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PRODUCTION A N D TRADE WITH SECTOR SPECIFIC INTERNATIONAL CAPITAL
HENRY THOMPSON
ABSTRACT
This paper examines capital crosshauling and otber production characteristics of a sinall open economy whichis a price t.&erin inkmationid markets for its finished goods and secror specific - capital input. The two sectors share a pair of domestic productive facton, including labor and perhaps natural resources, energy, or skilled labor. A higher price o f inkmotional capital in one secror auxs that capital to leave the cconomy, but may lead to capital ctosshauling. Prices of damesuc factors are altered, which raises the potential of using taxcs on interoationalcapird to influence income distribution With the higher price of intwtional capital, output may rive in oue sixlor and fa11 in the othet, or both outputs may rise Qr ffl. D q a e s of factor intensily and factor substitution determine whether crosshauling of capital or another partem of international capital movemenl occurs. Resource booms and varioun condiiions of Dutch disease are also studied.
1. INTRODUCTION
Many countries can be characterized as relying on international markets for productive capital input, much of which is sector specific. This capital machinery and equipmentfrom internationill rnarkels would provide the foundation for production in the various sectors of
the economy. A change in h e international price of a sector's capital input, perhaps through
Direct all correxporrdence to: Henry Tbompson, Economics Department, Auburn University, AL 36849. International Review o l E c ~ o m i c s and Fioaocr, ql): 9h105 Copyright O 1994 by JAI PICSS, Lrlc. ISSN: 1059-05M1 All righe of rcpmduc lion in MV farm rescwed.
94 HENRY THOMPSON
a tax or subsidy, would influence capital employment, dter the pattern of production, and redistribute income among domestic productive factors. International "crossliauling" of capital would occur if there were sim~taneous inflow and outfl ow of capital across sectors.
A higher international price of exports or imports would bolster that wctor and squeeze the rest of the economy. With international sector specific capital, the higher price would seun to be an attraction to international capital in that sector. If capital were released from the rest of the economy, tariffs and subsidies on traded goods would lead to capital c~vsshauling.
Consider a resource boom, the discovery of adomestic natural resource. Sectors using this newly discovered resource should expaud, but the rest ofthe economy might shrink. This is commonly known as the "Ducch disease." referring to the discovery of natural gas which shifted production in the Dutch econoniy during the 1970s. Crosshauling of international sector specific capital would seem to be a natural companion to such a resource boom.
This paper mamines indehil h e comparative statics of a competitive fully employed economy which is a price t&r in world markets for the goods it produces as well as corresponding types of sector specific capital input. Supplies of each sector's capital arc perfectly elastic at the exogenous world price, with demand deternlining the level of capital employed. Industry is constrained not by its endowment of capital, as in the Heckscher- Ohlin-Samuelson (HOS) model, but by t11e international price of capital. Such a general equilibrium model of production may come close to reflecting an economy with t iee foreign direct investment and a few major industries dominated by multinational firms.
Suppose such an economy produces two finished goods, each kaded at an international price. If labor is the only domestic input, the economy will be forced into co~nplele specialization in a single good. Formally, the model is overdetermined because there are more exogenous prices (four) than the total of productive factors (three). Difierent directions, each of inherent interest, have been taken in theoretical investigations. Burgess (1'378) and Jones. Neary, and Ruane (1983) assume one of the two goods i s not traded internationally. Baba and Ramachandran (1980) and Khandker (1981) let multinational firms in one sector employ sector specific domeslir: marketing skills. Srinivaran (1983) andThompson (1985b) suppose international capital is employed in only one sector, with a domestic specific fator employed in theother sector. Jones and Dei (1983)drvelop a model with endogenous capitd payments and sector specific capital in only one sector. Jones, Neary, and Ruant: (1991) examine the Dutch disease in a two sector model with shared labor and sector specific domestic resources as well as sector specific intemalional capital.
The present paper analyzes a model with sector specific international capital in each of its industries and a domestic input (natural resources, energy, or skilled labor) in addition lo labor. Both domestic inputs are shared by the economy's two sectors. There is ample motivation fbr the added domestic facror. Natural resources play a vital role in the pxoduction and t rde of many countries. Energy input is a viral part of most economies. Finally, skilled labor is necessary for explaining the empirical factor content of trade.
