would be able to be brought in the conference
room wherever it may be held, and a world link model simulation could be conductedon the spot.

What would happen if new models or data should be needed for continued
simulation? To prepare against this situation and to provide ak necessary information

whenever needed from overseas or at home econometric database centers should beestablished in major countries in the world. Then, econometricians can access the
database system to obtain models or data from arly place at any time whenever needed.

81
REALTIME DISTRIBUTED CONTROL OF WORLD LINK MODELSIN THE INTERNATIONAL COMPUTER NETWORKS

In other words, any econometric database system should be accessible from any
place in the world through telecommunication lines.

KOBE miversity World Economic Database System (KOBE-WEDS) aims to be oneof such econometric database centers. A network of "KOBE-WEDS" is shown in
Figure 3.

Econometric
Information Canter'telephonenetwork

DBNTT/internationalpublictelephonenetwork

KoUmK

UtvKm

l1E•3

models

'

KDD

data

t

AT&Tetc.

vENUS'PShX

lliltmternationalp"bTelenet,datanetwo(packet switching)

TYMNET etc.
Figure 3

A network of "KOBE-WEDS"

There are three ways to communicate with KOBE-WEDS. Most commonly used
are the public telephone netwdrks for domestic cals and the international public
telephone networks for international long distance cabs. The third way is the international

public data networks for international packet-switchng digital data communications-"Telenet'' provided by GTE and ``TYMNET" by McDonnell Douglas, for example.
A sample of the operational procedure of "KOBE-WEDS" is shown in Figure 4.

KO MrvAZAKI

82- VSlelcome

DATABASE
to KOBE WORI.DECONOMICSYSTEM! ,Menu No.Ooo - KOBE WORLD ECONOMIC DATABASE SYSTEM [KOBE-WEDS] -1 HOW 'IO USE KOBE-WEDS
2 WORLD ECONOMIC DATA & ECONOMETRIC MODELS

3 COMMUNICATION AMONG USERS
4 PROGRAMS & DATA TRANSFER AMONG USERS
5 UTILITIES
6 LOGOUT (qq)

YOU MAY COME BACK 'IO THIS 'IOP MENU ANYTIME BY TYPING `1'.

ENTER CHOICE NUMBER OR COMMAND: 2,

MenuNo.200 - WORLD ECONOMIC DATA & ECONOMETRIC MODELS 1 WRITE A BULLETIN OR SAVE DATAIMODELS IN WEDS

2 READ BULLETINS OR DOWNLOAD DATA!MODELS FROM WEDS
3 DELETE BULLETINS OR DATA/MODELS IN WEDS
4 CHANGE PR(]rlOCOLS (XMODEM, YMODEM OR YMODEM-BAncH)
5 QUIT (q)ENTERCHOICE NUMBER OR COMMAND: 2,- READ BULLETINS OR DOWNLOAD DATA/MODELS FROM WEDS -1. BULLETIN 2. ASIAN LINK MODEL 3.US-CHINA-JAPANMODEL

4. US-JAPAN MODEL 5. 'IOOLS
H: HELP Q: QUITENTER CHOICE NUMBER OR COMMAND: 2,-- ASIAN LINK MODEL -IP
1. KOBE WEDS
2. KOBE WEDS
3. KOBE WEDS
4. KOBE WEDS
5. KOBE WEDS
6. KOBE WEDS
7. KOBE WEDS
8. KOBE WEDS
9. KOBE WEDS

DATE

TITLE

89Al/24
89Al/2489nl/2489nl12489nl124

Asian Link
Trade
Rest Of theThailandSingapore

89M/24

Philippines

89Al12489nl/24

Malaysia
Indonesia

89fll124

Hongkong

10. KOBE WEDS

89nl124

Taiwan11. KOBE WEDS

89/11/24

Korea

tz. KOBE WEDS

B. KOBE WEDS

89Al/24USA

89ll1124

Japan

World

(Model/Data)(Model/Data)(Model/Data)(Model/Data)(Model/Data)(ModellData)(ModellData)(Model/Data)(Model/Data)
anodellData)(Model/Data)(Model/Data)(Model/Data)

