CHAPTER IV

INTERNATIONAL TRADE AND FACTOR MOBILITY*

INTRODUCTION t

Commodity movements and factor movements are substitutes. The 4

absence of trade impediments implies commodits-price equalization

and, even when factors are immobile, a tendency toward factor-price

equalization. It is equally true that perfect factor mobility re-

sults in f actor-price equalization and, even when commodity move-

ments cannot take place, in a tendency toward --price equal-

izat ion.

There are two extreme cases between which are to be found,khe

conditions in the real world: there may be perfect factor mobility6

but no t~ade, or factor immobility with unrestricted trade. The (=:

classical econqmists generally chose the special case where factors

of production were internationally immobile.

This paper will describe some of the effects of relaxing the

latter assumption, allowing not only commodity movements but also some

degree ok factor mobility. Specifically it will show that an increase 7

in trade impediments stimulates factor movements and that an increase in

restrictions to factor movements stimulates trade,_/ It will also make more

_/ This proposition is implied in Bertil Ohlin, Interregional and

* The American Economic Review. June 1957

Jnternational Trade (Cambridge, 1935), Ch. 9; Carl Iversen, p s ~ e c t s of

the Theow of International Capital Movements (London, 1935 ) , C h . 2;

and J. E. Meade, Trade and .Welfare (London, 19551, Ch. 21, 22. P

spec i f i c an old argument f o r protection.

TRADE IMPEDIMENTS ' AND FACTOR M O m N T S

Under certain rigorous assumptions the substitution of commodity

f o r factor movements w i l l be complete. In a two-country two-commodity

two-factor model, commodity-price equalization is suff icient t o ensure . 1

factor-price equalization and factor-price equalization is suff icient 1

t o ensure commodity-price equalization i f : ( a ) production functions are

homogeneous of the f i r s t degree ( i . e . , i f marginal produc t i v i t i e s ,

re la t ive ly and absolutely, depend only on the proportions i n which

factors are combined) and are i d e n t i c e ; (b ) one

uire - -.I

t e r - one f - commodity a t any factor prices a t a l l points on any production func-

tion; and ( c ) factor endowments are such a s t o exclude specialization. _/

For the necessity of these assumptions and a f a i r l y complete l i s t

of references to the l i t e ra tu re on factor-price equalization see P. A .

Samuelson, "Prices of Factors and Goods i n General Equilibrium," Review

of Economic Studies, 1953-54, XXI (1), pp. 1-21.

These assumptions a r e not always sa t i s f i ed i n the r e a l world,

so a model employing them is sanewhat l imited. But they do i so l a t e

some impor-tant influences determining ,the pa t te rn of internat ional

trade and f o r present purposes w i l l be adhered to . It w i l l become c lear

l a t e r that relaxing them does not ser iously a f f e c t the conclusions of

the paper.

F i r s t we s h a l l show that an increase i n trade impediments i

encourages fac tor movements, and t o do t h i s we s h a l l make some'xather 4

dras t i c assumptions regarding mobility. Assume two countries, A and B,

two commodities, cotton and s t ee l , and two factors , labor and cap i ta l .

Capital is here considered a physical, homogeneous fac tor which

does not create any balance-of -~-rnhl e- i t moves inter-

nat ional ly- It is fur ther assumed tha t c a p i t a l i s t s qua consuming uni t s

do not move with t h e i r capi ta l , so national t a s t e pat terns a r e unaltered.

Country A is well e n d o w e u t h 1nhnz but poorly endowed with cap i t a l

r e l a t i ve to'country B; cotton is labor-intensive r e l a t i ve t o s t e e l . For -I

expositional convenience we s h a l l use commodity indifference curves.

For the moment we s h a l l assume tha t country B is the r e s t of the

world and tha t country A is so small i n re la t ion t o B t h a t its production - conditions and fac tor endowments can have no e f f ec t on pr ices i n B. _/

_/ It w i l l become eGident in Section I1 t h a t the terms of trade and

a fac tor pr ices do not change even i f A is f a i r l y large. / -~ -

Let us begin with a s i tua t ion @here factor@ a re immobile between

A and B but where impediments t o trade a re absent. This r e su l t s in

commodity- and factor-price equalization. Country A exports its labor-

intensive product, cotton, i n exchange f o r s t ee l . Equilibrium is rapre-

sented i n Figure 1: TT is At:s transformation function (production-

poss ib i l i t y curve), production is a t P 8nd cansumption is a t S.

Country A is exporting PR of cotton and importing RS of s t e e l . Her

income i n terms of s t e e l or potton is OY.

