Migration Decision from Bangladesh: Permanent Versus Temporary;

The Heckscher-Ohlin Model

1. “A country is abundant in a factor, if the country’s endowment of that factor relative to the world endowment exceeds the country’s share of world GDP, then she should export that factor intensive commodity”- Prove the statement.

Heckscher-Ohlin-Vanek (HOV) Model: It is the “factor content” version of the Heckscher-Ohlin model, developed by Vanek (1968). The goal of that model is to predict the pattern of trade in goods between the two countries, based on their differences in factor endowments. Now let us consider many countries, indexed by i = 1,…,C; many industries, indexed by j=1,…,N; and many factors, indexed by k or l =1,..,M. We assume that technologies are identical across countries, and that factor-price equalization prevails under free trade. In addition, we assume that tastes are identical and homothetic across countries.

Let the (MxN) matrix A=[ajk]' denote the amounts of factors needed for one unit of production in each industry. Again, let Yi denote the (Nx1) vector of outputs in each industry for country i, and let Di denote the (Nx1) vector of demands of each good, so that the vector of net exports for country i can be written as; Ti =Yi– Di………………………(1) The factor content of trade is then defined as; Fi ≡ ATi = AYi– ADi ……...…...(2) which is an (Mx1) vector. For individual factor, we may write;

i For Capital; Fk >0  Capital is exported and vice versa.

i For Labor; Fl >0  Labor is exported and vice versa. The total demands for factors in country i to produce Yi is AYi. Using definition of full employment, AYi equals the endowments of country i, which we write as; AYi = Vi…………………………(3) Since product prices are equalized across countries by free trade and tastes are identical and homothetic, it follows that the consumption vectors of all countries must be propor- tional to each other. We may write this as Di = si Dw, where Dw denotes the world consumption vector and si is the share of country i in world consumption. It follows that; ADi= siADw……………………..(4) Note that if trade is balanced, then si also equals country i’s share of world GDP. Since world consumption must equal world production, we therefore obtain; ADi= si ADw = si AYw = si Vw……(5) From equation (2), (3) and (5), we may have: Fi ≡ ATi = Vi– si Vw ………(6) which is a statement of the Heckscher-Ohlin-Vanek (HOV) Theorem. In terms of individual i i i w factors, this is written as Fk =Vk  s Vk . If country i’s endowment of factor k relative the world i w i endowment exceeds country i’s share of world GDP (Vk /Vk > s ), then we say that country i is abundant in that factor. i w i i If Vk /Vk > s  country is abundant  Fk >0  Country will export capital

Redwan Ahmed, M.S.S, Economics, SUST. Hello:+8801716811466. Skypee: red1eco. E-mail:[email protected]. The Heckscher-Ohlin Model

in capital intensive goods i w i i If Vk /Vk < s  country is scarce in  Fk <0  Country will import capital capital intensive goods Again;

i w i i If Vl /Vl > s  country is abundant  Fl >0  Country will export labor in labor intensive goods

i w i i If Vl /Vl < s  country is scarce in  Fl <0  Country will import labor labor intensive goods

Therefore, we may conclude that, a country is abundant in a factor, if the country’s endowment of that factor relative to the world endowment exceeds the country’s share of world GDP, then she should export that factor intensive commodity.

2. Prove that if capital is abundant relative to labor in country i, then the HOV theorem implies that the capital/labor ratio embodied in production for country i exceeds the capital/labor ratio embodied in consumption, i.e.

