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Heckscher-Ohlin Model “Predicts trade across dissimilar countries and in dissimilar goods: it says that labour abundant developing countries will export labour-intensive products such as food and clothing, whereas capital abundant developed countries will export capital-intensive products such as machinery and computers”. (Debraj Ray) Heckscher-Ohlin Model Outline 1. Two goods model 1.1 Assumptions 1.2 Production Possibilities : Combination of Factors 1.3. Production possibilities : Combination of Goods 1.4. Efficient production and consumption in autarky 1.5. What happens to consumption when both countries open to trade? 1.6. Integrated economy equilibrium: division of production 1.7. Integrated equilibrium consumption and trade 1.8. Production and factor price equalization 1.9. Factor prices and redistribution of income inside a country 1.10. Endowment changes (at given factor prices) [ Nice « General Equilibrium » model : goods and factor quantities and (relative) prices ] [Gains 18] [H-O trade 29] [FPE 38] [Stolper-S. 41] [Rybcynski 44] = 5 theorems 2 1. Two goods model 1.1 Assumptions • 2 countries i : North (1) and South (2). • 2 goods j = X and Y. • 2 factors: capital (K) and labour (L). • Factors mobility across industries but not across countries in the medium term. • Perfect competition and price flexibility in goods and factors markets. Prices will be noted by: p ij . • Identical production and utility function in both countries. Both countries share the same knowledge. • Constant returns to scale and decreasing returns of individual factors. 3 1.2. Production Possibilities : Combination of factors • Production function is given by: Q j f j K , L for each good j. As countries have identical knowledge, even when they do not produce the same goods, this production function will be the same for all countries. The constant returns to scale of the production function can be expressed by: f aK , aL af K , L And the decreasing returns of individual factors implies that: f aK , L af K , L The marginal productivity of individual factors is decreasing. 4 • Isoquants: give the combinations of labour and capital needed to produce a certain amount Q of good j=X,Y, for a given production technology. K K QX A QX KA LAX < LAY QY L QY L At A, the same reduction of K, requires a lower increase of L to maintain the production of Y constant than to maintain the production of X constant. Labor is more efficient in Y than in X : Y is “labor intensive” (Y “prefers” L). The form of the isoquants shows that the factor intensity needed to produce each good is different. While the good X is capital intensive good, the good Y is labour intensive. 5 Combination of factors: How to determine the required labour and capital for 1 (monetary cost) unit of each good? Maximize profits. Prices of X and Y are given. Under perfect competition Factors prices, wages w and rental rate (interest rate) r, are given . For the given prices the producer will chose the quantity of labour and capital that minimize the costs : wL rK Isocost K w L r Then, the slope of the isocost is w/ r . 6 Cost minimization : tangency isoquant and isocost For a given output of X (isoquant QX,A), and a given relative factor price w/r, A is the cost-minimizing combination of factors K & L (with cost CX,A= wLA+rKA). K QX,A A B QY -w/r L For a given and equal factor cost, in the graph, A represents the optimum production level of good X, and B represent the optimum level of production of good Y. 7 Expansion of production: maintained proportions of factors for given w/r How can we see the relative use of factors for each goods production? In the expansion line: formed by the tangency points between the isocost (for given w/r) and each isoquant. KX/LX KX K Y LX LY K QX KY/LY Good X is more capital intensive than good Y. QY L 8 Relative factor price changes (w/r ) What happens to the capital intensive good if wages go down? As w goes down the isocost becomes less steep. On a new expansion line we can see that the production process uses labour in a more intensive way than before. however capital intensive good remains as such. K KX/LX (KX/LX)' Factor space w/r w'/r L Note : The capital intensive good remains capital intensive relative to the other good which remains labor intensive. 9 1.3. Production possibilities : Combination of Goods • Efficiency curve: Using the isoquants in a factor endowment space (K,L) - efficient allocations of factors in the production of both goods in one country. - tangency points of the isoquants, - equal marginal rate of substitution of K and L for both goods M K OY N O P QX QY OX L For any point that is not a tangency point of the isoquants there is a way to increase production of one good without reducing production of the other good. 10 •Production possibility frontier: is an curve in the goods space X,Y, that shows all the possible combinations of goods X and Y which use an efficient distribution of factors. It represents the maximal production of one good for a given quantity of the other. And it is formed by the points on the efficiency curve in the factor space K,L (Edgeworth box). QY J K Goods Space A L M QX The slope of the tangent curve in A represents the quantity of Y that must be given up (“paid”) in order to obtain an additional unit of X. 11 Why does the production possibilities frontier have this shape? Because it is more costly to do only one good. As soon as goods have different intensity in the use of factors, there will be a factor that will not be used in all it’s potential when we produce only one good. QY A QX If you free some capital and labor from Y’s production, the production of X will increase substantially using intensively the large amounts of capital freed by labor intensive Y. However the rate of increase in X will decrease as you free more capital from Y (because labor-intensive Y doesn’t have large quantities of K anymore to free up). 