Suppose now that same exogenous fac tor removes a l l impediments

t o the movement of cap i ta l . Clearly since the marginal product of

cap i ta l is .the same i n both A and B no cap i t a l movement w i l l take place

and equilibrium w i l l remain where it is. But now assume tha t A imposes

a t a r i f f on s t e e l and f o r s implic i ty make it prohibit ive. J I n i t i a l l y

J Actually, under the assumed conditions any t a a f is prohibitive,

a s w i l l ' ev&tually become cleay . t

i c e of s t e e l - i k d k ~ - - + & x of cotton i n w'-

and

both production and consumption w i l l move t o Q, the autarky (economic

self-sufficiency) point. Factors w i l l move out of the cotton in to the

s t e e l industry; but since cotton is labor-intensive and s t e e l is capi ta l - - \,

intensive, a t constant fac tor pr ices the production s h i f t creates an excess

But since cap i ta l is mobile, its higher marginal product i n A

induces a cap i t a l movement in to A from B1, changing fac tor endowments

so a s t o make A more capital-abundant. With more cap i ta l A f s trans- %

formation curve expands u n t i l a new equilibrium is reached. 4

Some help in determining where t h i s new equilibrium w i l l be is

provided by the box diagram in Figure 2. Country A i n i t i a 2 u . has OC

of cap i ta l and OL of labor; 00' is the efficiency locus along which

marginal products of labor and cap i ta l a r e equalized i n s t e e l and - cotton. Equilibrium is i n i t i a l l y a t P which corresponds t o P on the - production block i n Figure 1. Factor proportions in s t e e l and cotton

a re given by the slopes of OP and OIP respectively.,

After the tariff is imposed production moves along the efficiency b

locus t o Q, corresponding t o the autarky point Q i n Figure 1. The _I

slopes of OQ and O f Q indicate t ha t the r a t i o s of labor t o cap i t a l i n J

both cotton and s t e e l have r i sen ( i .e . , the marginal product of 1 cap i t a l has r i s en gpd +he m a r g q n - 1 y-sil l lp+ nf 1 O o r has f a l l en ) . / Capital flows i n and the cotton or igin 0' s h i f t s t o the r igh t . 1

With ge r f ec t mobility of cap i t a l the marginal products of both

labor and cap i ta l must be equalized i n A and B. This follows from the

assumption t h a t the production functions a r e l inear , homogeneous and

ident ical i n both countries. Since marginal products in the rest qf

the world can be considered constant, the re turns t o fac tors in A wilL

not chanc;e. Factor proportions i n both s t e e l and cotton i n A then must

be the same a s before the t a r i f f was imposed--so equilibrium must l i e

s t e e l is capital-intensive we should expect the production block a f t e r

the capi tal movement has taken place t o be biased i n favor of s t e e l

a t any given price ratio;; tha t this ~ S ~ S Q has been recently proved

by Rybczynski. J

J T. M. Rybczynski, "Factor Endowment and Relative Commodity

Prices, ".'Economics, November 1955, XXII, pp. 336-41. The proof can

be eas i ly demonstrated in Figure 2. A t unchanged prices equilibrium

m u s t l i e along OP-extended. With the larger endowment of capital ,

O"PT must be shorter than OP. Since these l ines have the same slope

and constant returns t o scale apply, output of cotton a t P r must be

l e s s than a t P. A paper by R. Jones written a t the Massachusetts

Ins t i tu te of Technology i n the spring of 1955 contained a similar

proof.

Since the same price r a t i o a s a t P w i l l prevail, the locus of a l l J

tangents t o larger and larger production blocks based on l a ~ g e r and

larger endowments of capi ta l must have a negative slope. Such a l ine,

which I sha l l c a l l the R-line, is drawn i n Figure 1.

and B, which w i l l be a t the point where A can produce enough s t e e l and A U m A + 4 -- --

cotton fo r c o n s m e i l l f h - i l l m a+. .c <nd a t the same

time make the required in teres t payment abroad. This point is clearly

reached a t PI d i rec t ly above S . A t any point along the' R-line t o the

-7-

northwest of P f , co

sume a t S ( i . e . , demand conditions i n A cannot be sa t i s f ied t o the - northwest of Pf 1. A t Pf deniand conditions in A a re sa t i s f ied and

4~ 9

the in te res t payment can be made abroad a t the same price r a t i o as - before the t a r i f f was levied. Thus the capi ta l movement need not \

continue past t h i s point, although any point t o the southeast of P1

would be consistent with equilibrium.

Production takes place i n A a t P f , consumption is a t S and the

transfer of in te res t payments is the excess of production over consump-

t ion i n A, SPf of cotton. _/ The value of A ' s production has increased

+/ SPf must equal i n value the marginal product of the capi ta l inflow

a t constant prices. In Figure 1, PPt is the change i n output associated

with the increase in capi tal ; s t e e l output increases by RS but cottop

output decreases by PW. The marginal product of the capi ta l inflow is

'the value of R S minus the value of PW which, i n terms of cotton, is P S.

from OY t o OY i n terms of s tee l , but YYf (which equals in valueAP of - cotton) must be transferred abroad, so income is unchanged.