i i i i i i K /L > ( K - Fk )/( L - Fl ) Proof: The HOV theorem states that; Fi ≡ ATi = Vi– si Vw…………….(1) In terms of individual factors.i.e, labor and capital, these are written as:

i i i w Fk =K – s K w i i i or, K = (K - Fk )/ s i w i i i i or, K /K = s K /(K - Fk )……………………(2) and; i i i w Fl = L – s L w i i i or, L = (L - Fl )/ s i w i i i i or, L /L = s L /(L - Fl )……………………..(3) Now from equation (2) by (3), Ki/Kw> Li/Lw implies that;

i i i i i i i i s K /(K - Fk ) > s L /(L - Fl )

i i i i i i or, K /(K - Fk ) > L /(L - Fl )

i i i i i i or, K /L > ( K - Fk )/( L - Fl )

i i i i i i  K /L > ( K - Fk )/( L - Fl ) ……..…………(4) Interpretation: To interpet this result, note that Ki and Li are simply the endowments of capital and labor, or alternatively, the capital and labor embodied in production. If we subtract the content of these factors

i i embodied in trade, then the remaining can be defined as the factor-content of consumption, or (K - Fk ) i i and (L - Fl ). Then equation (4) states that the capital/labor ratio embodied in production (on the left) must exceed the capital/labor ratio embodied in consumption (on the right). Therefore, the country is capital abundant and she should export that factor intensive commodity.

3. What does the HOV Theorem tell us about the Leontief test?

Explanation about the Leontief test: The HOV theorem states that; Fi ≡ ATi = Vi– si Vw…………….(1) In terms of individual factors.i.e, labor and capital, these are written as:

i i i w Fk =K – s K , …………………………………….(2) i i i w Fl = L – s L , ……………………………………..(3) i i i i where Fk and Fl are the computed factor contents of trade, and K and L are the capital and labor endowments for country i. Following Leamer (1980), we define capital to be abundant relative to labor in country i if Ki/Kw > Li/Lw. Then using (2) & (3), the implications of capital abundance are:

i i i i i i K /L > ( K - Fk )/( L - Fl )

i i i i where K and L are the capital and labor embodied in production respectively as well as ( K - Fk ) and ( i i L - Fl ) are the capital and labor embodied in consumption respectively. Table 1 describes the factors embodied in production & consumption for the U.S. in 1947.

Table 1: Leamer’s (1980) Reformulation of the Leontief Test. Production Consumption Capital ($ billion) $327 $305 Labor (person-years) 47 million 45 million Capital/Labor ($/person) $6,949 $6,737

In the first column we list the capital and labor endowments for the U.S., and in the second column we show the capital and labor embodied in consumption, i.e. Ki = $327 and Li =47 million,

i i i i (K - Fk ) =$305 and (L - Fl ) =45 million, Taking the ratio of these, we have;

i i i i i i K /L = $6,949 and ( K - Fk )/( L - Fl ) = $6,737. Considering the value of these ratios, we may write;

i i i i i i K /L = $6,949 > ( K - Fk )/( L - Fl ) = $6,737 Therefore, we may write, it is indeed the case that the capital/labor ratio embodied in production exceeds that in consumption. This is the precise application of the HOV Theorem, and it turns out to

Redwan Ahmed, M.S.S, Economics, SUST. Hello:+8801716811466. Skypee: red1eco. E-mail:[email protected]. The Heckscher-Ohlin Model be satisfied for the U.S. in 1947, contrary to what Leontief concluded. Thus, there was no paradox after all rather Leontief test was wrong!

4. For which reasons, the empirical analysis of Leamer is seen as robust in order to prove the Leontief paradox as wrong?

Reasons make Leamer’s result as robust: The empirical analysis of Leamer is seen as robust. To explore the reasons, It is useful to see the HOV Theorem and Leamer’s result in a diagram. In Figure 1, the length of the horizontal axis is the world labor endowment Lw = L1+L2, and the length of the vertical axis is the world capital endowment Kw = K1+K2. The origin for country 1 is in the lower-left corner, and for country 2 is in the upper-right corner.

