Can capital movements eliminate the need for technology transfer?

Journal of International Economics 12 (1982) 95-W. North-Holland Publishing Company

CAN CAPITAL MOVEMENl’S ELIMINATE THE NEED FOR TECHNOLOGY TRANSFER?

Rachel McCULLOCH* University of Wisconsin-Madison,

Madison, WI 53706, USA

Janet YELLEN Uniuersily of Calsfornia, Berkeley, CA 94720, USA Received August 1979, revised version received November 1980 This paper analyzes the welfare and effiency implications of barriers to international transfer of technology. We show that the consequencesof s?lchbarriers depend critically upon the extent of internotional capital mobility. When capital is perfectly mobik, polkies that impede technology transf’ermay have no effect on employment, income distribution, or national welfare, despite one country’s clear technological superiority in an industry. This conclusion holds even if there is a rigid v&e and resultingunempioymeni in one countj.

1.

Introduction

The welfare and eflkiency consequences of international technology transfer are the subject of ongoing analysis and debate in advanced and developing countries alike. Much of the analysis proceeds from the assumption that barriers to technology transfer have important effects on employment, incame distribution, and national welfare. However, in this paper we show that the consequences of such barriers depend crucially upon the extent of international capital mobility. When capital is perfectly mobile, policies that impede technology transfer may have none of the assumed consequences. Chipman (1971) has shown that trade and capital mobility together m.ay be sulikient to achieve full factor price equalization even when available technologies for one industry differ across countries. In this instance, barriers to technology transfer have no distributive or efficiency consequences. A necessary condition for Chipman’s result is that the two technologies are competitive, i.e. equally cost effective at some set of factor prices. *We are indebted to the Nationel Science Foundation for research support and to Jagdish N. Bhagwati and John S. Chipman for helpfui suggestions.

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Our analysis demonstrates that capital mobility can serve as a substitute for technology transfer when one country enjoys clear technological superiority in an industry, so that production cost is lower over the full range of possible input prices. In contrast to the case considered by Chipman, full factor price equalization can be achieved only with the technologically backward country completely specialized. The conclusion that capital mobility can substitute for technology transfer holds even if there is a rigid wage and resulting unemployment in one country. The results in this paper complement the classic theorems of Samuelson (1949) and Mundell (1957). Samuelson’s factor price equalization analysis demonstrated that trade in goods may substitute fully for movements of factors. Mundell established that capital movements may substitute fully for unimpeded trade in goods. Our work and Chipman’s shows that capital movements can substitute fully for technology transfer. At the heart of these ‘substitution* theorems lies the indeterminacy, within limits, of the location of production associated with a given global system of supply and demand.

2.I. 7Wlnology The starting point of OUTanalysis is the usual two-sector, two-country model. Goods A and B are produced using capital (K) and labor (L). Production functions are linear homogeneous and c kave the standard neoclassical properties. The technology for producing k is identical in the home country and abroad. Letting asterisks denote the values of variables abroad,

A=FK,,t,);

A* =F(KX, LX),

or, in terms of the intensive production function,

A* =LXf(Q).

(2)

In the absence ci technology transfer, the home and foreign countries possess d&rent technoiogies for producing good B:

R. McCulloch

an.4 J. Yellen, Capital mobility

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We assume that the home country technology is superior to the technology abroad in the sense that g(k,)> h(k*) for all kg. Equivalently, the factor price frontier corresponding to the home technology lies completely outside that for the foreign technology;’ i.e. +Jr)>$,,(r) for all r, where w=$Jr) and w =&Jr) denote the implied relationships between the wage rate w and the rental rate r.2 2.2. Factor supplies Total supplies of labor at home and abroad, L and P, are fixed; labor is immobile internationally. Assuming initially that flexible wages ensure full employment in both countries, we have k= (1 -&Jc*++&,,

where & =LJL and A,*= G/L* are the shares of each country’s labor force employed by the B industry and k=K/L and k* =K*/L* are the overall capital-labor ratios at home and abroad. Capital is assumed to be internationally mobile. Thus, the capital stock of each country is endogenous. However, the world capital stock is fixed and fully employed, so that K +K* =R or yk+ (1 -JQ/c*=E,