H: HELP Q:QUIT

ENTER CHOICE
NUMBER OR
COMMAND:
Figure 4 A sample of the operational procedure of "KOBE-WEDS"83
REALTIME DISTRIBUTED CONTROL OF WORLD LINK MODELSIN THE INTERNATIONAL COMPUTER NETWORKS

5. Realtime Model Simulation System
This is an integrated system combining the Distributed Link Model Simulation
System and the World Economic Database System with the telecommunication systemdescribed earlier. Using this system the user can carry out simulations of world linkmodels, however 1arge they might be, at any place in the world while models and/or

data necessary for simulation are being provided through telecommunication lines

whenever needed.
It is to be noted that this realtime simulation system should have such facthties

in the distributed model simulation system that the old models or data may bereplaced by the new ones downloaded from some database centers easily to continue
the simulation. This is a very important point of the ``realtime'' model simulation.

The concept of the Realtime Model Simulation System is shown in Figure 5.

Econometric
Informatien CenterDBMSte]ecommunication

line

LAN
modelsdata ll(lllilll1(llill7

Å~Figure 5 The concept of the Realtime Model Simulation System

84 KO MrvAZAKI
6. Experiments of Realtime Model Simulation System-- In case of the "Econometric Model of Asian Link" -The ``Econometric Model of Asian link''5) is an econometric link system for 11 areas- Japan, the United States, eight of the East and Southeast Asian countries, andthe rest of the world. This model consists of 550 equations in ab including the trademodels.
The details of equations are listed in Table 1.

Table 1 Econometric Model of Asian Link, Number of Equations

'

Model
Japan
U.S.A.

Korea
TaiwanHongkongIndonesia
Malaysia
Philippines

NumberofEquations
61

33
36
38
46
85
62

Trade

25
49
55
26
34

Total

550

Singapore

Thadand

RestOftheWorld

The procedure fiow of the Realtime Model Simulation is shown in Figure 6.

5) Shinichi Ichimura and Mitsuo Ezaki ed., Economic Models of Asian Link, Springer-verlag, -85. Mitsuo
Ezaki, Mamoru Shibayama and Shinichi Ichimura, An Economic Link System for the East and Southeast
Asian Countries, Japan and the United States, Southeast Asian Studies, Vol.22, No.3, te84.

85
REALTIME DISTRIBUTED CONTROL OF WORLD LINK MODELSIN THE INTERNATIONAL COMPUTER NETWORKS,

Step 1 Connect to Econometric lnformation

Center.

Start the terminal program.
Select a communication network.
af data network was selected,
Login to the network and set communication parameters.)
Login to an Econometric Information Center.
i

Step 2 Download models and/or datafrom Econometric lnformation

Select models and/or data items.

(Change communication parameters, if necessary.)
Send data to the terminal.
Receive data from the center.
s

Step 3 Terminate communication process.
Logout ftom the Econometric Information Center.
(Logout from the network, if necessary.)
Quit the terrninal prograrn.
lStep 4 Decompress the downloaded file.
Decompress the dcrwnloaded fle.
Transfer the data tosimulation

system.

s

Step 5 lnitialize
Initialize

Model Simulation System.

Distributed

Initialize the LAN system.
a machine including trade models

first.

Initialize the other machnes.
•

Start

Step 6 Start

Simulation.

the rnachne withthe tradeStart the othermachnes.

models.

l

Figure 6

The flow of theRealtime Model Simulation

Center.

KO MIYAZAKI

86

Two clifferent experirnents were undertaken. The first experiment was given at

Stanford University on November 3, te88 and the second at East West Centerin Hawaii on January 2, D90.
At Stanford University, we gave a demonstration of the "Distributed Link Model
Simulation System'' (shown at step 5 and step 6 in Figure 6). Three laptop computers(Toshiba's model J-3100SGTI041) were connected by LAN (Simple Corporation's
10-NET) and the link model is divided into 3 groups - Japan, U.S.A. and the others- each of which was assigned to one laptop computer. Then the final test was
simulated for 9 years from 1972 to te80. ln this case, the time needed to simulate

was about 3 minutes6). The experiment system is shown in Figure 7.