\

We i n i t i a l l y assumed a prohibitive t a r i f f ; in f a c t even the smallest

t a r i f f is prohibitive in t h i s model! A small t a r i f f would not prohibit - trade immediately: because of the pr ice change some capi ta l woad move in

and some trade would take place. But as long as trade continues there

must be a difference in prices i n A and B equal t o the ad valorem r a t e -

of tariff--hence a difference i n marginal products--so cap i ta l imports - must continue. Marginal prgducts and pr ices can only be equalized i n

A and B when A ' s imports cease. r

The t a r i f f is now no longer necessary! Since marginal products 1 I , and pr ices a r e again equalized the t a r i f f can be removed without r e v e r s i ~ g 117 the cap i ta l movement. The t a r i f f has eliminated trade, but a f t e r the 1 - capi ta l movement there is no longer any need f o r trade.

This ' is not r e a l l y such a surprising r e su l t when we r e f e r back t o

the assumptions. Before the t a r i f f was imposed we assumed both unimpeded

trade and perfect cap i ta l mobility. We have then two assumptions each

of which is su f f i c i en t f o r the equalization of commodity and fac tor

prices. T"ne e f f ec t of the tariff is simply t o eliminate one of these L assumptions--unimpeded trade; the other is s t i l l operative. -

However, one qual i f icat ion must be made. I f impediments t o trade

e x i s t i n both countries ( t a r i f f s i n both countries o r transport costs on

both goods) and it is assumed that capital-owners do not move with

t h e i r capi ta l , the i n t e r e s t payments on foreign-owned cap i t a l w i l l be

subject t o these impediments; t h i s w i l l prevent complete equalization of - fac tor and commodity pr ices . ( This question could have been avoided had 4

we allowed the c a p i t a l i s t t o consume h i s returns i n the country where

h i s cap i ta l was invested. ) The proposition tha t cap i ta l mobility is a

, perfect subs t i tu te f o r trade still stands, however, i f one is wil l ing t o

accept the qual i f icat ion a s an imperfection t o cap i ta l mobility.

T + t L I C t i = r r c ~ h

' r . , EFFECT OF ~ ~ L A T I v E SIZE

The previous section assumed tha t country A was very small i n rela-

t ion t o country B. It turns out however, that the re la t ive s i ~ e s of

the two countries make no difference i n the model, provided that

complete specialization does not result.

Suppose a s before tha t country A is exporting cotton i n exchange

f o r s t ee l . There a re no impediments t o trade and capi ta l is mobile.

But we no longer assume tha t A is small re la t ive t o B. Now A imposes

a t a r i f f on s t e e l ra is ing the internal price of s t e e l i n re la t ion to

cotton, sh i f t ing resources out of cotton in to s tee l , ra is ing the marginal

product of capi ta l and l ~ w e r i n g the marginal product of labor. A ' s

demand f o r imports and her supply of exports f a l l . This decline i n

demand f o r B t s s t e e l exports and supply of B t s cotton impo~ts ra i ses

the pr ice of cotton re la t ive t o s t e e l in B; labor and capi tal i n B

s h i f t out of s t e e l into cotton rais ing the marginal product of labor

and lowering the marginal product of capi tal i n B. Relative factor

returns i n A and B move i n opposite directions, so the pr ice changes

i n A which stimulate a capi ta l movement a re reinforced by the pr ice

changes in B. The marginal product of capi ta l r i s e s i n A and f a l l s

i n B; capi tal moves from B t o A, contracting B t s and expanding A ' s - \

production block. 4 -

The assumption that capi ta l is perfectly mobile means that factor

and commodity prices m u s t be equalized a f t e r the t a r i f f . It is necessary

now t o show tha t they a lso w i l l be unchanged. The price of cotton re la t ive

t o s t e e l is determined by world demand and supply curves. To prove tha t t

prices remain unchanged it is suff ic ient t o show tha t these demand and P

supply curves a re unchanged--or, tha t a t the pre tar i f f pr ice r a t i o

demand equals supply a f t e r the capi tal movement has taken place. But

we know tha t a t the old price r a t i o marginal products, hence incomes, are

unchanged-thus demand is unchanged. A l l tha t remains then is t o show A

tha t a t constant prices production changes i n one country cancel out - production changes i n the other country.