(7)

where y= L/(L+L*) is the fraction of the world labor force located in the home country and E=K/(L+L*) is the aggregate world capital-labor ratio. 2.3. Factor rewards International mobility of capital guarantees that the reward to capital is the same at home and abroad. Letting r and r* denote ;he domestic and foreign rental rates measured in terms of good A, we have r=r*.

If p is the relative price of good B, there are uniquely determined industry ‘La contrast, Chipman’s diversification equilibrium can occur only when factor price frontiers intersect. fFor any given r, choose &, such that It’(&) = r. Thea eb(r) = h(lE,) - &r, and, therefore, g(&) - sr>e,,(r). But @Jr)=max, [&)ksr] zg(&)- &,r. (This holds with equality when the g technology is a Harrod-neutrdimprovement over h.) On properties of the factor price frontier, see Burmeister and Dobell (1970).

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capital-labor

ratios k,, kg, ciz, and kg that satisfy (9)

In equilibrium, an industry may not operate in one country. For each industry producing positive output in a given country, competitive profit maximization entails that the actual capital-labor ratio used must satisfy (9), i.e. that the marginal value product of capital in every use will be equated to the world rental rate.3 Each industry’s demand price for labor is defined as the value of the marginal product of labor evaluated at the capital-labor ratio determined by (9). Denoting by WA, w;, wa, and wg*the demand prices for labor measured in terms of good A, we have WA=f(kd

- kA_f’(k,d,

wX=f(k:)wB=

k;f’(kE),

!‘k(k,) - k,g’( k&l],

wg*==p[h(kg*)- k,*h’(k,*)].

Perfect competition in labor markets ensures that labor is paid the value of its marginal product in its most profitable potential use, so that w=max

(WA,

w*= max (~2,

WB),

we*).

(10)

(II)

When an industry’s demand price for labor is less than the wage rate, the industry cannot cover its costs; in equilibrium it will not operate. Only if w =wA=wB can both industries operate simultaneously. Corresponding conditions apply abroad. 2.4. Market equilibrium We assume free trade between the two countries. The model is closed by postulating a world demand function for good B which depends on the relative price p, factor supplies (in this case exogenous), and factor rewards. 3However, for given p and r, the corresponding industry capital-labor ratios k,, k,, kt, and k$ are uniquely determined even when no output is actually produced. Likewise, each industry’s dernnnd price for labor can be determined as shown below, even when the industry’s output is zero.

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Product market equilibrium thus requires that D(p; w, w*,r; L, L*,R) = B,

(12)

where B= B + B* is total world output of good B.4 3. Efficient production and access to technology If both countries had access to the same technology, international capital mobility would ensure worldwide equalization of the rewards to labor as well as capital. However. our assumption that the home country possesses a superior technology for producing good B implies that the wage rate at home may exceed that abroad. ’ When wages do differ in equilibrium, it is apparent that barriers to technology transfer will have real1effects on factor prices and outputs. In this case, the cost of producing B with the superior technology is lower abroad at pre-transfer equilibrium factor prices. Thus, elimination of barriers to technology transfer results in world excess supply of good B at the former equilibrium product price. While barriers to technology transfer mlay confer an advantage on the home country by permitting domestic labor to earn a higher competitive wage than foreign labor, this outcome is not a necessary consequence of the home country’s technological lead. Factor prices may be equalized despite the home country’s superior technology, and in this case barriers to technology transfer will have no effect whatsoever on equilibrium factor and product prices. Our purpose in this paper is to show why factor price equalization can occur even with a technology gap, not just under very special conditions but in a broad range of circumstances. Intuitively, identical technologies and mobile capital together guarantee a world production pattern which is fully efficient. However, many efficient world output combinations can be achieved without identical technologies; over some range of outputs, the unrestricted (identical technologies) and restricted (differing technologies) world production possibility frontiers coincide.

