Advanced International Trade: Theory and Evidence, Second Edition - Chapter 1 1 Preliminaries: Two-Sector Models We begin our study of international trade with the classic Ricardian model, which has...

2*2*2 Heckscher-Olin Model



Advanced International Trade: Theory and Evidence, Second Edition - Chapter 1 1 Preliminaries: Two-Sector Models We begin our study of international trade with the classic Ricardian model, which has two goods and one factor (labor). The Ricardian model intro- duces us to the idea that technological differences across countries matter. In com- parison, the Heckscher-Ohlin model dispenses with the notion of technological differences and instead shows how factor endowments form the basis for trade. While this may be fine in theory, the model performs very poorly in practice: as we show in the next chapter, the Heckscher-Ohlin model is hopelessly inadequate as an explanation for historical or modern trade patterns unless we allow for tech- nological differences across countries. For this reason, the Ricardian model is as relevant today as it has always been. Our treatment of it in this chapter is a simple review of undergraduate material, but we will present a more sophisticated version of the Ricardian model (with a continuum of goods) in chapter 3. After reviewing the Ricardian model, we turn to the two-good, two-factor model that occupies most of this chapter and forms the basis of the Heckscher- Ohlin model. We shall suppose that the two goods are traded on international mar- kets, but do not allow for any movements of factors across borders. This reflects the fact that the movement of labor and capital across countries is often subject to controls at the border and is generally much less free than the movement of goods. Our goal in the next chapter will be to determine the pattern of international trade between countries. In this chapter, we simplify things by focusing primarily on one country, treating world prices as given, and examine the properties of this two- by-two model. The student who understands all the properties of this model has already come a long way in his or her study of international trade. RICARDIAN MODEL Indexing goods by the subscript i, let ai denote the labor needed per unit of produc- tion of each good at home, while ai ) is the labor need per unit of production in the foreign country, ,i 1 2= . The total labor force at home is L and abroad is L). Labor is perfectly mobile between the industries in each country, but immobile across countries. This means that both goods are produced in the home country only if the wages earned in the two industries are the same. Since the marginal product of labor in each industry is 1/ai, and workers are paid the value of their marginal © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. For general queries, contact [email protected] 2 • Chapter 1 products, wages are equalized across industries if and only if / /p pa a1 1 2 2= , where pi is the price in each industry. Letting /p pp 21= denote the relative price of good 1 (using good 2 as the numeraire), this condition is /p a a1 2= . These results are illustrated in figure 1.1(a) and (b), where we graph the production possibility frontiers (PPFs) for the home and foreign countries. With all labor devoted to good i at home, it can produce L/ai units, ,i 1 2= , so this establishes the intercepts of the PPF, and similarly for the foreign country. The slope of the PPF in each country (ignoring the negative sign) is then a1/a2 and /a a1 2 ) ). Under autarky (i.e., no interna- tional trade), the equilibrium relative prices pa and pa) must equal these slopes in order to have both goods produced in both countries, as argued above. Thus, the autarky equilibrium at home and abroad might occur at points A and A). Suppose that the home country has a comparative advantage in producing good 1, meaning that a1/a2 < a="" a1="" 2="" )="" ).="" this="" implies="" that="" the="" home="" autarky="" relative="" price="" of="" good="" 1="" is="" lower="" than="" that="" abroad.="" now="" letting="" the="" two="" countries="" engage="" in="" international="" trade,="" what="" is="" the="" equilib-="" rium="" price="" p="" at="" which="" world="" demand="" equals="" world="" supply?="" to="" answer="" this,="" it="" is="" helpful="" to="" graph="" the="" world="" relative="" supply="" and="" demand="" curves,="" as="" illustrated="" in="" figure="" 1.2.="" for="" the="" relative="" price="" satisfying="" p="" p="" a="" a="" a="" 1="" 2="and" p="" p="" a="" a="" a="" 1="" 2=")" )="" )="" both="" countries="" are="" fully="" specialized="" in="" good="" 2="" (since="" wages="" earned="" in="" that="" sector="" are="" higher),="" so="" the="" world="" rela-="" tive="" supply="" of="" good="" 1="" is="" zero.