This proposition can be proved i n the following way: If commodity

and factor prices a re t o be unchanged a f t e r the capi tal movement has

taken place then factor proportions i n each industry must be the same i

a s before; then the increment to the capi ta l stock used i n A w i l l , a t 7

constant prices, increase the output of s t e e l and decrease the output of

cotton i n A, and the decrement t o the capi ta l stock i n B w i l l decrease

the output of s t e e l and increase the output of cotton i n B. But a increase i n A ' s cap i ta l is equal t o the decrease i n B 1 s capi tal , and since

production expands a t constant prices and with the same fac tor proportions

i n each country, the increase i n resources used i n producing s t e e l i n A

must be exactly equal t o the decrease i n resources devoted t o the pro-

duction of s t e e l i n B. Similarly, the decrease i n resources used Yn P3

producing cotton i n A is the same as the increase i n resources devoted

t o cotton production i n B e Then, since production functions a re l inear

and homogeneous, the equal changes in resources applied t o each industry - ( in opposite directions ) imply equal changes i n output. Therefore, the

increase in s t e e l output i n A is equal t o the decrease i n s t e e l output

i n B, and the decrease i n cotton output i n A is equal t o the increase i

cotton output i n B (i..g., world produc,tion is not changed, a t constant

prices, by a movement of capi ta l from one country to another). In the

world we are considering it makes no difference i n which country a

commodity is produced i f commodity prices are equalized.' -

This proposition can perhaps be made clearer by a geometrical

proof. In Figure 3a, TaTa is A ' s transformation curve before the

t a r i f f , and Tat Tat is the transformation curve af.ter the t a r i f f has

been imposed and the capi ta l movement has ta&en place. A t constant

prices equilibrium moves along A ' s R-line from Pa t o Paf increasing

;the output of s t e e l by Waf and decreasing the output of cotton by RP . - a - Similarly, in Ffgure 3b, TbTb is country B ' s transformation curve before

the capi tal movement and Tb'Tbl is the transformation curve a f t e r capi ta l

has l e f t B. A t constant prices production i n B moves along B f s R-line

t o Pbf , s t e e l production decreasing by SPb and cotton production increas-

ing by SPb e

To demonstrate the proposition tha t world supply curves are un-

changed it is necessary t o prove tha t ma' equals SPb and tha t R 5

equals SPb . The proof is given i n Figure 4. OLa and OCa are, respectively,

A ' s i n i t i a l endowments of labor and capi tal ; OLb and OCb a re the endowments

of B. OOa and OOb a re the efficiency l o c i of A and B with production

taking place along these l o c i a t P and Pb, corresponding t o the same a

l e t t e r s i n Figures 3a and 3b'.

Now when A imposes a t a r i f f on s t e e l suppose tha t CbCbf of capi tal

leaves B, sh i f t ing B f s cotton origin from 43 t o Obf . A t constant prices

labor-capital r a t io s in each i n d u s t r y p s t be the same a s before so

equilibrium must move corresponding t o Pb Figure

Since the capi ta l outflow from B must equal the capi ta l inflow to A,

A t s cotton or igin must move t o the r igh t by just the same amount.as

B f s cotton origin moves t o the l e f t ( i . e . , from Oa t o Oi l ; and A ' s

production equilibrium a t constant prices must move fmm Pa to P I ) . a The proof tha t world supply is unchanged a t constant prices is now

obvious since JPaPaf and KPblPb are identical t r i a n g l e s . Papa1,

increase i n s t e e l output i n A, equals PbPbt, the

decrease i n s t e e l output i n B, and the decrease i n cotton output i n

A, JPa, equals the increase in cotton output in B, lPb\

J The R-lines i n Figures 3a and 3b must be para l le l when output

expands a t the same price r a t i o i n each country, and they must be

s t ra ight since production changes are compensating.

This relationship holds a t a l l combinations of commodity and

factor prices provided some of each good is produced i n both countries.

It means tha t world supply functions a re independent of the dis t r ibut ion

of factor endowments. More simply it means that it makes no difference

t o world supply where goods are produced i f commodity and factor prices

a r e equalized. Since world supply and demand functions a r e not changed

by the capi ta l movements, so tha t the new equilibrium must be established

a t the same prices as before, our e a r l i e r assumption tha t A is very

small in re la t ion t o B is an unnecessaq one. -d

-d One qualification t o the argument must be noted which is not

necessary when the other country is very large. A condition f o r the

marginal product of.capita1 i n A t o r i s e as a r e su l t of the t a r i f f is

tha t the price of s t e e l r i s e re la t ive t o the price of cotton. It is

possible, if the foreign offer curve is very inelast ic , tha t the improve-

ment i n A ' s terms of trade i n rais ing the re la t ive price of exports

(cotton) w i l l more than offset the e f fec t of the t a r i f f in raising the

re la t ive pr ice of imports ( s t e e l ) . The condition that the "normal"

case is sa t i s f ied requires tha t the sum of the foreign e l a s t i c i t y of

