2x2x2 Heckscher-Ohlin-Samuelson (H-O-S) Model with no factor substitution

Transcription

1 2x2x2 Heckscher-Ohlin-Smuelson (H-O-S) odel with no fctor substitution In the H-O-S model we will focus entirely on the role of fctor sulies nd ssume wy differences in technology. Therefore, unlike in the simle Ricrdin model (but like in the modified Ricrdin model!), in the H-O-S model trde is bsed on differences in fctor endowments nd not on differences in technologies (lthough like in the revious models trde in the H-O-S model is lso relted to differences in suly conditions nd not differences in consumer references). The H-O-S roch to interntionl trde is bsed on two min suositions: Goods differ in their fctor requirements nd cn be rnked by their fctor intensity, for exmle, crs require more citl er worker thn furniture (i.e. crs re citl intensive while furniture is lbor intensive) Countries differ in their fctor endowments nd cn be rnked by their fctor bundnce, for exmle, Englnd hs more citl er worker thn Portugl. These two suositions led to the fundmentl theorem of the H-O-S model tht chrcterizes the ttern of interntionl seciliztion nd trde: A CAPITAL ABUNDANT COUNTRY WILL TEND TO SPECIALIZE IN CAPITAL INTENSIVE GOODS AND THEREORE WILL EXPORT CAPITAL-INTENSIVE GOODS IN EXCHANGE OR LABOR-INTENSIVE GOODS. 1

2 Alterntively, this theorem cn be lso exressed in more generl terms: TRADE IS BASED ON DIERENCES IN RELATIVE ACTOR ENDOWENTS AND REDUCES THE PRINCIPAL EECTS O THESE DIERENCES. The following three issues will be ddressed: How differences in fctor endowments contribute to differences in suly conditions (roduction ossibility frontiers)? How differences in fctor endowments re reflected in fctor nd roduct rices (closed economy: fctor endowments fctor rices goods rices)? How trde ffects fctor rices nd income distribution (oen economy: trde goods rices fctor rices)? 2

3 Bsic redictions of the H-O-S model cn be summrized in the form of four fundmentl theorems: 1. ctor rice equliztion theorem tht dels with the imct of interntionl trde on fctor rices w w* r r * 2. Stoler-Smuelson theorem tht dels with the connection between goods rices nd fctor rices w r 3. Rybczyński theorem tht dels with the connection between fctor sulies nd outut L (, ), 4. Heckscher-Ohlin theorem tht dels with fctor bundnce nd the ttern of trde (Two versions) * the fctor roortions version, L L * w w* the reltive rice version, r r * A A 3

4 CLOSED ECONOY Demnd Side (Consumers): Identicl, homothetic references everywhere Suly Side (Producers): Neoclssicl firms, Perfect cometition, Constnt returns to scle (CRS) Homogenous roducts Demnd for finl commodities Derived demnd for fctors of roduction ixed suly of fctors of roduction (different in ech country) ctor rices Commodity rices (utrky) INTERNATIONAL TRADE 4

5 odel Assumtions Two countries: Home (Englnd) nd oreign (Portugl) Two goods: nufctures (cloth) nd food (wine) Two fctors of roduction: Lbor (L), Citl () Both countries hve the sme technologies (roduction functions), but hve different endowments of citl nd lbor. In rticulr, Englnd hs more citl thn Portugl, while Portugl hs more lbor thn Englnd. Both mnufctures nd food re roduced using citl nd lbor. The outut of ech good deends on how much citl nd lbor re used. This reltionshi is summrized by the neoclssicl roduction function:, L ), for i =,. i i( i i There re mny vrints of the H-O-S model. To kee things s simle s ossible we will strt with the esiest version of the H-O-S model with no fctor substitution (i.e. fixed fctor requirements er unit of outut, indeendent of reltive fctor rices). Citl nd lbor re mobile fctors which cn move freely between sectors within country. 5

6 Production Possibilities Recll tht in the simlest Ricrdin model the she of the roduction ossibility frontier deended on unit lbor requirements nd the totl suly of lbor. In the H-O-S model it will deend on both citl nd lbor requirements nd the sulies of both lbor nd citl. In the i-th industry one unit of outut requires Li units of lbor nd i units of citl so the totl mounts of lbor nd citl emloyed in the i-th sector re: Leontief roduction technology: L i i Li i i i Li i min, Li i i ore secificlly, in ech sector we hve: L min,, L L min, L, nd L. L 6

7 , L L k mnufctures L L k food L, L igure 1. Unit isoqunts for mnufctures nd food. 7

8 When country hs fixed sulies of lbor nd citl nd they re fully emloyed the sum of demnd for citl nd lbor must equl their totl sulies: L L L Solving for in terms of we obtin so-clled Rybczyński lines (lbor nd citl constrints): L L L L L L L When the lbor constrint is steeer thn the citl constrint. This corresonds to our initil L ssumtion tht the roduction of mnufctures is reltively more citl intensive thn roduction of food: (k > k ). L L If the country hd n unlimited suly of citl its outut would deend only on unit lbor requirements nd on the suly of lbor just like in the simle Ricrdin model. Alterntively, if the country hd n unlimited suly of lbor its outut would deend only on citl requirements nd the suly of citl. 8