4We assume that demand is unaffected, ceteris paribus, Sy changes in the location of the fixed world capital stock. ‘To demonstrate w 2 w*, we consider four possible cases: A produced at home and abroad, A produced only abroad, B produced at home and abroad, and B produced only abroad. From (8)(10) we have r-r+, k* = ki, and wA= wz. If, in equilibrium, good A is produced both at home and abroad, from (10) and (11) we have w = w, and wl = wi. If A is produced only abroad, then w=w&w*=wX= w*. If B is produced in both countries, w = w, = $,(r) and w* = Hf = $Jr), and t&(r)> SA(r) by assumption. Finally, if B is produced only abroad, w 2 wa=$,(r)> #,(r)= w*. It should be noted thlat the home wage must exceed the foreign wage whenever U is actually produced abroad in equilibrium. Chipman’s substitution theorem cannot hold under our technological specification.

R. McCulloch

loo

and J. Yellen, Capital mobility

Theorem 2. A range of points on the unrestricted world transformation curve can be achieved when good B is produced only in the home country; this range will be larger, the larger is the home labor force relative to the world labor force. Ifdemand conditions yield an equilibrium within this range when both countries have access to the superior technology, restriction of superior technology to home country use can be accommodated through international reallocation of capital and corresponding changes in production patterns within each country, leaving factor rewards, product prices, and aggregate outputs unaffected. Proof.

is well known that the international allocation of capital and the production patterns within each country corresponding to points on the frontier are, within limits, indeterminate. Starting with any efficient production pattern that entails complete specialization in neither country, the same aggregate outputs can be achieved if a unit of capital is moved from abroad to the home country (or the reverse). The proof that the initial and new equilibria are identical with respect to aggregate outputs and factor prices is then a straightforward application of the Rybczynski theorem. This argument suggests that it may be feasible to attain output combinations on the unrestricted world production frontier with one industry’s operation confined exclusively to the home country. When this is possible, it obviously makes no difference whether the most advanced technology for this industry is actually available abroad. To formalize the argument, we begin by characterizing equilibrium when the countries have equal access to technology and capital is internationally mobile. We can then specify conditions under which technology transfer is redundant in achieving this .equilibrium position. When both countries possess the superior technology, i.e. h(k)=g(k) for all k, equilibrium requires full international factor price equalization. With identical technologies and capital mobility, (9) implies kA = ki and kB= kg in equilibrium. It then follows that WA= wx and we= wg, so that, from (10) and (10 VJ= w*.As long as each good is produced in at least one country, WA =w =w=w*.6 Fh any value of p compatible with world production of both goods, we can derive a unique worldwide allocation of labor between the industries. Eqs. (9)-(11) allow us to solve for k, and k, in terms of p. Now let qs denote the fraction of the world labor force allocated to B production, It

% the equal-access equilibrium, each country may produce both goods or just one. In the latter case,however, the industry capital-labor ratio and factor rewards must nonetheless be the same as those associated with a diversified prodruction equilibrium. This~‘marginal specialization’ equilibrium can be achieved only if the country’s overall capital-labor ratio is the same as the capital-labor ratio determined from (9) for the one operating industry.

R. McCulloch and J. Yellen, Capital mobility

LB+LB*

vu=

L+L*

=&J+A,*(l

101

-v).

From W(7),

(1--rlBMP)+YIBkB(P)=~.