Under assumptions of competition andcost minimization, production of each good occurs when the endowment of domestic factors of production Iies within the implied cost nuni-
Sector Specific lnterna tionai Capital 95
mizing production cone. In most of the literature cited above, conlylete specialization and industrial shutdown are typical. In the present mudel, each type of capilal is found to have diminishing marginal productivity in the general equilibrium: a rising (falling) international price of capital will createoufflow (inflow) of thesector's capitd. The return to thedomestic factor used intensively in a sector is found to vary directly with the sector's capital employment in the general equilibrium. A rising iote~imtionill price of capital has the potential to increase output in both sectors, with crosshauling of the other sector's capital and net movement of domestic factors into the sector suffering the higher capital price.
A higher international price of a good increases output and raises payment lo the domestic factor used intensively in that sector. There is a presumption that capikl in that secror will subsequently enter the economy, wilh crosshauling of the other type of capital. Depending on technical conditions, however, both types of capitalmay comeinto the economy, "reverse crosshauling" [nay occur, or bvth types of capital may leave the economy. While production is found to unanlbiguously shift towurd the sector with arising price, the s'uength ofrhe shift depends partly on the underlying international capital movements. There is an increase in the return to the domestic factor used intensively in Uke sector with a rising price, while the price of the other domestic factor falls.
Domestic capital owners are assumed to receive the interntltional price of capital regardless of any domestic tax. The location of home owned capitd is irrelevant to domestic income sincedomesticcapital owners always receive theinternationalreturn. Domesticssupply their capital to international markets which are footloose and homogeneous. Kemp (1961) and Jones (1967) find the tax on foreign capiral which optimks national welfare when the domestic price of capital is endogenous. The present model departs from this tradition in chat the small economy is a price taker in the international capital markets.
Section I presents the sector specific international capital model. Section ll examines the effecb of changing international capital prices. Section III examines the potential of international capital tax policy to redistribute income. A conclusioti and suggestions for further research are presented in Section IV. The Appendix contains model specifications which illusbate the variety of possible comparative static outcomes.
11. THE SECTOR SPECIFIC INTERNATIONAL CAPITAL MODEL
Properties of h e fundamental con~petitive general equilibrium model with constant returns to scale and full employment have been developed by Jones and Scheinknm (1976), Chmg (1979), Takay ama (1982), Thompson (1987), and others. Endogenous oulputs are q and exogenous world prices p;, j = 12. Exogenous endowments of domestic productive factors are v~ and va, which can be some combinarion of labor and naruraI resources, energy, or skilled labor. Domestic factors receive endogenous payments, w3 and rv4.
The structure of the capital in.dskeb is based on the idea of Caves (1 97 1) and Jones (197 1) [hat capital is mobile internationally but sector specific due to its specialized form. The two sorts of international capita1 employed in amounts kl and kz are paid exogenous world prices r; and r;, which are determined in two distinct exogenous international markets.
96 HENRY THOMPSON
Cost minimizing factor inputs aq are functions of the vector of factor prices. Goods are numbered so domestic factor 3 is used intensively in Sector 1 and domestic factor 4 is used intensively in Sector 2: a31/~2 > u41/aZ For notation, b = ~3104~ - alfi1, which is positive.
Comparative shtic outcoms in rhree factor models depend on degrees offilctar intensity and factorsubstifxtion, as analyzed by Jones andEaston(1983)and'Thompson (1985a). Substitution terms sununarize how fm facing changing factor payments would alter their inputs:
S~ aay/awi (fi, i = 3.4) and sgk =Cyj &,/ar; (g = 1,2,3,4 and k = 1 , ~ ) . NO(^ that sit and szl ate zero, as firms do not respond to a c h a n ~ n g price of the other sector's capital. It is known that shk = 3kll due to Young's theorem. Also, s,~, < 0 due to concavity of the cost function. Given linear homogeneity of the production function, &wlshi = O (summed over domestic factors and cdpital). Factors are rescaled so each factor price equals one and hi = 0. Factors h and k are aggregate technical substitutes if JW > 0, and compIements if fhk<0 .