9 L L L L igure 2. Lbor constrint 9

10 igure 3. Citl constrint 10

11 L L E L L igure 4. Production ossibility frontier 11

12 The lbor nd citl constrints oerte together to determine country s roduction ossibility frontier. Both constrints re binding when sulies of lbor nd citl re both limited. Wht hens to the roduction ossibility frontier when the suly of one fctor increses? The Rybczyński theorem cn be used to study the imct of chnges in fctor sulies: WHEN ACTORS ARE ULLY EPLOYED AND ACTOR REUIREENTS ARE GIVEN AN INCREASE IN THE SUPPLY O ONE ACTOR O PRODUCTION RAISES THE OUTPUT O THE GOOD THAT USES THE ACTOR INTENSIVELY AND REDUCES THE SUPPLY O THE OTHER GOOD. Proof. Differentite totlly (ssuming tht fctor requirements do not chnge) nd write down the full emloyment conditions in the mtrix form, ly Crmer s rule nd solve for chnges in outut roduced in ech sector: L L d d dl d deta = L L 0 (since by ssumtion mnufctures re more citl intensive comred to food) 12

13 d d det A det A det A det A L L d L dl L dl L d L Assume tht only the suly of citl increse (d > 0) while the suly of lbor (dl = 0) remins unchnged, then we cn esily see tht n increse in rises nd reduces. This roves the Rybczyński theorem. The Rybczyński theorem cn be illustrted grhiclly in two different wys: In the roduct sce (, ) In the fctor sce (, L) 13

14 ' 1 E 0 E 1 0 L ' L igure 5. Rybczyński theorem nd roduction ossibility frontier 14

15 k ' E E k O L L igure 6. Rybczyński theorem nd Edgeworth box 15

16 INTERNATIONAL TRADE IN HECSCHER-OHLIN ODEL The Rybczyński theorem is fundmentl to the functioning the Heckscher-Ohlin model. We will use it to show how interntionl differences in fctor endowments determine the ttern of trde. To see how differences in reltive fctor endowments led to interntionl trde let us consider two countries: Englnd (citl bundnt) nd Portugl (lbor bundnt). Both countries hve the sme technologies (roduction functions), which mens tht the sloes of lbor nd citl constrints re the sme in these countries. oreover, countries hve the sme demnd references reresented by the set of indifference curves. Countries differ only in terms of their reltive fctor endowments. Englnd hs lot of citl nd little lbor while Portugl hs lot of lbor nd little citl. 16

17 A E T E C A E T C C C A P A P T P U T U A T E C A E A E T C C A P A P T P igure 7. Trde in the Heckscher-Ohlin model 17

18 Differences in fctor endowments led to differences in trnsformtion curves between countries. When Englnd hs more citl thn Portugl nd Portugl hs more lbor thn Englnd the reltive rice of food (exressed in terms of mnufcturess) under utrky is higher in Englnd thn in Portugl. In Englnd the reltive rice of food is determined sloe of the lbor constrint (idle citl), while in Portugl by the sloe of the citl constrint (idle lbor). A Englnd L L T A Portugl With free trde the reltive rice of mnufctures is the sme in two countries which mens tht the reltive rice of mnufctures increses in Englnd nd flls in Portugl. As result of the chnge in reltive rices of mnufctures outut of mnufctures increses in Englnd nd flls in Portugl nd outut of griculturl goods increses in Portugl nd flls in Englnd. As result of oening to interntionl trde both countries end u t their full emloyment outut oints. Recll tht there re two tyes of gins from trde: i) gins from interntionl exchnge due to the chnge in reltive rices, ii) gins from interntionl seciliztion due to the movement to the full emloyment. 18

19 We hve just demonstrted the fctor-roortions version of the Heckscher-Ohlin theorem, linking the ttern of trde to fctor endowments: THE LABOR ABUNDANT COUNTRY WILL ALWAYS EXPORT THE LABOR-INTENSIVE GOOD (AND INCREASES ITS PRODUCTION O THAT GOOD, I IT DID NOT START AT ITS ULL EPLOYENT POINT), THE CAPITAL ABUNDANT COUNTRY ALWAYS EXPORTS THE CAPITAL-INTENSIVE GOOD (AND INCREASES ITS PRODUCTION, I IT DID NOT START AT ITS ULL EPLOYENT POINT). Alterntive (fctor rice) version of the Heckscher-Ohlin theorem You cn notice tht there is strong reltionshi between goods rices nd fctor rices in the Heckscher- Ohlin model. An increse in the reltive rice of lbor-intensive good ( ) rises the reltive rice of lbor (w/r). This finding cn be illustrted grhiclly using the grh deicting the roduction ossibility frontier. 19