demand and the domestic marginal propensity t o import be greater than

~a&y ( the marginal propensity to import is relevant because the improve-

ment i n the terms of trade increases income). This is Metzler ' s qualif ica-

t ion t o the Stolper-Samuelson t a r i f f argument. See Lloyd Metzler, - "Tariffs, the Terms of Trade and the Distribution of the National Income,"

pournal of Po l i t i ca l Economv, February 1949, LVII, pp. 1-29. J a b

cr i te r ion is l e s s than unity a t a r i f f imposed by a labor-abundant coun-

t r y would stimulate foreign investment rather than a t t r a c t capital--a

resu l t , it should be noted, based on the s t a t i c assumptions of t h i s model;

i f dynamic elements were involved the direction of the capi tal movement

would depend on whether the e f fec ts of the t a r i f f on production preceded o r

followed the effects on the terms of trade.

The general conclusion of Sections I and I1 is tha t t a r i f f s w i l l

stimylate factor movements. Which factor moves depends, of course, on

which factor is more mobile. The assumption used here, tha t capl tal #

is perfectly mobile and that labor is completely immobile is an extreme

one which would have t o be relaxed before the argument could be made

useful. But a great deal can be learned qual i ta t ively from extreme

cases and the r e s t of the paper w i l l r e ta in t h i s assumption. When only

capi tal is mobile, a labor-abundant country can a t t r a c t capi tal by t a r i f f s

and a capital-abundant country can encourage foreign investment by t a r i f f s .

The same is true fo r an export tax, since in t h i s model the ef fec t of an

export tax is the same as tha t of a t a r i f f .

The analysis is not res t r ic ted t o t a r i f f s ; it applies a s well t o

changes i n transport costs. An increase of transport costs (of commodities) /

w i l l ra i se the r e a l return of and thus a t t r a c t the' scarce factor, and lower

the r e a l return and thus encourage the export of the abundant factor.

The ef fec t of any trade impediment is t o increase the scarci ty of the

scarce factor and hence make more profitable an international redis t r i -

bution of factors. Later we shal l consider, under somewhat more r e a l i s t i c

assumptions than those used above, the appl icabi l i ty of t h i s proposition as

an argument f o r protection.

FACTOR MOBILITY IMPEDIMENTS AND TRADE

To show that an increase i n impediments t o factor movements stimulates

trade we shal l assume tha t some capi tal is foreign-owned and i l l u s t r a t e

the effects on trade of taxing t h i s capi tal . S t r i c t l y speaking th i s is

not an impediment t o a capi tal movement; but if; it were assumed tha t a

steady capi tal flow was taking place $he tax on foreign-owned capi tal

would operate as an impediment.

We sha l l use Figures 1 and 2. Begin with equilibrium i n i t i a l l y

a t Pf i n Figure 1. No impediments to trade ex i s t but since factor and

commodity prices a re already equalized no trade takes place. We assume

that 0'0" of capi tal i n Figure 2 is foreign-owned so a transfer equal

i n value t o YY1 in Figure 1 is made. Consumption equilibrium i n A is

If a tax is now levied on a l l foreign capi tal its net return w i l l

be decreased, and since factor prices must be equalized i n A and B, a l l

of it ( O t O 1 ) must leave A. As capi tal leaves A, her production block *

contracts. A t constant prices more cotton and l e s s s t e e l is produced. - The price of s t e e l re la t ive t o cotton tends to r i s e but, since there are

no impediments to trade, is prevented from doing so by s t e e l imports and

cotton exports.

Sinc'e a l l foreign capi tal leaves A the f i n a l s ize of A ' s transforma-

t ion function is TT, tha t consistent with domestically owned capi tal .

Production equilibrium moves from Pf t o P, but consumption equilibrium

remains a t S because in teres t payments are no longer made abroad. PR

is now exported i n exchange for s t e e l imports of RS. The ef fec t of the - tax has been t o repatr iate foreign capi tal and increase trade. By

similar reasoning it could be shown that a subsidy w i l l a t t r a c t capi tal

IV- 19

and decrease trade, although i n the l a t t e r case the capi tal movement

w i l l only stop when factor prices change (*. , specialization takes

place )

In order t o achieve efficiency i n world production it is wnnecessary

that both commodities and factors move freely. A s long a s the production

conditions are sa t i s f ied it is suff icient that e i ther commodities or factors move freely. But if some restr ic t ions, however small, ex is t

I

t o both commodity and factor movements, factor- and commodity-price

equalization cannot take place (except i n the t r i v i a l case where trade is

unnecessary beaause'prices are already equal). This principle applies

only t o those res t r ic t ions which are operative--obviously i t does not

apply t o import t a r i f f s on goods which are exported, transport costs

fo r factors which are immobile anyway o r quotas large^ than those

required fo r equalization t o take place.