Full employment oi: each productive factor (vi = E,Q~X~ and k, = a&) leads to the first four equations in the system (2) below. Goods are rescaled so aJ= 1.
From competitive pricing (pi = Cilvgij) ar~d cost minimization,
Competitive pricing yields the two last equations in (2). Exogenous changes are collected on the right side of (2). The complete compat~tive static system is stated:
The determinant A ofthe syslem mtrix in (2) equals bZand is positive. Comparative static partial derivative efkcts of changes in 4, or va are found with Cramer's rule. The model can dternatively be solved recursively, first for changes in factor pries, then outputs, and finally employmen1 levels OF international sector specific capital. These chunges all occur simultaneously and influence each other in the general equilibrium. The production possi- bility frontier is found to be locally concave lo the origin: a.r,/apj>O 0' = 1 , 2) and Sx,/ap, < 0 ( j + m).
The total number of factors (four) equals the number of international rnilrkets (two for each good plus two for each type of capital). AS u result, changing endowments of domestic factors do not affect their prices: awh/avk=O (h ,k=3 ,4 ) . If two such economies with identical production functions traded freely with each other, their factor prices would be equal. This is the factor price equalization propwty Fmiliar hom the 2x2 Heckscher-Ohlin- Samuelson (HOS) model.
In fact, the structure of this model in ib domestic inputs is identical to the HOS model. Reciprocal Rybczynski and Stolper-SamueIson results are found for the domestic factors:
Sector Specific /nternationa( Capical
abv3/aP; = ax2/avs = - ~ 1 * ~ / b < 0, and
A tariff wilI raise the price of the domestic factor used intensively in the protected sector while lowering the price of rhe other domestic factor. Production of each good is positively related with the endowment of the domestic factor used inknsively in its production md negatively related with the endowment of the other domestic factor. These results ilre
identical to those for an HOS model with only domestic factors. The underlying HOS structure of !he model in the two domestic factors is suggested with
dkj = dr; = 0 ti = 1,2) in (2). 'Ihe Lerner-Peace diagram of Figure 1 ilIustrates this HOS structure. Unit value isoquanh for Goods 1 and 2 are drawn forpi= 1 and equilibrium levels of international sector specific capital. With cost minimiziltio~l and zero profit, a commcm unit value isocost line suppon the two isoqumts. Endpoints of the isocost line determine domestic factorprices. hput ~atios are uniquely determined in each sector by cost minimiz- ing behavior. Changing endowments of domestic factors within the production cone do not affect domestic factor prices, and factor price equalizauon ~ s u l t s . If the endowment moves from point E but remains inside the production cone, y and w4 are unaffected, while rl and xz adjust according to factor intensity as in (3).
An increase in the price of a good lawers that unil value isoquant in Figure 1 loward the origin, raising ihe price of its intense domestic Pdctor. Production shifts toward the sector
Ci -i - - factor 4 w4 w4
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Sector Specific International Capital 99
A higher price of a sector's capital ciauses it to leave the economy and lowers the productivity and price of the don~estic factor used intensively in that sector. There is an "intensity link" in equation (4), an inverse relationship between a capital price and the price of that sector's intensive domestic factor.
A rising price of one sector's crtpital causes that capital to leave the economy and lowers the productivily of domestic factors in that sector. The inrcnsive domestic factor suffers a falling price in the general equilibrium, ils excess supply develops in the move to the other sector. It is curious to note that factor prices in this model are more dependent on the prices of inlernational capital than on their own supplies. The potential of using ?lutes on interna- tional capital to influence domestic factor income distribution is emmined in the next section.
An ''inverse reciprocity" is found betwezn these results A d the effects of changing endowments of domestic factors on capital employments:
There is thus a positive relation belween the endowment of a domestic factor and h e employment of cdpital in lhe sector where that domestic factor is used intensively. An increased endowment of factor 4, perhaps through a resource boom, will create capital crosshauling with capital coming into Sector 2 as Sector 1 capital departs. Counkies with relatively abundant or growing domestic factors of production will be natural havens for international capital in the sectors using those factors intensively. International cilpital mobility thus contributes to symptoms of the Dutch disease.