Figure 1 Thus, any point in the world endowment box measures the endowments (Li, Ki) of the two countries. Suppose that the endowments are at the point Vi, where country 1 is labor-abundant, L1/K1 > Lw/Kw > L2/K2. Under the assumptions of the HOV model, the factor-content of consumption must lie along the diagonal in the world endowment box, as illustrated by point ADi. Therefore, a line from point Vi to i 1 point AD measures the factor content of trade. In Figure 1, country 1 exports Fl of labor services, and 1 i i imports Fk of capital services. The slope of the line between V and AD measures the ratio of factor prices. The theorem of Leamer (1980) states that if country 1 is labor-abundant, then the capital/labor ratio embodied in consumption must exceed the capital/labor ratio embodied in production. That is, since the consumption point ADi must lie on the diagonal, it is necessary above the endowment point Vi. While this is graphically obvious, note that it does not depend in any way on whether trade is balanced or not. For example, if country 1 is running a trade surplus (with the value of production exceeding consumption), then we should move the consumption point ADi to the left down the diagonal. This would have not effect whatever on the capital/labor ratio embodied in consumption as compared to the capital/labor ratio embodied in production. So Leamer’s test of the HOV theorem i i i i i i in {K /L > ( K - Fk )/( L - Fl )} is completely robust to having non-balanced trade. Therefore, the empirical analysis of Leamer is seen as robust in order to prove the Leontief paradox as wrong.

5. “Though Baldwin’s partial test is a wrong test like Leontief, even it makes a good sense”- Prove the statement.

Or, as a descriptive tool to show how trade is related to industry factor requirements Baldwin’s partial test makes good sense, but as a definitive test of the HOV Theorem it is inadequate.

Baldwin’s test:

The HOV theorem can be written as; F i  AT i  (V i  s iV w ) i 1 i i w T  A (V  s V ) ………………………………………….……. (1)

This equation could be tested in several ways. First, if we think about the matrix A-1 as data, then we could run a regression of Ti on A-1, and coefficients obtained would serve as an estimate of the relative i i w abundance (V  s V ) of each factor. However, Baldwin regressed Ti on A' instead of regressing Ti on

 a1L a1K    -1 a a A . With two factors and three goods, for example, A' is the matrix  2L 2K  . Thus, Baldwin a3L a3K  regressed the adjusted net exports of each industry8 on their labor and capital requirements needed for one unit of production. Using data for 60 U.S. industries for years around 1960, and disaggregating workers by their types, Baldwin obtained the following result;

Adjusted net exports = –1.37* (Physical Capital/Worker) + 7011* (Scientists/Worker) – 1473 (Managers/Worker) + 71 (Clerical Staff/Worker) +1578* (Craftsmen & Foremen/Worker) +248(Operatives/Worker) + 761 (Unskilled Employee/Worker) + 845* (Farmers/Worker) + (Other variables included for industry scale and unionization), N=60, R2=0.44, * = significant at 95%level

Thus, looking across the U.S. industries, Baldwin gets a surprising finding, which is the negative coefficient found on the very first variable, physical capital/worker. This coefficient says that U.S. industries using more capital/worker will tend to export less. This is exactly the opposite of what we would expect if the U.S. were capital-abundant. Thus, this result appears to be similar to the “paradox” found by Leontief. From (1), a valid test would be to regress Ti on A-1, but instead, Baldwin regressed Ti on A'. To see the consequences of this, we use the ordinary least squares (OLS) formula for the coefficients  that would be obtained from this regression:

T i  A  ˆ  (AA)1 AT i  (AA)1 (V i  siV w )

Thus, we see that ˆ is a contaminated estimate of the vector of relative factor endowments (V i  siV w ) . Rather than equaling the relative factor endowments vector, ˆ equals the positive i i w definite matrix (AA')-1 times (V  s V ) . Because (AA')-1 is certainly not the identity matrix, it is entirely possible that the sign pattern of the elements in ˆ will differ from the sign pattern of i i w (V  s V ) . In other words, even if the U.S. was capital-abundant and the HOV Theorem held, it would still be possible for the Baldwin regression to find a negative coefficient on capital; this does not contradict the HOV Theorem, because like the original Leontief approach, it is the wrong test. The possible differences in the sign pattern of ˆ and (V i  siV w ) can presumably be checked for using the