TOSHIBATOSHIBATOSHIBAJ•3100SGTI041

J-3100SGTI041

J-3100SGTf041

llllliiili!ZI:iliil]7

Japan

U.S.A.

Other

model

model

modelsLAN (10-NET)

Figure 7 The experiment system at Stanford Universitytion

At East West Center, we

showed an experiment of the

System, The experirnent

system IS shown in Figure 8.

Realtime Model Simula-.

6) The tirne needed to carry out this simulation by using just one laptop computer was about 40 seconds.

87
REALTIME DISTRIBUTED CONTROL OF WORLD LINK MODELSIN THE INTERNATIONAL COMPUTER NETWORKSHITACHI
Work-Station 2050132-ttll
OMRON MODEM-t-

MD24FS5x/-

VENUS-PKDD
TOSHIBATOSHIBATOSHIBA

J-3100SGTIIOI

J-3100SGTIIOI

J-3100SGTIIOI(lllllll)

lillllliil]1(liliil7

AT&T
Telenet

Japan

U.SA

Other

model

model

modelsLAN (10-NET)
Figure 8 The experiment system at East West Center
The order of the demonstration is as follows:
1) Installing the models except Japan in every laptop computer.

2) Downloading a Japan model from KOBE-WEDS into the disk fles of thelaptop computer through a international public telephone network.

3) Simuladng the entire Asian Link Model.

In this case, the time needed to download the Japan model (Me size: 6,656
bytes7)) was about 1 minute, that is to say, about 1 second needed to transfer one

data block (rz8 bytes) in the XMODEM protocol.
We also made the same experiment with success by using ``Telenet'', one of theinternational public data network services.

D This fle

is compressed.

The original fle size is 81,408 bytes.

& BUSINESSREVIEWKOBE ECONOMIC
CONTENTS
NO. 27 (1981)
Accounting Systems of Non-Market Oriented Activities•••••••••••••••••••••••••••••••••••••••••••• Nobtzko Nosse

Current Situations of World Economy andGlobal Adjustment of lndustries••••••••••••••••••••••-••••••••••••••••••••••••••••••••••••••••••••• Hikoji' Katano

Current Cost Accoundng and the Conceptof Specinc Purchasing Power Capital••••••••••••••••••••••••••••••••••••••••••••••••••j•••••••••••• Isao Nakano

An lnput-Output Table for Evaluation of the
Shipping Activities •••••J••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• Tetsufi' Shimojo

The Function of Modern Corporate Financial Reportingin a Mass Democratic Society ••••••••••••••••••••••••+••••••••••••••••••••••••••••••-•••••••••• Hi'detoshi YamaJ'V

NO. 28 (1982)
The Internationabzation of Japanese Commercial Banking-Experiences in the 70's-•••••••••t•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• Masahiro Fujita

Kenichi Ishigakr'
A Synthesis of Simultaneous Equations Estimators•••••••••••••••••••••••••••••••••••••••••••••• Hiroshi Sadami'chi
A Database System of Economic Time Series ••••••••••••••••••••••••••••••••••••••••••••••••••• HirDshi Sadamt'chi

Yasuo Nunokanv'

NO. 29 (1983)
An lnterpretation of Conventional Accounting
Income Information••••••••••••••••••••••••••••••••••••••ny•••••••••••••••••-•••••••••••••-••••••••••••••• Isao Nakano

A Production System for Transport Services••••••••-•-•••••••••••••••••••••••••••••••••••••t••••••• TetstijV Sin'mojo

Some Evidences between Foreign Direct Investments
and Foreign Exchange Rates:
A Preliminary Note••••••••••••••••••••••-•••••••••••••••••••••ny•••••••••••j•••••••••••••••••••••••-• Kazuhiro Igawa

Two Types of Railroad Regulation by Statesin the 19th Century of the U.S.
-Search for the Social Foundation of Modern
Corporate Financial Reporting-••••••••••••••••••••••t••••••••••••••••••••••••••••••••••••••••• Hidetoshi Yarnaji'

NO. 30 (1984)
National Monetary Policy in an International
Capital Market •••••••••••••••••••••••••••-••••••••••••••••••••--••••••••••••••••••••••••••••••••••••••••• Jdirg Niehans