A change in a capital price also affech employment of the other type of capital. Solving equation (2) for h e cross effect of a change in < on employlnenlof Sector 2 capital:
where ~ ~ = a ~ ~ + b , c z = a ~ l - b , ~ ~ = a ~ ~ - b , c ~ = a ~ ~ + b , ~ l & , a n d c ~ = n , ~ + a ~ ~ . Analysis is symmetric for the other cross effect: Jkl/a$ = akz/dr;. Substitution terms sii have been eliminated according to the property s.shi= 0 for every h.
The sign of equation (6) cannot be settled since the substitution terms vary in sign and the signs of cz and c3 depend on factor intensity. There is at least a presumption that equation (6) is positive. If akz/ar; is positive, a higher r; causes crosshauiing. With a rising r;, crosshauling occurs with incltased productivity and inflow of Secror 2 capital as domestic factors leave Sector 1, which is also losing capital. There are, however, no necessary conditions at this level of generality for the sign of equation (6) or for capital aosshauling.
Efiwts of changing capital payments on the pattern of output are:
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. .- . .- - . . . . . . . . . . .
HENRY THOMPSON
V. CONCLUSION
This paper presents the first complete picture of an economy which i s a price taker in international markets for sector specific capital as well as finished goods. This two secror model is the prototype for a productive economy with any number of sectors, the same number of shared domestic factors, and sector specific international capital. Underlying such a model is a Heckscher-Ohlin-Smluelson type of model in the domestic productive factors. Domestic capital owners act as suppliers in the international capital markets, receiving b e international return to their sector specific capital input.
A tariff increares oulput in the protected s ~ t o r and has traditional Stolper-Samuelson eKwts on the distribution of income among the domestic factors. Crosshauling of capital is a likely oulcome of a tariff, but genera[ capital ilight, inflow of capital into both sectors, or even reverse crosshauling can occur, depending on technical conditions of factor intensity and Pactor substitution.
Resource booms lead to probIems associated with Dutch disease. The discovery of a domestic resource deposit would cause expansion of the sector using the resource intensively and would attract international capital to the expznding sector. Production of the o h s e c t o r falls as does the employment of its internationalcapital. Prices of domestic factors, including the expanded resource, are unaffected in the present long run competitive model. One general lessonis thatmore flexibility in both output adjustment and internatiowd capital employment would mean smaller dislu~bances in domestic factor prices in the face of a resource boom. Another lesson comes from considering international differences in domestic resources. Free trade and international capital mobility would result in similar prices of the same types of domestic resources across countries.
An increase in the international p r i e of atype of sector specific capital causes that capital to leave the economy. Inconle is distributed away from h e domestic factor used intensively in that sector. Depending on technical conditions of factor substihtion and factor intensity, the other sector's capita1 may enter or leave tlle economy as output adjusts across sectors. It is possible that an increase in the price of one sector's capital, perhaps tluough a tax, would locally expand the production frontier. A tax on international capiral has the potential, in other words, to expand the economy's resource b a e .
An appeaI for empirical research on the modelling of international capital is in order. Which assumption is more rd id for a pa-ticular country: international capital at an exoge- nous price, or domestic capital tit anendogenous price?Trade theorists make one assumption or the other without clear empirical guideposts. The profession needs to develop the empirical nalure of international markets for productive capital.
APPENDIX
Model specifications reported in Tb le 1 illusaate the variety of: possible comparative static results across different substitution terms. Factors of production are rescaled in these specifications s o y = v4 = 4 = ri = 1. Cost minimizing domestic factor-mix terms are set at
Sector Specific international Capital 103
Table 1. Different Model Snecificalions and Comparative Static Outcomes
a31 = aq2 = 0.4 and = a32 = 0.1. It follows that b = 0.15, c~ = c4 = 0.55, cz = c j = 4.05, and cg = cg = 0.5. Full ehloyment of both domestic factors implies that the endogenous output levels must be .ti = xz = 2. Rescaling g o d s so a; = 1. endogenous employment of each type of capital is kl = ap j= 2. Assuming pi = p z = 1.5. competitive pricing implies w3 = 1v4= 1.