="" for="" p="" p="" p="" a="" a),="" the="" home="" country="" is="" fully="" specialized="" in="" good="" 1="" whereas="" the="" foreign="" country="" is="" still="" specialized="" in="" good="" 2,="" so="" that="" the="" world="" relative="" supply="" is="" (="" )/(="" )a="" l="" al="" 1="" 2="" )="" )="" ,="" as="" labeled="" in="" figure="" 1.2.="" finally,="" for="" p="" p="" a="" and="" p="" p="" a),="" both="" countries="" are="" specialized="" in="" good="" 1.="" so="" we="" see="" that="" the="" world="" relative="" supply="" curve="" has="" a="" “stair-step”="" shape,="" which="" reflects="" the="" linearity="" of="" the="" ppfs.="" to="" obtain="" world="" relative="" demand,="" let="" us="" make="" the="" simplifying="" assumption="" that="" tastes="" are="" identical="" and="" homothetic="" across="" the="" countries.="" then="" demand="" will="" be="" independent="" of="" the="" distribution="" of="" income="" across="" the="" countries.="" demand="" being="" homothetic="" means="" that="" relative="" demand="" d1/d2="" in="" either="" country="" is="" a="" downward-sloping="" function="" of="" the="" relative="" price="" p,="" as="" illustrated="" in="" figure="" 1.2.="" in="" the="" case="" we="" have="" shown,="" relative="" demand="" intersects="" relative="" supply="" at="" the="" world="" price="" p="" that="" lies="" between="" pa="" and="" pa),="" but="" this="" does="" l="" ∕="" a1="" y1="" l*="" ∕="" a1="" y1="" (a)="" home="" country="" (b)="" foreign="" country="" y2="" l="" ∕="" a2="" y2="" l*="" ∕="" a2="" pa*="" p="" c*="" a*="" b*="" p="" pa="" c="" a="" b="" *="" *="" *="" *="" figure="" 1.1="" ©="" copyright,="" princeton="" university="" press.="" no="" part="" of="" this="" book="" may="" be="" distributed,="" posted,="" or="" reproduced="" in="" any="" form="" by="" digital="" or="" mechanical="" means="" without="" prior="" written="" permission="" of="" the="" publisher.="" for="" general="" queries,="" contact="" [email protected]="" preliminaries:="" two-sector="" models="" •="" 3="" not="" need="" to="" occur:="" instead,="" we="" can="" have="" relative="" demand="" intersect="" one="" of="" the="" flat="" seg-="" ments="" of="" relative="" supply,="" so="" that="" the="" equilibrium="" price="" with="" trade="" equals="" the="" autarky="" price="" in="" one="" country.1="" focusing="" on="" the="" case="" where="" p="" p="" p="" a="" a),="" we="" can="" go="" back="" to="" the="" ppf="" of="" each="" country="" and="" graph="" the="" production="" and="" consumption="" points="" with="" free="" trade.="" since="" p="" p="" a,="" the="" home="" country="" is="" fully="" specialized="" in="" good="" 1="" at="" point="" b,="" as="" illustrated="" in="" figure="" 1.1(a),="" and="" then="" trades="" at="" the="" relative="" price="" p="" to="" obtain="" consumption="" at="" point="" c.="" conversely,="" since="" p="" p="" a),="" the="" foreign="" country="" is="" fully="" specialized="" in="" the="" production="" of="" good="" 2="" at="" point="" b)="" in="" figure="" 1.1(b),="" and="" then="" trades="" at="" the="" relative="" price="" p="" to="" obtain="" consumption="" at="" point="" c).="" clearly,="" both="" countries="" are="" better="" off="" under="" free="" trade="" than="" they="" were="" in="" autarky:="" trade="" has="" allowed="" them="" to="" obtain="" a="" consumption="" point="" that="" is="" above="" the="" ppf.="" notice="" that="" the="" home="" country="" exports="" good="" 1,="" which="" is="" in="" keeping="" with="" its="" com-="" parative="" advantage="" in="" the="" production="" of="" that="" good,="" a="" a="" a="" a1="" 1="" 22="" )="" ).="" thus,="" trade="" patterns="" are="" determined="" by="" comparative="" advantage,="" which="" is="" a="" deep="" insight="" from="" the="" ricardian="" model.="" this="" occurs="" even="" if="" one="" country="" has="" an="" absolute="" disadvantage="" in="" both="" goods,="" such="" as="" a="" a1="" 1="" )="" and="" a="" a2="" 2="" ),="" so="" that="" more="" labor="" is="" needed="" per="" unit="" of="" production="" of="" either="" good="" at="" home="" than="" abroad.="" the="" reason="" that="" it="" is="" still="" possible="" for="" the="" home="" country="" to="" export="" is="" that="" its="" wages="" will="" adjust="" to="" reflect="" its="" productivities:="" under="" free="" trade,="" its="" wages="" are="" lower="" than="" those="" abroad.2="" thus,="" while="" trade="" patterns="" in="" the="" ricardian="" model="" are="" determined="" by="" comparative="" advantage,="" the="" level="" of="" wages="" across="" countries="" is="" deter-="" mined="" by="" absolute="" advantage.