Craft Unions, Wages and Employment•••••••••ny•••••••••••••••••-••••••••••••••••••-••••••••••••••• Murray C. Kemp

On the ApplicabMty and Implementabdity ofthe (Finite) Compensation Principle ••••••••••••ny•••••••••••••-•••••••••••••••••••---••••••••• Murray C. Kemp

Internationalization of Japanese Commercial Banking-The Recent Experience of City Banks-•••••-••••••••••••••••••••••••••••••••••-t-•••••••• Masahiro Fujita

Kazuya Mizushima
Ryoichi Mikr'tani'
Ethciency of the Least Squares Estimators in
Linear Models with Idempotent CovarianceMatrix of the Error Terms ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••-••••••••• Hiroshi Sadami'chi

Diversincation of Large Japanese
Manufacturing Firms••••••••••••••••••••••••••-••••••••••••••••••••••••••-••••••••••••••••••••••••• Hideki Yoshiham

Indexing Policies and Macroeconomic Stabruty in
Brazil: Rational Expectation Model••••••••••••••••••••-•••••••••••••••••••••••••••••••••••••••••• Shoji Nishilifma

A Simple General Equilibrium Model lnvolving
a Maximizing Labour Union•••••••••••••••••••••••••-•••••••••••••••••••••••••••••••••••••••••• Kazuo Shimomura

NO. 31 (1985)
Toward the Nagative Picture Theory of Commercial
Double-entry Bookkeeping and Financial Accounting•••••••••••••••••••••••-•••••••••••••••••••• Isao Nakano
Stabdity of the Demand for Money: Austraban Experiences •••••••••••••••••••••••••••••••••••• Kem'chi Ishigaki'"Emphical Study of Changes in Accounting Policy" in the Case ofJapanese Enterprises •••••••••••••••••••••••••••••••••-••••••••••••••••••••••-••••••••••••••••••••• Hidetoshi Yamaji

An Emphical Study on International Short-Term Capital
Movements in Japan•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••-•••••••••••• Hideki Izawa

NO. 32 (1986)
Import Demand Stmctural Change in the Pacinc
Basin Countries•••••••••••••••-•••••••••••••••••••••••-•••••••••••••••••••••••-••••••••••••••••••••• Seficin' Katayama

Kenichi Ishigakr'
A Synthetic Analysis of Structurakst and Monetarist
Theory of Latin American Inflation••••••••••••••••••-•••••••••ny•••••••••••••••••••••••ny•-•••••••• Shoji Nishi'ima
Stagflation -Causes and Policies- ••••••••••••••••••••••-•-•••••••••••••••••••••••••••••••••••••••••••• Nobuo Okr'shio

A Computable General Equilibrium Model of theJapanese Economy••••••ny••••••••••-••••••-••••••••••-••••••••••--•••••••••••••••••••••••••••••••••••••• Mitsuo Ezakr'

NO. 33 (1988)
Agency Problems and Accounting Cornrnunication •••••••••••••--••••••••••••••••••••••-•••••••••-•••••• Isao Nakano

Strategic Corporate Innovation andJapanese Management•••••••-••••••••••-•••••••••••••••••••••••-••••••••-••-••••••••-•••••••••ny••• Hi'dein' Yoshihara

Financial Deregulation and Financial
Relationships between Japan and Australia••••••-••••••••••••••••••••-•••••••••-•••••••••••••• Kenichi Ishigaki'

Keynes' User Cost and the Theory ofInternational Trade•••••-••••••••••••••••••••••••••••••-••••••••••••t••••••••••••••••••••ny•••••••• Kazuo Shimomura

A Note on International Transmission ofDisturbances and Policy Interdependence
under Flexible Exchange Rates••••••••••-••••••••••••••••••••-•••••••••••••••••••••••••••••••••••••• Hideki Izawa

Monetary Pollcy and Foreign Disturbances

in a Smad Open Economy under Flexible
Exchange Rates and Rational Expectations••••••••••••••••••••••••••••••••••••••••••-••••••••••-• Hideki Izaiva
A Sketch of the Theory of Trade Cycle••-•••••••••••••••••••••••••••••••••-•••••••••••-•••••••••••••• Nobuo Okr'shio