(13)

We can now solve for VBin terms of p using (13). The aggregate quantities of A and B, denoted A and & produced at the price ratio p,’ are given by

&P)=f1-

qB(P))(L+

L?)f(k,(p)),

The set of all A(p) and B(p) for p in the feasible range constitutes the unrestricted world production frontier. While vi&) is UniqUdy determined, As and ng are, within limits, indeterminate. Given p, and hence ki= k,(p) and kg = kB(p), (5 j(7) constitute a set of three equations in four unknowns: Ai,, $, k, and k*. Any values of A, and A$ between zero and unity can be chosen that satisfy YAB +

( 1- d&i = tlB(P)-

(14)

It is now straightforward to determine the range of points on the unrestricted world- transformation curve that can be attained when B is produced only at home, i.e. A: = 0. Setting dg =0 in (14) yields AB = VB (p )h-

Since in cannot exceed unity, this is a feasible allocation only if ~B(pk% Letting pcrit denote the value of p that satisfies tf&) = y, then any equilibrium with P 5 pcrit3 or, equivalently, ojB~Y(L+L*)g(kB(P~,i,)),

can be achieved without foreign production of B. When the foreign country does not have access to the superior technology for producing B, equilibrium is determined by eqs. (lj(12), but with g no longer identical to h. Eqs. (lj(11) can be used to calculate the quantities A and ii that would be supplied for alternative choices of p. The restricted ‘Because Q, is constrained to lie between zero and unity, only those values of p which yield a solution for qa(p) in this range are compatible with world production of both goods. We denote by pmln and pwx those values of p which yield ~a(p,,,ia)=0 and ~,(p,,,,,,)= 1. Incomplete specialization requires pmlnc p < p_ . We assume pmrn S p _Ip_.

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world production frontier is rhus obtained. By the previous reasoning, however, .the restricted and unrestricted frontiers coincide for p Speri,, or B 5 i’(L+ P )g(kB(Pc&)).8 If PI P&t (i.e. if qe y) when both countries have equal access to technology, the foreign country will speciahze completely in A production when it does not have access to the superior technology for producing B. Eqs. (l)-(12) continue to be satisfied at the equal-access equilibrium p with the same kA, kg, and k,, the same w= w’* a.nd r=r*, but with A,*=0 and & =~I~(F)/;‘. If I3 were produced abroad, the capital-labor ratio used in the industry would be kg satisfying (9), i.e. such that

s

ph’(

k;) = i-.

But since

a foreign producer of B would not be able to break even. Thus, there is no incentive to produce B using the inferior technology. 4. Capital movements and barriers to technology transfer An immediate corollary 01’theorem 1 is that when ever the world miirket equilibrium price is below pcri,, any positive royalty charged to foreign users of the superior g technology will be prohibitive.’ Imposition of a royalty will induce relocation of any foreign B production to the home country; factor and product prices will be unaffected. If with equal access some B is produced abroad, restriction of access would be accommodated by a shift of foreign labor out of B production and into A production. At unchanged factor-use ratios: the total capital relquired for production abroad would change by L;r(k.t - kg). In the home country, an identical quantity of labor would be shifted from A to B production, giving rise to an equal but opposite change in capital requirenxnts at home. The cessation of B production abroad would therefore cause a capital inflow for the home country if k,> k, and a capital outflow if kB < k,. 5. Technology transfer and unemploymeDd The conclusion that the transfer abroad of superior technology

can leave

sFor plpcrit, eqs. (l)-(11) are satisfied by the same k,, kB, and kz, and the same W=W* and r=r* as in the identical technology case, but with A:=0 and &,=q,{p)/y. ‘This result parallels Mundell’s finding that with mobile capital any positive tariff is prohibitive.

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factor and product prices unchanged when ca.pital is internationally mobile continues to hold - within limits - even if there is a rigid real wage and unemployed labor in the home country. Whenever this theorem applies, moreover, technology transfer is also neutral in that it leaves home unemployment unchanged. The implications of this result are striking. It means, for example, that policies to impede technology transfer in order to expand domestic employment mag be utterly ineffective in accomplishing this goal. Even when the policy succeeds in stifling competing production abroad and even when the result is not only expanded home production but also an inflow of capital, the impact on unemployment and labor earnings at home may nevertheless be nil. To show that our result can be extended to situations with rigid wages and home unemployment, it is necessary to modify slightly the model developed in section 2. We now assume that the real wage in the home country is Fixed in terms of good A, so that w = G and the actual level of employment at home, denoted N, is endogenously determined. An immediate implication of the fixed real wage is that there is a unique relative price, j(W), corresponding capital-labor ratios 1LA and kri, and rental rate F, that allow both industries to operate at home.“” Theorem

2.