="" 1="" this="" occurs="" if="" one="" country="" is="" very="" large.="" use="" figures="" 1.1="" and="" 1.2="" to="" show="" that="" if="" the="" home="" country="" is="" very="" large,="" then="" p="" pa="and" the="" home="" country="" does="" not="" gain="" from="" trade.="" 2="" the="" home="" country="" exports="" good="" 1,="" so="" wages="" earned="" with="" free="" trade="" are="" w="" p="" a1="." conversely,="" the="" foreign="" country="" exports="" good="" 2="" (the="" numeraire),="" and="" so="" wages="" earned="" there="" are="" w="" a="" p="" a1="" 2="" 1=")" )="" ),="" where="" the="" inequal-="" ity="" follow="" since="" a="" ap="" 1="" 2="" )="" )="" in="" the="" equilibrium="" being="" considered.="" then="" using="" a="" a1="" 1="" ),="" we="" obtain="" w="" p="" a1="">< /p a w1 ) ). (l ∕ a1) ∕ (l* ∕ a2) relative supply relative demand pa* p p pa (y1 + y1) ∕ (y2 + y2)* * * figure 1.2 © copyright, princeton university press. no part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. for general queries, contact [email protected] 4 • chapter 1 two-good, two-factor model while the ricardian model focuses on technology, the heckscher-ohlin model, which we study in the next chapter, focuses on factors of production. so we now assume that there are two factor inputs—labor and capital. restricting our attention to a single country, we will suppose that it produces two goods with the production functions ( , )y f l ki i i i= , ,i 1 2= , where yi is the output produced using labor li and capital ki. these production functions are assumed to be increasing, concave, and homogeneous of degree one in the inputs (li, ki). 3 the last assumption means that there are constant returns to scale in the production of each good. this will be a main- tained assumption for the next several chapters, but we should be point out that it is rather restrictive. it has long been thought that increasing returns to scale might be an important reason to have trade between countries: if a firm with increasing returns is able to sell in a foreign market, this expansion of output will bring a reduction in its average costs of production, which is an indication of greater efficiency. indeed, this was a principal reason why canada entered into a free-trade agreement with the united states in 1989: p="" a="" w1="" )="" ).="" (l="" ∕="" a1)="" ∕="" (l*="" ∕="" a2)="" relative="" supply="" relative="" demand="" pa*="" p="" p="" pa="" (y1="" +="" y1)="" ∕="" (y2="" +="" y2)*="" *="" *="" figure="" 1.2="" ©="" copyright,="" princeton="" university="" press.="" no="" part="" of="" this="" book="" may="" be="" distributed,="" posted,="" or="" reproduced="" in="" any="" form="" by="" digital="" or="" mechanical="" means="" without="" prior="" written="" permission="" of="" the="" publisher.="" for="" general="" queries,="" contact="" [email protected]="" 4="" •="" chapter="" 1="" two-good,="" two-factor="" model="" while="" the="" ricardian="" model="" focuses="" on="" technology,="" the="" heckscher-ohlin="" model,="" which="" we="" study="" in="" the="" next="" chapter,="" focuses="" on="" factors="" of="" production.="" so="" we="" now="" assume="" that="" there="" are="" two="" factor="" inputs—labor="" and="" capital.="" restricting="" our="" attention="" to="" a="" single="" country,="" we="" will="" suppose="" that="" it="" produces="" two="" goods="" with="" the="" production="" functions="" (="" ,="" )y="" f="" l="" ki="" i="" i="" i="," ,i="" 1="" 2="," where="" yi="" is="" the="" output="" produced="" using="" labor="" li="" and="" capital="" ki.="" these="" production="" functions="" are="" assumed="" to="" be="" increasing,="" concave,="" and="" homogeneous="" of="" degree="" one="" in="" the="" inputs="" (li,="" ki).="" 3="" the="" last="" assumption="" means="" that="" there="" are="" constant="" returns="" to="" scale="" in="" the="" production="" of="" each="" good.="" this="" will="" be="" a="" main-="" tained="" assumption="" for="" the="" next="" several="" chapters,="" but="" we="" should="" be="" point="" out="" that="" it="" is="" rather="" restrictive.="" it="" has="" long="" been="" thought="" that="" increasing="" returns="" to="" scale="" might="" be="" an="" important="" reason="" to="" have="" trade="" between="" countries:="" if="" a="" firm="" with="" increasing="" returns="" is="" able="" to="" sell="" in="" a="" foreign="" market,="" this="" expansion="" of="" output="" will="" bring="" a="" reduction="" in="" its="" average="" costs="" of="" production,="" which="" is="" an="" indication="" of="" greater="" efficiency.="" indeed,="" this="" was="" a="" principal="" reason="" why="" canada="" entered="" into="" a="" free-trade="" agreement="" with="" the="" united="" states="" in="">