NO. 34 (1989)
Recent lnflation of Land Prices in Metropolitan

Areas of Japan-A Case Study of Regional Accounting-•••••••••••••••-••••••••••••••••••••••••••••••••••-•• Nobuko Nosse

Little Basics and Employeeism

Japanese Management ininternational Perspective •••••-••••••••-••••••••••••••••••••••-•••••••••••---••••••••••••••••••••• Hidekr' Yoshihara

Bank's Loans to Developing Countries:
A Normative Approach•••••••••••••••••••••••••••••••••••••••••••••••••••-••••••••••••••••••••••••• Kazuhiro Igawa

Japan's Trade Diplomacy:
Yesterday, Today, Tomorrow••••-•••••••••••••••••••••--••••••••••••••-•••••••••••••••••-•••••••• Peter Drysdale

A Labour Union in Every Country-A Game-Theoretic Approach- ••••ny•--•••••••••••••••••••••••••••••••••••••••••••••••••••• Kazuo Shimomura

The Costs and Benefits for Finns of
Accounting Information Disclosure ••-•••••••••••••••••••••••••••••••••••••••••••••••••••••••••• Hjdetoshi Yamapt'

Increasing Returns to Scale and Optimal
Investment Policy of the Regulated Firrn•••••••••••••••••••••••••••••••••••-•••••-•••••••••• Setichi Katayama

Fumio Abe
Problems and Method of Economics ••••••••••••••••••••••••`••••••••••••••••••••••••••••••••••••••••••• Nobuo Okishiolndustrial Organization and Intemational Trade-Textile Industries in theWestern Pacific Region- •••••••••••••••••••••••••••••••••••••••••••••••••••••••••-••••••••••••• Katuhiko lkeda

35, 1989
KOBEUNIVERSITYECONOMICREVIEW
Edited by Faculty of Economics,
Kobe University, Kobe, JapanCONTENTS
On the Theories of Determination of
the Real Wage Rate ••••••••••••••••••••••••-••••••••••••-••••••••••••••••••••••••••t•••••••••••••••• Nobao Okishio

Monopoly and the Metamorphoses ofBusiness Cycles•••••-••••••••••••••••••••••••••t-•••••••••••••••••••••••••••••••••••••••••••••••••j Takeslv' NakataniJ

On Cournot-Nash Non-Cooperative Games•••••••••••••••••••••••••it•••••••••-ny••••••••••-••••• Toshitaka Ftrkuharu

On Interbranch Scientific-Technical Complexes:
A New Soviet Scientific-Technical Organization••-•-•••••••••••••••••••••••••••••••••••••••• Masahiko Yoshfii

On a Theory Concerning International
Fiscal Policies••••••••••••••••••••-•••••••••••••t•••••-••••••••••••••••••••-••••••••••••••••••••••••• Kunkazu Tanaka

Einige Bemerkungen zum Paradigma dertheoretischen Wirtschaftspolitik-Vom Standpunkt der universakstischen
Volkswirtschaftslehre aus••••--•••••••••••••••••-••-•••••••ny••••••••••••••••••••••••••••••••••••• Toshiya Nagao••.i,=--,-i•.--•..-.-•.i,g,=e,g,=Å}=••==.s7,s••s,s••s,i,s-••g,ia-f,i-•.t,g.-=-••a-F-•s,s•.-=•.--••s••i,.e••J-==•-=-••s-,s••g•L=-,is=r•.='••i.s,-s,s-F•-i..j-t.S.s,s,S••i-F,sr-s••==•i,s,.s•.-=••in-F•.---,The ANNALS
OF THE SCHOOL OF BUSINESS ADMINISTRATIONKOBE UNIVERSITY No. 34, 1990
Edited by the School of Business Administration,

Kobe University, Kobe, JapanCONTENTS
Organization Design - Some Theoretical
Considerations•••••••••••••••••••••••••••••••••••

Transplantation of Japanese Management••••••••
Venical Market Structure and Price
Competition•••••-•••••••••••••••••••-••••••••••--•