If demand conditions yield an equilibrium with p= jj and B s (K -L*~Jg(~n)/& when both countries have access to the superior technology, restriction of superior technology to home country use can be accommodated through international reallocation of capital and corresponding changes in production patterns within each country, leaving factor rewards, product prices, aggregate

outputs, and employment

unaected.

As before, we start by considering the characteristics of equilibrium when both countries have equal access to technology. We show that if p=p in equilibrium, indeterminacy in the world allocation of production (and capital) may permit world production of B to be concentrated in the home country. We then demonstrate that, under reasonable restrictions on tastes, equilibrium must occur at p= jj if the home cotmtry is sufficiently large.’ 1 Assume that both countries have equal access to technology (g(k)s:h(k)) and the equilibrium price is p. It is straightforward to prove that the foreign country must be incompletely or just marginally specialized,‘* with &= kZ, I;B= kg, w=w*, and r=r*.13 Proof

‘OFor details of t&e tw’o-sectoropen economy model with fixed real wage, see Brccher (1974). “We assume throughout that the world endowment of capital is large enough (or the wage rate 9 is low enough) so that i@?>min(k,,, Et,), i.e. that labor abroad could be fully employed in the less capital-intensive industry. “A country is marginally specialized if factor prices are consistent with prothtction of both goods but only one is actually produced. See footnote 6. ‘.‘lf the foreign country were nonmarginally specialized in production of the I&or-inlensiw good at p= jk this would imply K./f? F. But r* can exceed F only if

104

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In sharp contrast to the ‘normal full employment case, equilibrium at p = p’ is compatible with a range of output combin?tions. Within broad limits, changes in demand at p=p’ can be accommodated through expansion or contraction of home employment N at constant factor prices and corresponding reallocation of capital and labor between industries. The world transformation curve relating A and B possesses a linear segment.14 Each world output combination (A,& on the linear segment of the world transformation curve is characterized by full employment of the world capital stock and foreign labor and a unique level of home country employment.r5 For each world production combination, the fraction of the world labor force employed in the B industry, 17 B= (L, + LB*),‘(N + L?), can be determined from (15):

Parallel to the full employment case, for any combination j7 and B (and corresponding N), there is an indeterminacy in the allocation of production and the world capital stock between countries. Any values of & and Jg between zero and unity that satisfy

where & = LB/Nand 7 = N/(N +L*) are consistent with equilibrium. It is now straightforward to determine the range of world outputs that can be achieved at p=p without foreign production of B. When .ihe foreign country is specialized in A, the amount of capital employed abrnad is LYE*, and A& L*f(k,,).” Maximum world production of B is equal EI:the quantity

no capital is employed at home, and if all capital is used abroad, we would h:vti K*/L? =x/L?, which by assumption exceeds min (I;,, la). Likewise, foreign country specialixattou in the capitalintensive good would be profitable only if KS/L? >max (E*, En). But then r* *: ?, which is ruled out by capital mobility. 14The slope of this linear segment is not equal to -p’. See Brecher (1994). “N varies directly with world production of the labor intensive good. 16Full equilibrium at p requires a feasible value of N satisfying

The maximum feasible value of N at p=p is that which yields fE=min (&, !&), i.e. where all employment is concentrated in the less capital-intensive industry. The minimum feasible value of N is zero if E XL? max (E*, La), in which case it is possible for the entire world capital stock to be absorbed abroad; otherwise, the minimum feasible N is [K/max &, En)] -I.?, which yields Fi = max (EA,17~). “Foreign specialization in A is possible only if Kg)?&‘,, a condition that must be satisfied if the home country is sufficiently large, i.e. R > L* max (/&, Et,), or if A is the relatively ‘aborintensive industry. Putting this another way, the foreign labor force L* must be sufftciently small relative to the total world capital stock R.