Redwan Ahmed, M.S.S, Economics, SUST. Hello:+8801716811466. Skypee: red1eco. E-mail:[email protected]. The Heckscher-Ohlin Model actual data on (AA')-1. This is exactly the approach taken by Baldwin, who argues that such sign reversals are very unlikely to occur in practice. Thus, the Baldwin regression may be acceptable in practice. As a descriptive tool to show how trade is related to industry factor requirements this regression makes good sense, but as a definitive test of the HOV Theorem it is inadequate for the reasons we have described.

6. “While the approach of Leamer (1984) provides interesting results on the Rybczynski effects, it is of limited usefulness in testing the HOV Theorem”- prove the statement in light of Leamer’s partial test.

Leamer’s partial test:

The HOV theorem can be written as;

F i  AT i  (V i  s iV w )

i 1 i i w T  A (V  s V ) ………………………………………….……. (1)

i i w This equation could be tested in several ways. First, if we think about the matrix (V  s V ) as data, i i w then we could run a regression of Ti on(V  s V ), and coefficients obtained would serve as an estimate of the elements of A-1. To describe this test, (1) applies across all countries i. Focusing on a -1 single industry j, and letting the elements of A be written as  jk , we can write (1) in scalar form as: N i i i i T j    jk (VK  s VK ) ; i=1….C ………………..….……. K 1 (2) where the summation in (2) is across factors, but the observations are across countries. Thus, to estimate this regression we would combine the observation for a single industry j across multiple countries i=1…,C, where the coefficients  jk are estimated. These coefficients should be interpreted as Rybczynski effects can be positive or negative. To run this regression, we first need to choose some aggregation scheme for net exports and factors of production. Leamer (1984) works with the trade data for 60 countries in two years, 1958 and 1975. He organizes traded goods into 10 aggregates, as shown in the first column of Table 1: two primary products (petroleum and raw materials); four crops (forest products, tropical agricultural products, animal products and cereals); and four manufactured products (labor-intensive manufactures, capital-intensive manufactures, machinery and chemicals). Implicitly there is an eleventh product in the economy, making up all the non-traded goods, so Leamer includes total GNP as an aggregate to reflect this. There are also eleven factors of production, listed along the top row of Table 1: capital, three types of workers (distinguished by skill), four types of land (distinguished by climate), and three natural resources. So the number of goods equals the number of factors by construction. The estimates of  jk from regressing the 1975 net exports of each of these aggregates on the country factor endowments are shown in Table 1. Leamer emphasizes that the point estimates should not be taken too seriously, but the sign pattern of the coefficients is of interest, especially when the estimates are significantly different from zero. The estimated coefficients can be positive or negative, but they do not provide any basis to test the HOV Theorem. Instead, we have to

rely on the overall fit of the regression: a linear relationship between endowments and trade, as in (2), is implied by the theory and can be assessed by the R2 of the regressions. In the final column of Table 2.3 we show the R2 from each cross-country regression, and these vary from 0.13 to nearly unity. Admittedly, these fits are a very weak test of the theory, because we generally do not want to rely on

l l l 2 e

l s a a a t 1 2 3 4 l l R a t i a n n d d d d i a o r r o o n n n n O p e i i C e a a a a a t s s i n s s l L L L L C i l e e I f f