If it were not fo r t h ~ problem of transporting in teres t payments,

referred t o ear l ie r , one mobile factor would be suff icient t o ensure A

price equalization. When the labor-abundant country imposes the t a r i f f ,

equalization w i l l take place as long as the other country continues a

free-trade policy and there are no transport costs involved. But i f the

capital-abundant country imposes a t a r i f f , inducing the export of capital ,

prices cannot be equalized even i f the labor-abundant country maintains

f ree trade unless the transfer of goods constituting in teres t payments is

also tar i ff-free. ,;/

.l If trade were a perfect subst i tute fo r factor movements i n the

absence of trade impediments, a-idea of the cost of trade impediments

could be acquired by calculating the increase i n world income which could

take place if capi tal were redgs t r ibut~d from capital-ricth t o capital-

poor countries u n t i l its marginal product throughout the world wap

-zed. Alternatively t h i s could be considered the ucrst of capi tal

immobility. This statement would have to be qualified i n the many-factor

case.

AN ARGUMENT FOR PROTECTION?

The proposition tha t an increase i n trade impediments stimulates

factor movements and an increase i n impediments t o factor movements

stimulates trade has implications as an argument f o r protection. In

order t o examine these implications we sha l l relax some of the assump-

tions previously made--first, by introducing trade impediments, then

decreasing the degree of factor mobility, and f ina l ly relaxing the

assumption tha t constant returns t o scale apply by taking account of 2

external economies. We shal l begin w i t h a model similar %Q'th€it b f l ' - Section I1 except tha t we shal l assume country A t o be considerably

smaller than country B. ;_/

i/ I make th i s assumption so that the change i n the terms of trade

resulting from A f J s t a r i f f is small. In passing, however, it should be

noted that the more mobile is capital , the smaller is the m g e i n +he

terms of trade resul t ing fram a t a r i f f ; t h i s means tha t the optimum \

t a r i f f w i l l be smaller with, than without, capi tal mobility; and i n

the l imiting case where capi tal is peryectly mobile, discussed i n

Sections I and 11, the optimum t a r i f f is zero.

Also, in what follows I neglect t o discuss the t a r i f f prooeeds

which are b q l i c i t l y assumed t o be redistributed i n such a way a s t o

leave A ' s indifference map unchanged. Alternatively, t o abstract both

from changes i n the terms of trade and the t a r i f f prooeeds, it could

be assumed tha t the t a r i f f is prohibitive.

Take a s a s ta r t ing point the absence of trade impediments; trade

is suff ic ient t o ensure commodity- and factor-price equalization. Now

suppose that, overnight, transport costs come into existence; t h i s ra ises

the price of importables re la t ive t o exportables, s h i f t s resources into

importables, ra ises the marginal product of the scarce factor and lowers

tha t of the abundant factor i n each country. Incomes of A-capitalists

and B-workers increase while incomes of A-workers and B-capitalists

decrease. These changes in factor returns create tihe incentive fo r a

capi tal movement from B t o A, a labor movement from A t o B, o r a combina-

t ion of both movements. Where the f i n a l equilibrium w i l l be depends on 4

the degree of factor mobility. I sha l l assume that labor is immobile

between countries but tha t capi tal is a t l e a s t pa r t i a l ly mobile.

If we assume that capi ta l is perfectly mobile, but tha t cap i t a l i s t s

do not move with the i r capi tal , the l a t t e r w i l l move from B t o A u n t i l the

return from capi tal invested i n A is the same as from tha t invested i n

B; but th i s implies that marginal physical products cannot be equalized

since transport costs at be paid on $he,goods constituting in teres t

payments. The introduction of transport costs would, then, reduce

However, in teres t ra tes must be the same! Since capi ta l goods--

c a l l them machines--can move costlessly from one country t o the other,

the price of machines i n money terms w i l l be the same in both countriesi

and since machines w i l l move t o A u n t i l marginal products i n money t e r n

are equal, in teres t rates ( the return t o a machine a s a proportion of

the price of a machine) must be the same i n both countries, The in teres t

rate, of course, is not commensurable with the marginal product of capi tal

unless the l a t t e r is defined a s a proportion of the price of machines;

i n the new equilibrium the two are equal when the marginal product of

capi tal is so defined.

world income even i$ capital were perfectly mobile unless cap i t a l i s t s - are willinp t o consume the i r income i n the country i n which the i r capi tal v is invested. -

But we shal l not assume that capi tal is perfectly mobile. Instead

suppose that B-capitalists i n s i s t on receiving a higher return on any

capi tal they invest i n A than on tha t which they invest i n B, p e r b p s

because of po l i t i ca l instabi l i ty , patriotism, r i s k or economic uncer-

ta inty. Let us assume that B-capitalists require a 10 percent higher "'"'''''''''''''''''''''''''''''''''''

re turn on cap i ta l invested in A than on t h a t invested i n B, but tha t L

if t h i s i n t e r e s t d i f f e r en t i a l rises above 10 percent, c ap i t a l is perfect ly

mobile. Suppose fur ther t ha t .the rsrtuyn t o cap i ta l i n both countries

before introducing transport costs was 12 percent; and t h a t the e f f ec t c

of introducing transport costs is t o lower the marginal product of

capital, i n B t o 11 percent and t o r a i s e it i n A t o 17 percent. Since \ ,

the i n t e r e s t d i f f e r en t i a l is l e s s than 10 percent no cap i ta l movement

w i l l take place.

