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Fragmentation in simple trade models - by Alan V. Deardoff
Fragmentation • Fragmentation = the splitting of a production process into two or more steps that can be undertaken in different locations but lead to the same final product • Fragmentation = “intra-product specialization”; “outsourcing” • Fragmentation occurs both within countries and across countries.
Fragmentation in simple trade models • The paper focuses on fragmentation that occurs across countries (internationally). • Examines the implications of fragmentation on: • Trade • Patterns of specialization • Factor markets Looking especially at its effects on: • Factor prices • The overall welfare of the countries involved
Fragmentation: A small open Ricardian economyI. Case with only two goods Assumptions: • One country, small open economy • A fixed amount of labor L that can be used to produce only X or only Y (two goods) • The unit labor requirements for each good: aX, aY • Country’s wage is w, the supply prices of the two goods will be: w*aX and w*aY • Fixed priced for the goods: pXpY (buy / sell unlimited quantities) • The country has a comparative advantage in X (pX /aX>pY /aY , or aX/aY<pX/ pY) and will export X and import Y.
Fragmentation: A small open Ricardian economyI. Case with only two goods– cont. • Fragmentation: production of X is fragmented in two parts, each part requires amount of labor aX1 , aX2 • The first part produces an intermediate good Z (of price pZ ), required one-for-one with production of good X in the second part (Z is tradable) • Assume that pX ,, pY do not change due to the fragmentation • Labor will engage in the activity that earns more wage (revenue): • Produce only X form scratch, yields: pX / aX • Produce only Y, yields: py / aY • Produce only Z, yields: pZ / aX1 • Produce X from Z, yields: (pX - pZ )/ aX2
Assumption of comparative advantage in production of X , so do not produce Y If pZ is low, below (aX-aX2)/aX:– import Z and produce X If pZ is above (aX-aX2)/aX but below aX1/aX :produce X from scratch If pZ is high enough, above aX1/aX - produce only Z (and export all of it b/c produce no X) The fragmented technology occurs only when: aX1/aX >(aX-aX2)/aX , or aX1+aX2>aX, the fragmented technology uses more resources than the original, fragmentation is costly X, Z, Tz X=L/ax2 Tz=Z=L/ax1 X=L/ax Z=0 Tz=Z=0 X=0 Pz ax1/ax (ax-ax2)/ax Tz=-X=-L/ax2 Fragmentation: A small open Ricardian economyI. Case with only two goods– cont.
Fragmentation: A small open Ricardian economyII. Many goods, many fragments If the technology j for producing each of the n goods is fragmented into nj parts: • The country will tend to specialize in using only one fragment of one technology, unless parameters and prices coincidentally align so that more than one process yields the same wage • As long as prices of final goods in the rest of world are given and unchanged by the introduction of fragmentation, the small country cannot lose from it. • A particular fragment will be employed, and its intermediate product exported if its price is high enough • A low price for the intermediate product will not necessarily assure that it will be imported • A small country cannot lose from fragmentation as long as prices of final goods remain fixed
Fragmentation: A two country Ricardian worldCan a country lose from fragmentation? • Country A specializes in good X, and has comparative advantage in producing X • fragmentation in production of good X is costless, • good Z has no use except in producing X • The world’s net output of Z must be zero • Fragmentation: an increase in the world’s consumption of both goods • if the prices of B do not change, country A gains from fragmentation • if the prices change (lower pX / pYand lower pX / pZ): • Country A loses from fragmentation (imports Y and Z , and produces some X from scratch) • Country B gains
Fragmentation in Hechscher-Ohlin • If prior to fragmentation there is factor price equalization, and if fragmentation is costly, then there will be no incentive to fragment production. • Assumptions: • Start with a world economy in which factor prices are different: • Factor endowments differ sufficiently across countries that they are unable, in free trade, to produce enough goods in common to cause factor price equalization • Fragmentation is costless
K 1/r0 1/r E Kx Oxz X=1 Ky Y=Px/Py 1/w0 1/w L Before fragmentation: A small country trades with a large rest-of-world in which the prices of the two goods, X and Y, are given Unit isoquant for X Diversification cone: rays Kx and Ky (factor prices w, r) The small country is not inside the cone: endowment point E, so it specializes in good X with factor prices w0 , r0 Fragmentation: A small open H-O economy
K 1/r0 Kz 1/r E Kx Z=1 Oxz X=1 Ky XZ=1Y=Px/Py 1/w0 1/w L Fragmentation: The technology for X includes the possibility of producing an intermediate input, Z, unit isoquant for Z (Z=1) Fragmentation is costless The isoquant for producing X from Z, is tangent to Z=1 The technology for Z is more capital intensive than for X The diversification cone is enlarged by ray Kz The small country is inside the diversification cone, so it will be able to fully employ its factors Fragmentation: A small open H-O economy
K 1/r0Kz 1/r E Kx Z=1 Oxz X=1 Ky XZ=1Y=Px/Py 1/w0 1/w L Factor prices: The wage falls from w0 to w The rental on capital rises from r0 to r, so the country gains from fragmentation The small country will produce some of intermediate good Z together with some either X and/or Y Fragmentation: A small open H-O economy
Fragmentation: A two-country H-O world • Fragmentation enhances the possibility of factor price equalization: there may be allocations of the world’s factor endowments for which FPE is not possible without fragmentation, and for which FPE becomes possible with fragmentation
Conclusions: • If fragmentation does not change the prices of goods, then it must increase: • the value of output of any country where it occurs and • the value of output of the world • If fragmentation does change prices, then: • fragmentation can lower the welfare of a country by turning its terms of trade against it • Even in a country that gains from fragmentation, it is possible (but not necessary) that some factor owners within that country will lose • To the extent that factor prices are not equalized internationally in the absence of fragmentation, fragmentation may be a force toward factor price equalization.