12 1.4 Which is the efficient production and consumption in autarky? Consumption of goods: It will depend on consumers preferences. The optimal production choice in autarky is given by the tangency point between the indifference curve of consumers and the production possibilities frontier for a given relative price level. QY YC C Consumers indifference curve. Goods Space -pX/pY XC QX 13 In autarky point C represents production and consumption quantities of goods X and Y. This point given by the tangency between production possibility frontier and indifference curve respects the budget constraint given by: B p X X C pY YC where: p X is the price of good X. pY is the price of good Y. The slope of the budget constraint is given by the relative prices: pX pY 14 Consumption of factors Where can we see the factor consumption? Factor space K,L and isoquants X,Yof goods K Factor Space LY KX OY KY C XC YC -w/r OX LX L The production and consumption decisions in the goods space correspond to tangent isoquants in the factor space (Edgeworth box). For the chosen isoquants, the use of factors for the production of each good X and Y appears reading from each one’s origin, OX and OY. At the tangent isoquants, the relative price (-w/r) of factors (rate of substitution for autarky) appears. 15 1.5 What happens to consumption when both countries open to trade? Countries are not longer bounded by their autarkic production possibilities but by their budget. The budget constraint will be now given by the international prices of goods that are being traded. It takes the form: B pWX QX pYW QY The slope of the new budget constraint is: W p X pYW The new consumption point is given by the tangency between the new budget constraint and consumers indifference curve. While production takes place in the tangency of the new budget constraint and the production possibilities frontier. Under trade production takes place in P’ and consumption in C’, this is possible because the country imports the quantity X’P- X’C and exports Y’P-Y’C. 16 Labor-intensive country (East) : C QY Establishing Gains from Trade in the Goods space C' Production of Y Consumption P' Y'P YC Y’s exports P Y'C of Y Indifference curve X’s imports New budget constraint with W slope: pX W pY -pX/pY X'P Production of X XC X'C QX Consumption of X 17 Where are the gains from trade? According to the new relative prices, consumption will take place on a different indifference curve, that belongs to the same family than the initial one, but corresponds to a higher utility level of consumers. The world relative price will be in between the relative prices existing in autarky: X p1X pW p2X Y p1Y pW p2Y 1 is West, 2 is East : see graph 18 How do endowment differences between countries appear ? -Shape of the production possibility frontier and relative prices Production possibility frontiers in the East and in the West. QY Establishing Comparative Advantage in the Goods Space Identical preferences pX/pY West < pX/pY East PPF-East pX/pY East PPF-West QX -Size of the factor space (Edgeworth box) (see sub 6) 19 Conclusion of graphs: Heckscher & Ohlin Theorem: “A country exports the good which uses intensively its abundant factor, and it imports the good which uses intensively the other factor” N.B. Specialisation in “trade” not in “production” Proof: world prices “between” domestic prices, which were determined by endowments : see previous 2 graphs. 20 1.6. Integrated economy equilibrium and division of production When studying the integrated economy it is necessary to consider the world factor endowment as a starting point to determine where production is going to take place and which consumption level of each good is going to be chosen by each country. To see the world factor endowment we can build an Edgeworth box where both countries factor endowments are represented starting from O1 and O2 for the North and the South respectively. At equilibrium point E, the endowments of the North are represented by O1-L1 and O1-K1 for labour and capital respectively. For the South the endowments are given by O2-L2 and O2-K2. 21 World factor endowment = Sum of countries’ endowments L2 O2 EAST K K1 O1 E K2 WEST L1 L West = “capital abundant” ; East = “labour abundant”. How do endowment differences between countries appear ? -Shape of the production possibility frontier (as seen above 1.5.) -Size of the factor space (Edgeworth box) 22 The efficiency curves and expansion lines of both countries can also be represented in the world endowment box: L2 O2Y A B O1Y K1 O2X C K2 D O1X L1 A and B are the expansion lines of goods Y and X, respectively, in the East. C and D are the expansion lines of goods Y and X, respectively, in the West. From an integrated world consumption view, the countries efficiency curves are inefficient in terms of consumption … 23 The worldwide economy: if the world was a single country and all people had the same preferences, the consumption would not longer be constrained by each countries endowment (E) but by global factor endowment and it could reach Q’: L2 OY Q’ K1 OX E K2 L1 However, a point like Q’ can not be reached by separated endowments. The best option is to choose a production division between two countries under which all factors are fully used, i.e. at point E, but consumers are satisfied better (i.e. obtain quantities Q’). 