20 L L E1 1 0 E 0 2 E L L igure 8. ctor rices nd goods rices. 20

21 The reltionshi between goods rices nd fctor rices cn be summrized in the following tble: PP Point Reltive goods rice Reltive fctor rice E1 w 0 lbor is free fctor (Lbor constrint is not binding) r E0 w L (Both constrints re binding), 0, L r E2 L w citl is free fctor (Citl constrint is not binding) r L The reltionshi between goods rices nd fctor rices cn be summrized in the following figure which tells us tht the reltive rice of lbor rises with the reltive rice of the lbor intensive good (food): 21

22 Reltive rice of lbor (w/r) 0 L L reltive rice of food / igure 9. The reltionshi between goods rices nd fctor rices. 22

23 The reltionshi between goods rices nd fctor rices cn be lso derived lgebriclly. Recll tht in the Heckscher-Ohlin model we ssumed erfect cometition which mens tht goods rices equl totl unit costs. L L w w r r Let s rewrite this system of equtions in mtrix form to obtin fctor rices s functions of goods rices. L L w r det Aw w det A deta = L L 0 L L A 0 det Ar L L L L r 0 det A L L A L (ssuming full emloyment of both fctors of roduction) 23

24 To derive the generl reltionshi between reltive fctor rices nd reltive goods rices let s divide one eqution by the other which yields: w r L L L f Now we cn esily see tht n increse in the reltive rice of food rises the reltive wge since it increses the numertor nd decreses the denomintor of the bove exression. (This roof shows tht the reltionshi demonstrted in our figure holds when both countries hve the sme roduction technologies). This reltionshi hs three uses: i) To rove the reltive-rice version of the Heckscher-Ohlin theorem ii) To show how trde ffects income distribution in ech country (Stoler-Smuelson theorem) iii) To show when trde will equlize the two countries fctor rices (ctor rice equliztion theorem) 24

25 The reltive-rice version of the Heckscher-Ohlin theorem Before oening to interntionl trde the reltive rice of food ws lower in Portugl thn in Englnd, therefore the curve (in figure 9) tells us tht the reltive rice of lbor in Portugl hd to be lower before trde ws oened. This leds us directly to the reltive-rice version of the Heckscher-Ohlin theorem: I THE RELATIVE PRICE O LABOR IS LOWER IN ONE COUNTRY BEORE TRADE WAS OPENED, THE RELATIVE PRICE O THE LABOR-INTENSIVE GOOD UST ALSO BE LOWER, AND THE COUNTRY WILL EXPORT THE LABOR INTENSIVE GOOD. The Stoler-Smuelson theorem The effects of interntionl trde on fctor rices nd the distribution of income within country re described by the Stoler-Smuelson theorem which cn be stted s follows: THE OPENING TO INTERNATIONAL TRADE RAISES THE RELATIVE PRICE O LABOR IN THE LABOR ABUNDANT COUNTRY AND REDUCES IT IN THE CAPITAL ABUNDANT COUNTRY. Income redistribution effects: Trde will rise the shre of lbor in the ntionl income of the lbor bundnt country nd reduce the shre of citl (it will hve the oosite effects on income distribution in the citl bundnt country). 25

26 Intuition: An increse in the reltive rice of food encourges food roduction nd discourges the roduction of mnufctures. But remember tht food roduction is lbor intensive! Hence, the resulting increse in food roduction rises the demnd for lbor by more thn the decreses of mnufctures roduction reduces it. This drives the reltive wge u. At the sme time the decrese of mnufctures roduction reduces the demnd for citl by more thn the increse in of food roduction rises it. This drives down the rewrd to citl. The Stoler-Smuelson theorem cn be ut in stronger form: THE INCREASE IN THE RELATIVE PRICE O OOD THAT OCCURS IN THE LABOR ABUNDANT COUNTRY RAISES REAL WAGE O LABOR AND REDUCES REAL RETURN TO CAPITAL IN TERS O BOTH GOODS. (ALTERNATIVELY, THE DECREASE THAT OCCURS IN THE CAPITAL ABUNDANT COUNTRY REDUCES THE REAL WAGE AND RAISES THE REAL RETURN TO CAPITAL). These ssertions hold for both definitions of rel wge nd rel return to citl exressed both in terms of food nd mnufctures. 26

27 w r A A L L L We cn esily see tht n increse in the reltive rice of food (lbor intensive good) rises the rel wge nd reduces the rel return to citl when they re mesured in terms of mnufctures (citl intensive good). Now exress the rel wge nd the rel return to citl in terms of food: w A A 1 r A L L L A L L L 1 An increse in the reltive rice of the lbor intensive good lso rises the rel wge nd reduces the rel return to citl when mesured in terms of food. 27

28 ctor Price Equliztion (PE) theorem PE theorem is secil cse of the Stoler-Smuelson theorem: I THERE ARE NO IPEDIENTS TO TRADE (TRADE BARRIERS OR TRANSPORT COSTS) TRADE EUALIZES COUNTRIES ACTOR PRICES, NOT ONLY REDUCES THE DIERENCE BETWEEN THE. (in other words, there is comlete comenstion for the effects of differences in fctor endowments). When the reltive rice of goods is the sme in both countries rel wges nd rel returns to citl re the sme in both countries (ssuming tht both goods re roduced in both countries). This is obvious since reviously we derived the reltionshi between goods rices nd fctor rices: w r L L L 28