It is a t t h i s point t ha t we sha l l consider the argument f o r a

t a r i f f i n A. Let A impose a t a r i f f , fu r ther increasing her r e l a t i ve

scarc i ty of cap i t a l and B f s r e l a t i ve scarc i ty of labor. Rates of re turn

on cap i ta l change to, l e t us say, 25 percent i n A and 9 percent i n B,

creating an in t e r e s t d i f f e r en t i a l of 16 percent. C a ~ i t a l w i l l now move

from B t o A u n t i l t h i s d i f f e r en t i a l is reduced t o 10 percent. Obviously \

the r a t e s of returm cannot re turn t o the p re t a r i f f r a t e s of 17 percent

f o r A and 11 percent f o r B: f i r s t , because pa r t of the t a r i f f w i l l be

"used up" i n bringing the marginal products of cap i ta l i n A and B t o

the point where B has an incentive t o export capi ta l ; and second, because

transport costs must be paid on the in t e r e s t returns.

If cap i ta l moves u n t i l the re turn i n A f a l l s t o 20 percent and i n

B r i s e s t o 10 percent, what can be said about the economic e f fec t s of the

t a r i f f a s f a r a s country A is concerned?

F i r s t , A-capitalists a r e be t t e r off ; the t a r i f f increases and the

cap i ta l inflow d e c r - , hllf.d&e net e f f ec t is a higher

re turn than before the t a r i f f . Second, A-workers a r e worse off i n s p i t e - of the f a c t t h a t the t o t a l r a t i o of cap i ta l t o labor i n A has increased.

Marginal products a r e determined not b s the t o t a l r a t i o o f - c a p i t a l t o

labor i n a country, but by the r a t i o of cap i ta l t o labor i n each industry.

The cap i ta l - from B is la rge ly absorbed by increasing the output of J

capital-intensive importables i n A; it can never aucceed in ra i s ing the

c ~ i t a l - l a b o r r a t i o i n each industry t o its p re t a r i f f l eve l . Real wages - must be lower than before the t a r i f f .

Third, r e a l national income i n A is l e s s than before the t a r i f f ;

the t a r i f f makes A t s scarce fac tor r e l a t i ve ly more scarce, and her abundant

fac tor r e l a t i ve ly more abund-n~ her po ten t ia l gains from in ter-

national trage. Even under the most favorable assumptions, with cap i t a l

perfect ly mobile and c a p i t a l i s t s moving with t h e i r capi ta l , A ' s income

would remain the same; it could not improve.

So f a r no valid t a r i f f argument has been produced. -1 Capital

.J It is t rue tha t B t s national income has increased since the e f f ec t

of A t s t a r i f f is t o r a i s e B-wages and stimulate cap i ta l investment i n A,

where B-capitalists receive a higher r a t e of re turn than a t home; but it

cannot Be said t ha t B-capi.talists a r e b e t t e r off since, ex hmothesi,

they.are indifferent between investment a t home and an investment i n A

i n which the r a t e of re turn is 10 percent higher. In any case the purpose

of policy makers i n A f s to r a i s e A t s not B t s income.

can be at t racted to a capital-scarce country by a t a r i f f , but the capi tal

movement can only a l lev ia te some of the unfavorable effects of the t a r i f f ;

it can not e l i m i n a m . '

-- t

The argument can be rescued i f we assume the appropriate

i/ It is sometimes overlooked tha t internal economies of scale do

able t o compete some years a f t e r the t a r i f f ; it must a l so earn a suff icient

return t o repay the economy fo r the loss of income resulting from the

only be worthwhile i f future output is suff icient to earn fo r the firm

nonlinearit ies of scale. If external economies of scale ex i s t

It may be possible t o rescue the argument i n other ways by assum-

ing i rrat ional , though possibly not implausible, behavior. For example,

a f t e r B-capitalists have begun investing i n A, they may acquire more

confidence, and be willing t o accept a smaller in teres t d i f ferent ia l .