24 The quantity of factor used ensures the full employment of factors. The division of production replicates the integrated economy: -thanks to constant returns to scale -thanks to an endowment point E within the integrated expansion paths L2 K O2 Q’ K1 E K1X Y1 K1Y O1 K2 X1 L1X L1Y L1 L 25 1.7. Consumption by country at integrated equilibrium and trade Assumptions: • Identical and homothetic preferences. • Goods prices are equal between countries as trade takes place. Consumption will take place according to preferences and budget. Both countries consume both goods in the same proportion (identical preferences), then consumption will take place over the diagonal of the Edgeworth box. The budget constraint is given by the factors income: wLi +rKi of each country i. Under factor equalization prices the budget constraint has equal slope for both countries. Consumption takes place at the intersection of the budget constraint and the Edgeworth box diagonal. 26 L2 K O2 Q’ E K1 K2 X1 K 1X C1X Import C1Y Y1 Y 1 K O1 Gains from Trade in the Factor Space : Consumption outside of Endowment C Export wr L1X LY1 L1 Comparative advantage in the Factor Space : relative factor L endowment The West produces O1-X1 and O1-Y1 of good X and Y respectively; while it consumes O1-CX1 and O1-CY1 of the same goods. This implies that it is a net importer of good Y and a net exporter of good X. 27 Consumption point C will be outside the endowment possibilities of each country: = gain from trade ! Preferences are satisfied better ! Comparative advantage Theorem (Hecksher-Ohlin): (Export according to factor endowment) “A country exports the good which uses intensively its abundant factor, and it imports the good which uses intensively the other factor” Proof : See graph. Note: Production level can be measured along the expansion lines. Then, production of good X in the North is O1-X1and production of Y is O1-Y1. The use of factors can be read in the projection along the axes: O1-K1X and O1-L1X of capital and labour for the production of good X in the West. O1-K1Y and O1-L1Y of capital and labour for the production of good Y in the West. 28 1.8. Production and factor price equalization If factor’s prices are equal in both countries, for given price of goods, the intensity in the use of factors are equal in both countries, and equal to the integrated economy use of factors. We can see this in the Edgeworth box: K O2 Factor price equalization across countries depend upon their endowments. We consider 2 cases: A – E is within the expansion paths at w/r B – E is outside these expansion paths O1 L Through trade, countries produce more of what they do best, i.e. of the goods which use their abundant factor more intensively. This raises the price of this relatively cheap factor and brings it closer to the price of this factor in the country where it is scarce. This trade effect can be strong enough to equalize factor prices. If not, then one country will be unable to produce one of the goods and pressures for factor mobility will remain to try to equalize factor prices and replicate the integrated economy. 29 A. Endowment point E is inside the diversification cone (expansion paths): The division of production can be organized between the countries at identical factor prices, so that both countries keep producing both goods (cfr slide 25, box with division of production). Reminder: graphical presentation of expansion paths for goods (X,Y) at given factor prices (w/r) and factor abundance of countries (1,2) for endowments E1 and E2: K GOODS KX/LX K1/L1 Countries E1 K1 K2/L2 E2 K2 KY/LY -w/r L1 L2 L 30 Production of both goods (rather than full specialization): The West is relatively abundant in capital. If it uses all the endowment for the production of good X (capital intensive good) at given w/r, there will be some labour that will be underemployed (see graph). The country needs to keep producing both goods to ensure the full employment of factors. As the same can be shown for the East at the same relative factors prices (w/r, see previous graph), then there is factor price equalization: East and West can work at the same prices and fully use all their factors. K K1 L1 K X LX E1 K X K1 K Y LY O1 L X L1 L Labour underemployment when country 1 produces X only at given w/r. 31 B) Endowment point is outside the diversification cone If the North is too rich in capital the real constraint will be given by the amount of labour available. It is only going to produce good X, which consumes all the endowment of labour, and leaves K1X-K1 underemployed. L2 O2 K K1 Unemployed capital in West (North) at FPE K2 E K1X O1 L1 L 32 The North is over-endowed in capital as to produce under the price of the integrated economy. The price of capital will have to decrease in order for this economy to use all its endowment. r goes down w/r increases As a consequence the North will keep producing good X, which now becomes more capital intensive than before, but still not as much as if FPE could occur (w/r will stay higher in the capital rich country than in an integrated economy and than in the other country). 33 E1 Capital over-endowment in the North K X' L'X K K1 K X LX Production of X at w/r’ instead of w/r<w/r’ E1 and at K’/L’ > K/L K FPE No production of Y, given at w’/r’ : less output at w’/r’ than at w/r. K Y' L'Y Equal cost (K,L) point : wL+rK = w’L+r’K K Y LY O1 L1 w r' w r L 34 The same situation can be reproduced for the South if it’s endowment point is outside the diversification point. If the South is over-endowed in labour, it can’t produce at the price of the integrated economy. Then, the price of labour will have to decrease in order for this economy to use all it’s endowment. w goes down w/r decreases As a consequence the South will keep producing good Y, which now becomes more labour intensive than before. 