M s o o r r r e p P l - k r a n c o o i n N W s h r c e e k T r

o & s W r e k r o W GNP 453** 15,683** -445* -480** 30** -49** 81* -27* 9.0** 2.8* 2.1** 0.99 7 Primary Products Petroleum -18.4** -248 -.8 31* 0.5 7.9** -5.4 0.3 -1.0** -0.4 0.6** 0.92 Raw -8.9** 127 -31.2* -2.3 0.89 0.47 1.1 3.3** 0.45** 0.86** 0.04* 0.86 Materials Crops Forest -1.7 34 -18.8 8.4 -0.45 -2.7* 0.3 3.3* -0.17 0.53* 0.08* 0.53 Products Tropical -2.9** -30.1 8.9 5.6 2.0** -1.1 4.5* - -0.30** - 0.05* 0.72 Agricultural 3.9** 0.44** Products Animal -0.5 -42 -29.3 14.0 0.09 -0.34 5.6* -1.3 0.17 0.28 0.05 0.22 Products Cereals -4.5** 70 -51.0* -6.8 1.3* -4.8** 16.1** -3.6* 0.39** 0.97** 0.24** 0.86 Manufacturing Labor- 1.9 -397 42* 7.4 -0.97 .00 -0.6 -1.6 -0.10 -0.09 -0.07* 0.13 Intensive Capital- 18** -1,900** 116** 49** -0.89 3.2* -12** -0.63 -0.12 -0.46* -0.17** 0.86 Intensive Machinery 29** -1,471* 38 33 -1.6 -1.5 -24** -7.9* 1.0** -1.1* -0.27** 0.76 Chemicals 4.1** -154 -16.0 3.0 -0.57 -0.30 -6.0* -1.0 0.3** -0.15 -0.04* 0.51 only the R2 of an equation to judge the validity of the theory underlying it. So while this early approach of Leamer (1984) provides interesting results on the Rybczynski effects, it is of limited usefulness in testing the HOV Theorem.

Table 1: Estimates of Rybczynski Effects from Leamer (1984) Notes: GNP is scaled in thousands of dollars; Capital is in millions. * indicates that t >1, ** that t >2.

7. Define Sign test and Rank test.

Sign test:

It is a test, which simply compares the sign pattern on the left and right of the HOV theorem { F i  AT i  (V i  siV w ) }. With M factors and C countries, there are MC observations in total, and we are interested in what percentages of these have the same sign on the two sides of the equation. Notice that a completely random pattern of signs would still generate correct signs 50% of the time in a large sample. Therefore, the sign test must do considerably better than this in order to conclude that the HOV Theorem is successful. Mathematically;

Rank test: It is a test, which involves a pair wise comparison of all factors for each country, so there is M (M–1)/2 pairs for each of C countries. If the computed factor content of one factor exceeds that of a second factor, then we check whether the relative abundance of that first factor also exceeds the relative abundance of the second factor. Again, a completely random assignment of factor abundance and relative endowments would imply that in 50% of the comparisons in a large sample, the rank test would be satisfied, so we would hope that the actual data perform considerably better than this in order to conclude that the HOV Theorem is successful. Mathematically;

8. How does the article “The Leontief Paradox, Reconsidered by Edward E. Leamer” proved that the Leontief’s test was a wrong test. Proof:

Let the (MxN) matrix A=[ajk]' denote the amounts of factors needed for one unit of production in each industry. Again, let Yi denote the (Nx1) vector of outputs in each industry for country i, and let Di denote the (Nx1) vector of demands of each good, so that the vector of net exports for country i can be written as; Ti =Yi– Di The factor content of trade is then defined as; Fi ≡ ATi = AYi– ADi …………………………………. … (1) which is an (Mx1) vector. As we know; AYi = Vi………………………………………………………..…….. (2) and ADi= si ADw = si AYw = si Vw……………………………………….. (3) Therefore, we may write from (1), (2) and (3); Fi ≡ ATi = Vi– si Vw ………………………………………………...… (4) which is a statement of the Heckscher-Ohlin-Vanek (HOV) Theorem. In terms of individual i i i w factors, this is written as Fk =Vk  s Vk i i i w i For capital abundant country; Fk =Vk  s Vk or KT = Ki – s Kw or i Kw= (KT - Ki)/s i where, Fk or KT are capital content of trade, Ki is country i’s endowment of capital and Kw is world endowment of capital. i i i w i For capital abundant country; Fl =Vl  s Vl or LT = Li – s Lw