In t h i s case a f t e r the capi tal movement the marginal product of labor

may be higher, and the marginal product of capi tal lower, than before

the t a r i f f , thereby increasing A ' s national income. O r , while some

( re la t ive ly) capital-scarce countries may fear "exploitation" from

foreign investment, others may view the increase i n productive capacity

resulting from it a s desirable i n i t s e l f (perhaps with the intent of

future expropriationt )--in which case t h i s factor would have t o be

balanced against the reduction i n national income.

the current r a t e of in te res t on the capi tal involved. But when economies

to scale a re internal the investment w i l l be profitable f o r private

enterprise. Only when divergances betrween private and social costs

due t o external economies of scale are present is the case f o r govern-

ment intervention valid.

i n the production of A-importables, the t a r i f f w i l l encourage more capi tal

t o enter than would otherwise be at t racted ~ i n c e the marginal product

of capi ta l entering A w i l l not f a l l a s mpidly a s it would f a l l i n the /'-

/ absence of economies of scale. The new equilibrium w i l l be established

with a higher marginal product of labor, factor returns now being dependent

not only on the proportions i n which factors a re combined, but a l so on

the t o t a l output of importables. Real wages w i l l be higher i n A w i t h

than without economies of scale, though it is not cer tain that they w i l l

be higher than before the t a r i f f ; t o demonstrate the l a t t e r it would have

t o be established tha t the economies of scale a re suff ic ient t o make up

f o r the transport costs which must be paid on the in te res t returns. If

they a r e s2f icient , the t a r i f f would be unequivocally beneficial . J

\ J But i f the same nonlinearit ies of scale ex i s t i n B the argument

is weakened; economw of sca.le i n A-importables w i l l cause the marginal

product of capi ta l t o f a l l a t a slower r a t e than i n the i r absence, but i n 3 :i

t h i s case the marginal product of capi ta l i n B w i l l r i s e a t a much fa s t e r -

r a t e as capi ta l is exported* S b i l a r econbmies of scale i n B, then, -

- 1 ' A ? -

- &ma~-~L

may cancel out the e f f ec t of economies i n A i n inducing a la rger cap i ta l

movement, although t h i s e f f ec t could be neglected if B were the r e s t of

the world and A a small country.

It is easy t o see that economies of scale i n importables o r dis- -- economies of sca le in exportables increase the likelihood t h a t the ne t

e f f ec t of the tariff i n a labor-abundant country is favorable, and vice

versa. To ju s t i fy an argument f o r protection on the above grounds it

would have t o be established tha t capital-intensive industr ies a re subject

t o external economies of scale and/or t ha t labor-intensive industries a re

s d j e c t t o external economies of scale; and these nonl inear i t ies a r e of

the required s ize .

A possible extension of the model t o allow f o r many goods could

be made a s follows: All goods could be ordered i n terms of t h e i r cap i t a l

i n t ens i t i e s (a*, the r a t i o s of cap i ta l t o labor a t any given pr ice

r a t i o ) . B would export those goods tha t a r e most capital-intensive and

A those goods which a r e most labor-intensive. In the absence of trade

impediments one of the intermediate commodities would be produced i n

c m o n , establishing the r a t i o of f ac to r re turns i n much the same way

a s goods produced i n common es tab l i sh the r a t i o of internat ional values

i n a Graham model. Now the e f f ec t of a t a r i f f in A ( a s of any impediment)

is t o increase the r e l a t i ve pr ice of capital-intensive goods i n A and t o r

lower them i n B thus raisin^ in A and I n w t - + n w R the marginal product -

of capi ta l . Now not one commodity but a whole s e r i e s of commodities would

be produced i n cammon, A's exports comprising only the most labor-intensive

and B r s exports only the most capital-intensive goods. In A new capi ta l -

intensive industries, and i n B new labor-intensive industries, would be

created. If same capi ta l were not allowed t o move t o A, the margin of

comparative advantage would be extended t o capital-dmtensive industr ies - i n A, thus increasing the number of goods produced i n common i n both

countries. - CONCLUDING l?EMmm

Like a l l theory, the above analysis is remote from rea l i t y . The

problems of many factors , goods and countries, monopolistic competition

do not in te r fe re with the eent ra l theme, although any policy considera-

and differences i n production functions have not been considered. In

t ions night have t o take them in to accaunt.

Che model is nonmonetary a,nd s t a t i c .

A nunper of questions present themselves. Did t h e m of PEP,-

S t i l l , these l imita t ions

tept ion i n the late nineteenth century i n North America stimulate the

la rge labor and c a ~ i t a l inflows of t ha t period (assuming land t o have . been the abundant f ac to r ) ? Did the increased protection i n Bri ta in

i n t h i s century st imulate cap i t a l export? Did the breakdown i n inter-

national fac tor movements in the interwar period stimul.ate trade? And

t o what extent have the high t a r i f f bar r ie rs between Canada and the United

States contributed t o the stimulus of American investment i n Canqda?

It would be interesting t o see what help t h i s model offers i n finding

answers t o these questions. , P