35 Labour over-endowment in the South K X LX K K Y LY K2 w' r wr O2 K ' 'Y L' 'Y E2 L2 L 36 The situations discussed in point B will lead to countries specializing in the production of one good only. The North will specialize in the production of capital intensive good, X; and the South will specialize in the production of labour intensive good, Y. When full specialization in production takes place there is no reason for factor prices to equalize across nations. Full specialization happens in 1 country, but need not to happen in both when FPE is not reached (see next slide). Factor Price equalization theorem: If both countries produce both goods, factor price equalization will take place when there is international trade on a perfect competitive market and countries have access to the same production functions. This requires factor endowments that are similar enough Note : Unequal factor prices indicate an inefficiency (See chap. 3). Specialization is then inefficient from a world consumption point of view. 37 Demonstration of FPE and specialization distribution using isoquants and isocosts K Same total production of X, Different factor intensities, same total cost at w/r and w’/r Not same production of Y Equal cost (K,L) point : wL+rK = w’L+r’K Qx at same total cost of X and different w/r and w’/r [QED] (Y can only be sold by low w/r country) Qy -w’/r Q’y -w/r To produce and trade both goods at same price (and cost) than other country, same factor prices required in both countries. Otherwise only one good can be produced at same cost by both. L 38 1.9. Factor prices and redistribution of income inside a country What happens to production and to factor prices when goods price change ? (due to trade opportunities or to change in worldwide preferences) How does production react to the output price shock? Try to increase the production of the good whose price goes up. E.g. when opening up to trade, countries will increase the production of goods that can be exported and reduce the production of those that will be imported. How are resources freed for this production? By freeing capital and labor from the other sector. Suppose, the price of the labor-intensive good goes up. The capital intensive good will free factors, but it will tend to free more capital than labor (because it has more) in such a way that the laborintensive good will use capital in a more intensive way. 39 What happens to the relative price of the factors? The rising price of labor whose demand has increased (to produce more of a labor-intensive good by assumption) will lead to factor mobility and to economizing on this (now relatively scarce) factor in both sectors. Illustration: the giants and the dwarfs Imagine people ranked by their height, and divided in two groups at some cut-off point : the tall ones (the giants) and the lower ones (the dwarfs). Now assume the cut-off point is changed, so that the tallest of the dwarfs moves to the group of the giants. The effect is that the average height in both groups has fallen ! Similarly, the shifting “the most labor one can” from a “capitalintensive” sector to a labor intensive one, leads to a reduction in the labor-intensity of both sectors! 40 Effect on the purchasing power of each factor ? Use perfect competition P=Cost, Assume PY + 10% , PX unchanged, We know W up: How much ? At least 10% allowed by PY + 10% , Must R go down? Yes if W up and PX unchanged, Then W up by more than all prices, R down compared to all prices. Stolper-Samuelson theorem: (relative price theorem) : a relative increase in a good’s price leads to an increase of the income and purchasing power of the factor that is used intensively in it’s production and to a fall in the income of the other factor. This applies, whatever the source of the price change. In North-South trade opening, the scarce factor loses in each country, the abundant one gains (they are the opposite ones in each country). 41 Graphical illustration : Goods factor intensity after reduction of capital intensive good price K K X LX ' K X LX KY LY ' KY w r ' w r LY L 42 Decrease of capital intensive good price in the endowment box. OY K X Y X’ Y’ wr w r ' OX General Equilibrium view : L All change in price (factor and goods) and quantity (factor and goods) are visible and explained in 1 graph ! 43 1.10. Endowment changes (at given factor prices) What happens if factor endowments change? In the case of small open economies it is common that the availability of capital increases. If the goods and factors relative prices remains equal, an increase in the capital endowment leads to an increase in the production of the capital intensive good and reduction of the labour intensive good. Factor quantity theorem (Rybczynski): for given factor prices, an increase in the available quantities of one factor leads to an increase in the production of good that use it on an intensive way. The production of the other good is reduced. Note : Capital is a factor that can be accumulated through savings ! 44 OY K A B OX OX' L Initial production levels: OX-A of good X and OY-A of good Y. Final production levels: O’x-B of good X and OY-B of good Y. 45 5 key results of 2x2x2 model Gains from trade Comparative advantage in good that uses intensively the locally abundant factor (general effect of indirectly exporting the abundant factor through the goods exported) (Heckscher-Ohlin-Vanek) Factor price equalization if both countries produce both goods (Heckscher-Ohlin) Price change in goods benefits to factor intensively used in higher priced goods, and hurts other factor but gains > losses (Stolper-Samuelson) Increase in one factor increases production of good using it intensively and decreases production of other good (Rybczynski) ! Model is static, reality is dynamic : capital and technical progress accumulation… 46