or i Lw = (LT - Li)/s i where, Fl or LT are labor content of trade, Li is country i’s endowment of labor and Lw is world endowment of labor. Thus we have; i Ki/Kw = s Ki/(KT - Ki) i and, Li/ Lw = s Li/(LT - Li) Therefore; capital is revealed by trade to be abundant relative to labor if and only if; Ki/Kw> Li/ Lw i i Or s Ki/(KT - Ki) > s Li/(LT - Li) Or Ki/(KT - Ki) > Li/(LT - Li) Or Ki/Kc > Li/Lc [ Lc =(LT - Li), Kc =(KT - Ki)] …………..………………..(5) which means that a country is revealed to be capital abundant if its production is more capital intensive than its consumption. Again from (5), we may write; Ki Lc > Li Kc …………………………………………………………………..….(6) Or Ki (LT - Li) > Li (KT - Ki) Or -Ki LT > -Li KT ……………………………………………………………..……..(7) Or -( Kc + KT) LT > -( Lc + LT) KT Or - Kc LT > - Lc KT…………………………………………………………….…… (8) We know that if the net export of capital services and the net export of labor services are opposite in sign, then the factor with positive net exports is revealed to be the relatively abundant factor i.e. if KT > 0 and LT < 0, then Ki/ Kw > Li/ Lw………………………………………………………. (9)

Now suppose first that KT > 0 and LT < 0, then by definition we have; KT > 0 and LT < 0  (Kx- Km ) > 0  (Lx – Lm) < 0  Kx/ Km > 1  Lx / Lm < 1  Kx- Km / Km > 0  Lx - Lm / Lm < 0  (Kx- Km) > 0  (Lx - Lm) < 0 Therefore; a country is revealed to be relatively well endowed in capital compared with labor if and only if; (Kx- Km) > 0, (Lx - Lm) < 0………………………..……………… (10) Now again, if LT is positive i.e. LT > 0 and KT > 0, then (8) becomes; KcLT < Lc KT Or KT/LT > Kc /Lc Or (Kx- Km)/ (Lx - Lm) > Kc /Lc Therefore; a country is revealed to be relatively well endowed in capital compared with labor if and only if; (Kx - Km) >0, (Lx - Lm) >0, (Kx- Km)/ (Lx - Lm) > Kc /Lc…………….. (11) Again, if LT is negative i.e. LT < 0 and KT < 0, then (8) becomes; Kc LT > Lc KT Or KT/LT < Kc /Lc Or (Kx- Km)/ (Lx - Lm) < Kc /Lc Therefore; a country is revealed to be relatively well endowed in capital compared with labor if and only if; (Kx - Km) <0, (Lx - Lm) <0, (Kx- Km)/ (Lx - Lm) < Kc /Lc…………………………….(12)

Finally, we may write a country is revealed to be relatively well endowed in capital compared with labor if and only if one of the following three conditions holds, where Kx, Km, Lx, Lm, Kc, Lc are capital and labor embodied in exports, imports, and consumption:

a) Kx - Km >0, Lx - Lm < 0. b) Kx - Km >0, Lx - Lm > 0, (Kx - Km)/( Lx - Lm) > Kc/ Lc c) Kx - Km < 0, Lx - Lm < 0, (Kx - Km)/( Lx - Lm) < Kc/ Lc

Now, we need to concentrate on the test conducted by Leontief. The empirical tables used in his test are given below;

Tables 1, 2, and 3 contain information extracted from Leontief (1954) and from Travis (1964). Table 1 is Leontief's basic summary table, which reveals that Kx/Lx < Km/Lm. But table 2 indicates that the United States in 1947 was a net exporter of both capital services and labor services. For this reason, the information contained in table 1 does not reveal the relative factor abundance of capital and labor (see b). The appropriate comparison is reported in table 3. Since net exports are much more capital intensive than consumption, the United States is revealed by its trade to be relatively well endowed in capital compared with labor. Therefore; we may conclude that the Leontief’s test was wrong!