----

----

• ••ny•••••••••••••••••-•••••••••••-•ny••••-• Arthur Frmcis

Tadao Kagono---- ----.........•..•••-•••••••••••-•••••••••••-••t••••--- -------•••••••••••••••••••••••••••••••-•••--- -ny---.................•.-..••••t•-••••••••••-•• Hisakatsu Sakurai----••••••••••••••••••••••••••••••••••••••••••••••

Masayoshi Maruyama

Stock Price Reaction to the Depreciation
Switch and Its Tax Implication ••••••-•••••••

Mocation Practices of Corporate
Costs in Japan•--••••••••••••••••••••••••••••••••-----

Takeyuki Tam''=s,=--.s-g•.g.s-T•ss..s•.fi,-=-,i,s,s;t,st.s-•-s-F.s,s,-E•.=s••i.s.s,i-i-••!,g.i-,st.J,s.s,s.S••S,==.••i,s.S••==•s-i,s.s,-E,i.s.i.g•s.s••i•s,g.g,i,s,.=.=•ff--s••.

KOBE UNIVERSITY LAW REVIEW 23, 1989
International Edition No. 23, 1989
Edited by Faculty of Law Kobe University, Kobe, JapanCONTENTSThe German Monopolies Commission •••••••••••••••••••••••••••••••••••••-••••••••••••••••••••••••••• Ulrich Immenga

Scandal and Hard Reforrn:
Implications of a Wiretapping Case to the Controlof Organizational Police Crimes in Japan •••••-•••••••••••-•••••••••••••••••••••••••••••••••• Setsuo Miyazawa

Labor Mhistry Offensive in Japan:
A Case of Autonomy of the State Agency?••••-•••••••••••••••••••••••k••••••••••••••••••••••••••• lkuo Kume

RESEARCH INSTITUTE FOR ECONOMICS AND
BUSINESS ADMINISTRATION, KOBE UNIVERSITY

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HISTORICAL SKETCH
In 1919, a research organization named the Institute for Commerce was founded in
Kobe Higher Commercial School, one of the chief predecessors of Kobe University,with a gift made by F. Kanematsu & Company, a leading mercantile firm in Kobe.
The organization was designed to carry on and facilitate integrated research on businessand commerce and to formulate and publish the results of these studies andinvestigations in such form as to make them available to the business commumty.

With the founding of Kobe University of Commerce, successor of Kobe Higher
Commercial School, in 1929, the Institute extended its research activities by adding

several divisions. One was the famous Latin-American Library, which soon became
the center of research in this field in Japan. A room for statistics equipped with various

computing machines was established and began publication of Jiiyo Keizai Tlokei and
Sekai Bbeki' Tbkei annualy. A fi1ing room was prepared te deposit press clipping fies

systematicaky arranged by topics and dates. Another room was designed to become
the center of ad possible original records and data having to do with the beginningand progress of Japanese business.

On the campus of Kobe University of Commerce, another organization named
the Institute for Business Mechanization was founded in 1941 utilizing business machines

donated by the IBM Corporation and others. With Professor Yasutaro Hirai as its heada broad and forward-lookng plan for business mechanization in Japan was deve!oped.

In 1944, Kobe University of Commerce changed its name to Kobe University of
EcOnomics. After the War, however, the University was consolidated with three othercolleges in Hyogo Prefecture to become Kobe University. With this development, thetwo Institutes were also amalgamated into the Research Institute for Economics andBusiness Administration, Kobe University. At present, the Institute, with its twenty-one
full-ime professional staff members, canies on studies and investigations in international
economics, international environrnent, international comparative economics, international

business, management information systems and international cooperation.