Prices of domestic factors adjust to a rising r i according to aw3/a4=-2.67 and aw,/ar; = 0.67 from equation (4). Due to resealing, these two parrial derivatives are also elasticities. A 1% increase in r; (dr; = 0.01) implies dw3 = -0.027 and dw4 = 0.067; w3 would drop to 0.9733 while w4 climbs to 1.0067. Income of the domestic inputs changes according to ayD/a< = v3(awdar,) t- v4(dw4/drl) = -2.67 + 0.67 = -2 < O. The 1% in- crease in rl would drop YD from 2.0 to 1.98.
Different sets of substitution tenns are specified in Table 1. h c h column in Table 1 represents a different model specitication. The substitution matrix is completed according to sii = -(SO + sio), i = 1,2, andsi = -(st, + szj 1- q4), j = 3.4. Each of the postulated substitu- tion matrices is negative semidefinite. Comparative static results from equations (6) and (7) describe crosshauling and the output e h t s of a change in r;. If ak2/arf < 0, both axl /ar; and a.~,/ar; c w o t be positive since resources deparr the economy. The olher seven possible sign patterns of'the three compatative static partial derivatives are illustrated in Table 1.
In Specification A. all factors are substitutes and crosshauling of international capital occurs. Output in Sector I would decline with the higher r;, while ourput in Srctor 2 rises. This is the base case, with all influences working in rhe sane direction as described in the body of the paper.
Domestic factors 3 and 4 are weak complements in Specificdon B and do not move as easily to Sector 2 with the higher r;. The factor 4 which does move to Smtor 2 is substituted for the capital in that sector, which leaves the economy. Output in Sector 2 just manages to rise with the higher rT.
Domestic factors are stronger complemenb in Specification C. Outpub in both sectors fall as both types of capital leave the economy with the higher r;.
In Specifcation D, domestic factors are strong cvmplements and Factor 4 is a relatively strong substitute for capita1 in Sector2. Even with a higher r;, output in Secior 1 rises. The
104 HENRY THOMPSON
complernentiuy domestic faclor 4 is pulled in10 Sector 1. Output and capital employment drop in Sector 2.
Seuager substitution between capital in Sector 2 and domestic factor 4 creaks the crosshauling in Specification E. Output in Sector 2 barely falls as complementary domestic inputs are athacted to Sector I . ?he incoming capital in Sector 2 soflens lhe output decline relative to Specification D.
In Speciticalivn F, capival in Sector 2 and domestic factor 3 are complements. A higher r; causes w3 to fall, and demand for complementary capital in Sector 2 rises. Enough domestic factor 4 is attracted to Sector 1 that output in Sector2 falls, even with crosshauling. Thedeparting capital in Sector 1 leads to the decIine in Sector 1 output.
Stronger compbmentatity between c a p i d in Sector 2 and domestic factor 3 characterizes the last specification. Factor4 is strongly substiluted for capital in Sector 1, whilecapiral is strongly substituted for factor 4 in Sector 2 in Specification G. Crosshauling occurs, and both outputs increase with the higher r f .
These model specitktttions indicate only one way each of the seven possible sign patterns of these comparative stalic results can occur. These specifications exhaust the possible qualitativeco~nparative static outcomes, but not the ways of atiainingthem. Other situations of substitution, complemenmity, and factor intensity could lead to the same range of outcomes. Writing out the statics would develop a picture of how outputs and capital inputs adjust. Elasticities of each endogenous variable with respect tor; are one half'of thereported partial derivative, since 4 = I and kz = 9 = 2.
A tariff would create theexpected crosshauling of capitalin Specifications A and B, alkact both types of capital to the economy in Specifications C and F, create reverse crosshauling in Specifications D and E, and result in an ouMow of both types of capital in Specification G.
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