9. Explain the Heckscher-Ohlin Model/ Heckscher-Ohlin-Samuelson (HOS) model Heckscher-Ohlin Theorem: “Each country will export the good that uses its abundant factor intensively”. To explain the theorm, we should consider some assumption, these are given bellow; Assumption:

1. There are two countries, two goods, and two factors (or the 2x2x2 model). 2. Technologies are identical across countries. 3. Identical and homothetic tastes are experienced across countries. 4. Factor endowments differ between two countries. 5. Free trade in goods (but not factors) is possible. 6. The possibility of factor-intensity reversals is assumed away. 7. The home country is labor abundant, so that L/K > L*/K* 8. Good 1 is labor intensive. So good 2 is capital intensive 9. The countries engage in free trade. 10. Trade is balanced (value of exports = value of imports). Explanation To prove this theorem, let the factor endowment differences be as L/K>L*/K*, where L*=L, and K*> K. In order to derive the pattern of trade between the countries, we proceed by first establishing what the autarky relative product price is in each country. Since a country will export the good whose free trade price is higher than its autarky price and import the other, autarky price is important.

The 450 line shows homothetic tastes and indifference curves reflect demand. The autarky equilibrium occurs at the point where an indifference curve is tangent to the home PPF, at point A. The price line drawn tangent to the PPF and indifference curve has a slope of (negative) the autarky relative price of good 1, pa = / . Let us now consider the foreign PPF, which is drawn outside the home PPF in the Figure 2.1. In order to determine where the foreign autarky equilibrium lies, let us initially suppose that pa is also the autarky equilibrium abroad. If pa is also the autarky price in the foreign country, then production must occur at the tangency between the price line with slope pa and the foreign PPF, or at point B . However foreign consumption occurs at point C because of homothetic test instead of at point B . Therefore, it is clear that the relative price of good 1 is different in foreign country than that of hone country. As the autarky equilibrium prices are different in both countries, there will be scope for mutually beneficiary trade. The trade pattern is described in figure 2.2 bellow;

Let us illustrate the free trade equilibrium, in Figure 2.2. In panel (a) we show the equilibrium at home, and in panel (b) we show the equilibrium in the foreign country. Beginning at the home autarky

Redwan Ahmed, M.S.S, Economics, SUST. Hello:+8801716811466. Skypee: red1eco. E-mail:[email protected]. The Heckscher-Ohlin Model point A, the relative price of good 1 rises at home, p > pa. It follows that production will occur at a point like B, where the price line through point B has the slope p. The home country’s consumption occurs at point C. The difference between production at point B and consumption at point C is made up through exporting good 1 and importing good 2, as illustrated by the “trade triangle” drawn. This trade pattern at home establishes the HO Theorem stated above. In the foreign country, the reverse pattern occurs: the relative price of good 1 falls, pa* > p, production moves from the autarky equilibrium point A* to production at point B* and consumption at point C*, where good 1 is imported and good 2 is exported. Notice that the trade triangles drawn at home and abroad are identical in size: the exports of one country must be imports of the other. In addition to establishing the trade pattern, the HO model has precise implications about who gains and who loses from trade: the abundant factor in each country gains from trade, and the scarce factor lose. This result follows from the pattern of price changes (Pa*>p>pa) and the Stolper-Samuelson theorem.