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that can be produced at home using the remaining available capital, i.e. (17) As in the full employ_rnentcase, w!ten equilibrium can be attained without B production abroad, barriers to transfer of superior technology have no effect whatsoever on aggregate outputs and factor rewards. Employment in the home country is also unaffected. Any required reduction in foreign output of B again entails international capital movements, the direction and magnitude of which depend on relative factor intensities, but there is no accompanying effect upon national welfare or employment.18 It remains to show that equilibrium must occur at p==p except in ‘uninteresting’ circumstances. Equilibrium with p#p implies that A, B, or N is equal to zero. I9 Consumption of only one good in equilibrium can be ruled out by reasonable restrictions on tastes. Positive world output levels for both industries can occur at p #fp’ if R CL* max (E,,, &,), but in this case iV must be zero; i.e. no production takes place at home. This is possible when the home country is very small. Any attempt on the part of domestic labor to raise its wage above the prevailing world level causes a complete exodus of capital - the minimum wage in effect prices that country out of world markets. The same outcome is also possible if a larger country attempts to fix a very high real wage.2o Our analysis thus pertains to a country large enough to remain economically viable with a fixed real wage, i.e. when R ‘*International capital movements may have important consequences for national tax revenues,a welfareconsiderationruled out by assumptionin our tax-freeworld. “Consider first the case of equilibriumwith p#Lp and N ~0. We have shown above that d p >p and N ~0, only B is producedat home. Since ka must satisfyfi= p[g(ka) - kag’(ka)],kn< k,, and r =pg’(k,) > E Capital mobility ensures r*= r. Now if kg satisfies r ==r*-pg’(kg), then kB = Y anti we’==ptg(kd - k,g’(kdl =I?. To achieve an equal returnon capital on the A industry would require kX< r,, and, therefore,WEO and pO and p#p’ must entail production of the only one good worldwide, Equilibriumat p#p with production of both goods is only possible when N =O and K cI?max(k~,&,). If A*>0 and B*>O with p#A kX and kg must satisfy~(k~)=pg’(k~)=r* anUiklt;)-kV’(kX)=pCg(ka)-kgg’(kt)l = w*. If p# 6, by the Stolper-Samuelsontheoremr* is greaterthan or less than F,dependingon which industryis capital-intensive.It is only profitable, however,to employ capital abroad if r*h F, which impliesthat incompletespecializationabroad can occur with p cd only if B is labor-intensiveand with psp’ only if B is capital-intensive.In either case, r*> r’=r is compatiblewith capital mobility only if K-N ~0. If K =0, the entzre world capitalstock must be employedabroad,i.e. K*=4?. Incompletespecializationabroadthus a&clrequires

‘OAnintezsting feature of the model is that as long as N>O, foreign workers as well as domestic workers must receive the minimum real wage. This is a consquence of capital mobility. All resulting unemployment,however, is concentratedin the country imposing the minimumwage, becauseunemployedworkersthereare preventedfrom biddingfor jobs.

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> L*max (k,,, &); in this case equilibrium with identical technologies must occur at p=ji if both goods are consumed. References Brecher, R.A., 1974, Minimum wage rates and the pure theory of international trade, Quarterly Journal of Economics 88,98-l 16. Burmeister, E. and A.R. Dobell, 1970, Mathematical theories of economic growth, (Macmillan, New York). Chipman, J.S., 1971, International trade with capital mobility: A substitution theorem, in: J.N. Bhagwati et al., eds., Trade, balance of payments and growth (North-Holland, Amsterdam) 201-237. Mundell, R.A., 1957, international trade and factor mobility, American Economic Review 47, 321-335. Samuelson, P.A., 1949, International factor-price equalisation once again, Economic Journal 59, 181-197.