ORGANIZATIONThe Institute consists of six sections. Each section and its research subjects are
as follows:

1. International Economic Studies
International Economics, International Monetary Economics,

Maritime Economics, Intemational Labor Relations

2. International Environmental Studies
Resource Development, International Organizations,
Intemational Industrial Adjustment

3. International Comparative Economic Studies
Pachic Basin I (Oceanian Economy),
Pacfic Basin II aatin American Economy),

Pacfic Basin III (Nomh American Economy)

4. International Business Studies
Comparative Business, Multinational Enterprise,International Business Finance

5. Management Information Systems
Business and Accounting Information, Information Processing System,
International Comparative Statistics

6. International Cooperation
In addition to the ordinary work of each section, several research committees,whose members are not limited to the Institute staffs, are regulanly held to carTyon joint studies. At present, there are ten standing research committees, as follows:

Comrnittee of lnternational Economics, Committee of Maritme Economics, Committeeof Labor Market, Committee of International Studies on Economic and Industrial
Structure, Committee of World Link Model, Committee of International Comparative

Economics, Committee of International Comparative Monetary Systems, Committee

of International Business Finance, Committee of Management and Accounting
Information Systems, and Committee of International Comparative Statistics.
For convenience and greater eficiency in carrying out its research activities, theInstitute has a general ofice which is responsible for 1) the collection and preservationof a comprehensive collection of books, periodicals, pamphlets, and original records

and data of finance, trade, commerce, industry and business generaly; 2) theclassincation, cataloguing, indexing, arranging, annotation and compilation of theseresearch materials; and 3) the formulation and publication of the results of theinvestigations and studies accomplished by the professional staff members of theInstitute.

As an afiiliated institute, the Documentation Center for Business Analysis has been
established in 19M. It is the fust systematic•information facilities in the field of businessadministration in Japan that has been recognized and authorized by the Ministry of

Education. The purpose is to collect and to make intensive control of ak kmds ofmaterials on business adrninistration and to make them avalable to scholars,
universities, govemments, and business world with the aid of modem documentation
techniques.

RESEARCH INSTITUTE FORECONOMICS & BUSINESS ADMINISTRATIONKOBE UNIVERSITY
Director: Isao NAKANOSecretary: Takashi YAMAZOE

INTERNATIONAL ECONOMIC STUDIESInternational Economics
International Monetary Economics

Prof. Kazuhiro IGAwA
Prof. Kazuhiro IGAwA
Assoc. Prof. Hideki IzAwA

Maritime Economics

Prof. Hiromasa YAMAMOTo
Assoc. Prof. Masahiro ToMiTA

Prof. Hiromasa YAMAMOTo
Assoc. Prof. Kazuo SHIMoMuRA

International Labor Relations

INTERNATIONAL ENVIRONMENTAL STUDIES
Resource Development

Prof. Hikoji KATANO
Assistant /ll(ihiro NAKAHARAInternational Organizations
International Industrial Adjustment

Prof. Hiroshi SADAMICHIProf. Hiroshi SADAMIcHI
Assistant Ko MIyAzAKIProf. Akira NEGISHIINTERNATIONAL COMPARATIVE ECONOMIC STUDIES
Pacific Basin I

Prof. Kenichi ISHIGAKI(Oceanian Economy)

Assistant Ryuzo MIyAo

Pacific Basin II

Prof. Yoshiaki NIsHIMUKAIAssoc. Prof. Shoji NIsHulMA
Prof. Yoshiaki NIsHIMUKAIAssoc. Prof. Seiichi KATAyAMA(Latin American Economy)
Pacific Basin III(North American Economy)Prof. Hideyuki ADACHIINTERNATIONAL BUSINESS STUDIES
Comparative BusinessProf. Hideki YosHIHARA
Assoc. Prof. Kenji KoJIMA
Prof. Hideki YOSHIHARA
Assistant Rin Ko
Assoc. Prof. Hidetoshi YAMAJI

Multinational EnterpriseInternational Business Finance

ProL Akio MoRl

MANAGEMENT INFORMATION SYSTEMSBusiness and Accounting Information
Information Processing System

Prof. Isao NAKANO
Prof. Isao NAKANOAssoc. Prof. Komayuki ITow

Intemationa! Comparative Statistics

Prof. Hiromasa YAMAMOTO
Prof. Yasuo KoNrsHi

INTERNATIONAL COOPERATION

Prof. Chung HooN LEE(scheduled)

Office:The Kanematsu Memorial Had

KOBE UNIVERSITYROKKO, KOBE, JAPAN