10. Explain the extended version of the HOV model An extended version of the HOV model: Trefler identified the assumption of equal technologies across countries as wrong assumption and developed the HOV incorporating different technologies across countries. The revised version is known as an extended version of the HOV model. There are two ways that technological differences can be introduced into the HOV model. One approach is to model the productivity of factors in different countries, whereas another approach is to model differences in the factor requirements matrix A. First approach: “All factors in every country differ in their productivities”. In this case the U.S. is considered as the benchmark country, with factor productivities normalized at unity. So let denote the productivity of factor k in country i relative to its productivity in the U.S. In terms of efficiency units, the effective endowment of factor k in country i become . Let A now denote the amount of effective factors needed per unit of output in each industry. We continue to assume that factor price equalization holds in terms of effective factor prices, so with identical technologies, the matrix A is the same across countries. Thus, we continue to measure the factor-content of trade as Fi = ATi. Then the HOV equation (Fi ≡ ATi = Vi– si Vw) is re-written in terms of effective factor endowments as:

………………….(1)

There are MC equations in (1), and M(C–1) productivity parameters. These equations are not independent, however. For any factor k, if we sum (1) across countries i=1… C then we must obtain zero on both sides: exports equal imports for the world, even when measured in terms of factor contents. So we can drop the equations for one country, and we do so for the U.S. This leaves M(C–1) equations in M(C–1) parameters. These equations will be independent “almost everywhere,” i.e. for almost all sets of data on endowments and factor-contents of trade. Second approach: “ The factor requirements matrix Ai differ across countries” while assuming that the factor endowments do not differ in efficiency units. Thus the matrices Ai differ by a uniform amount across countries:

…………………………………..…………….(2)

Which implies Ai = AUS /δi. With δi < 1 , this means that Ai > AUS, so that country i is less productive and requires more labor, capital, and other resources for a unit of production relative to the U.S.. With the assumption (2), we need to re-derive the HOV equation (Fi ≡ ATi = Vi– si Vw). From full- employment, we still have Ai Yi = Vi. We continue to make the assumption of identical and homothetic tastes across countries, so the factor content of trade is computed as:

……..……….(3) To make further progress with (3), let us multiply both sides by δi. On the left, we would obtain δiAiTi = AusTi ≡ Fius . That is, we define Fius as the factor-content of trade for country i, computed by using the U.S. factor requirements matrix. By also multiplying the right of (3) by δi, the matrix Ai appearing in the last term becomes instead δiAi = Aus . Since this term now does not depend on the country i, it can be brought inside the summation on the far right of (3), to obtain

Where the final equality makes use of the full employment conditions in country j=1… C. Substituting these results back into (3), we have therefore derived:

This becomes the statement of the HOV Theorem when we allow for uniform technological differences across countries: the factor–content of trade, measured with the U.S. technology on the left, should equal the relative factor endowments on the right, where these are each adjusted by the technological parameter of each country.

11. Explain the Leontief’s Paradox with criticism. Leontief’s Paradox:

“the country with the world's highest capital-per worker has a lower capital/labor ratio in exports than in imports”. Leontief (1953) was the first to confront the HO model with data. He utilized U.S. trade data for the same year to compute the amounts of labor and capital used in the production of $1million of U.S. exports and imports. His results are shown in Table 2.1.

From the table, we may write; Kx/ Lx = $13,700 and Km/ Lm = $18,200 Thus; Km/ Lm > Kx/ Lx Therefore,we may write that the U.S. imported capital intensive goods and exported labor intensive goods. However the U.S. is technologically advanced country at that time. So the empirical finding is reverse to the H-O theorem. It is known as Leontief’s Paradox! A wide range of explanations have been offered for this paradox: • U.S. and foreign technologies are not the same;

• By focusing only on labor and capital, Leontief ignored land; • Labor should have been disaggregated by skill (since it would not be surprising to find that U.S. exports are intensive in skilled labor); • The data for 1947 may by unusual, since World War II had just ended; • The U.S. was not engaged in free trade, as the HO model assumes.

Theorem (Trefler, 1993) Allowing for all factors in all but one country to differ in their productivities for almost all datasets there will be a solution for productivities such that the HOV equation (

) hold with equality for i=1,…,C, k=1,…,M.

Redwan Ahmed, M.S.S, Economics, SUST. Hello:+8801716811466. Skypee: red1eco. E-mail:[email protected].