Problem Set 2 - Solutions PS2 PDF

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International Economics Universidad Carlos III The Heckscher-Ohlin model 1. Consider a world with two goods (beer and tulips). There are two countries (Belgium and Holand) which have identical technolgies and preferences. Assume that the production of tulips is relatively labour intensive while the production of beer is relatively capital intensiive. Assume that in a free trade equilibrium , Belgium produces only beer whereas Netherlands produces both the goods. a) What can you say about the relative endowments of the two countries? Which Trade theorem are you using to answer this question? Given that tulips are labour-intensive and beer is capital-intensive, and given that Belgium specializes in beer (complete specialization) and the Netherlands in tulips (partial specialization), Belgium must be relatively capital-abundant and the Netherlands must be relatively labour-abundant. This is simply restating the Hecksher-Ohlin theorem. b) There is free capital movement between countries of the European Union. Will there be any movement of capital between the two countries? Given that Belgium is fully specialized in beer, the conditions for factor price equalization do not hold. Especially, the capital/labor ratio in Belgium is too high so that full specialization is reached before factor prices completely converge. See Figure 1 below.

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Since in equilibrium w/r remains higher in Belgium than in the Netherlands, we know that wB > w N L and r B < r N L . Capital will therefore flow from Belgium to the Netherlands. c) If your answer to part (b) was yes, in which direction is capital going to flow? And what will be the effect of this capital movement on production in both countries? Which Trade theorem are you using to answer this question? As pointed out in (b), capital will flow from Belgium to the Netherlands. The effect of an increase in capital in the Netherlands will be an increase in the production of beer and a decrease in the production of tulips (see diagram below). This is nothing other than the Rynczynski effect. In Belgium, though, the decrease in capital will not get translated into a RELATIVE change in production, since Belgium is fully specialized in beer. See Figure 6 below.

d ) What will be the effect of capital mobilty on factor prices in the two countries? The returns to capital will obviously converge if capital is mobile. Interestingly, wages will also converge. To see this, consider the following. If returns to capital in the beer industry converge, both countries must be using the same capital/labour ratio to produce beer; if they use the same capital/labour to produce beer, wages in the beer sector must be the same in Belgium and the Netherlands. Given, moreover, that wages always equalize across sectors in each sector, we can conclude that Belgian and Dutch wages have converged. 2

e) If in addition to capital mobility both countries decide to allow for Labour mobility, is there going to be migration of labour? If yes then in which direction? No. Labor will not migrate.Indeed, given our answer in (d), capital mobility is enough to ensure wage convergance. Since wages equalize across countries, nobody has an incentive to migrate. f ) ”The persistence of regional inequalities is much worse in Europe than in the U.S. beacuse of the lack of labour mobility”. Discuss this statement in light of your previous answers. This is not entirely obvious. Capital mobility would be enough to eliminate regional differences in the context of the HO model 2. Consider two countries (Spain and Romania), two goods (textiles and cars), and two factors of production (skilled and unskilled labour). Romania is relatively abundant in skilled labor, and textiles are relatively intensive in the use of unskilled labour. Both countries use the same technologies. a) In the case of Spain, which group will be in favour of free trade between the two countries? And which group will be in favour of free migration? Use a graph to answer this question, and explain. Denote Spain as Home and Romania as Foreign (∗). Skilled labour as the capital factor and unskilled labour as the labour factor. Cars as the capital-intentive good and clothes as the labour-intentive good.

PT PC RS*

P

PC*



P

PC



* T

T

RS

closed

closed l d

RD=RD* QT Q*T ; QC Q*C

Figure3

Closed economies: Then, since Romania is capital abundant (skilled workers) and cars are capital-intensive, Spain’s relative supply of clothes will be to the right of Romania’s relative supply of clothes, such that the relative price of clothes is lower 3

in Spain than in Romania. As the consumers have identical preferencies in the two countries, the relative demand curve is the same for both countries. See figure above (T is the clothes sector and C is the car sector) Free trade: Spain will be specialized in producing clothes and Romania will be specialized in producing cars, since in absence of trade (PT /PC )closed < (P ∗T /PC∗ )closed (but we don’t have full specialization, only tendency of specialization). The new world relative price will be in the between of the relative prices that the countries had before trade: (PT /PC )closed < (P TW /P CW )open < (PT∗ /PC∗ )closed According to Stolper-Samuelson theorem: Free-trade increases the real rate of return to the country’s abundant factor an reduces the real rate of return to the country’s scarce factor. Then, in Spain the clothes sector will be in favour of the free-trade since the relative price of the exported good (clothes) is increased. If we allow for migration, labour (unskilled workers) will migrate from Spain to Romania because of the difference in wages. b) Explain why (or why not) will the same group favour free trade and the absence of barriers to migration. It is the same group that is in favour of the free-trade and the absence of barriers in labour migration. Let us see the two policies separately: Free trade ⇒ the real rate of return for labour (unskilled workers) increases in Spain. Gains for the unskilled workers. Free mobility of labour ⇒ the unskilled workers of Spain want to move to Romania where the wages are higher. Although both policies give the same result: equalization of factor prices ⇒ trade and labor migration are substitutes. c) How does free trade and free migration affect the incentive of Spanish workers to acquire skills? Explain. According to the theorem of factor price equalization, free-trade tends to equalize absolute and relative factor prices in the two counties when the three conditions are satisfied. (This explains why we won’t have migration of production factors but only trade of goods.) So after trade the relative wages of spanish workers will be higher than it was before trade. Workers loose incentives to get more education in order to be skilled labor and to have more gains from work. The same thing happens when we allow for labor mobility since unskilled workers can migrate to the other country and achieve higher wage.

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1/3 3. The production function of furniture in Spain is : YF = KF LF . The production function 1/2 1/2 of steel is: YA = K S LS . The relative price of steel is pS /pF = 1. The endowment of labour is L = 1000 and the capital endowment is K = 1000.

a) Calculate the production of furniture and of steel in Spain. The problem amounts to maximizing the value of output, subject to the production possibility frontier. In other words, m´ax

KS ,LS ,KF ,LF

s.t.

pF QF + pS QS 2/3

1/3 QF = K F LF 1/2

QS = K S LS1/2 KS + KF = 1000 LS + LF = 1000 Normalize the price of furniture pF = 1. In that case, pS = 1. Substitute all the constraints into the maximizing function. This gives us 1/2

1/2 m´ax (1000 − KS )1/3 (1000 − LS )2/3 + K S LS

KS ,LS

The two first order conditions are 1 −1/2 1/2 1 (1000 − KS )−2/3 (1000 − LS )2/3 = K LS 3 2 S 1 1/2 −1/2 2 (1000 − KS )1/3 (1000 − LS )−1/3 = K L 3 2 S S

(1) (2)

Dividing the first condition by the second condition gives us 1 1000 − LS LS = 2 1000 − KS KS

(3)

Replacing (3) into (1) allows us to solve for LS

1 3

    LS 2/3 1 LS 1/2 2 = 2 KS KS 6  3 KS ֒→ LS = 25/3

Now substitute LS by this expression in (??). This allows us to solve for KS .

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(4)

 6 6  3 3 KS 5/3 1 1000 − 25/3 KS 2 = 2 1000 − KS KS ֒→ KS = 595,336 (5) We can now easily determine KF = 404,664, LS = 423,828 and LF = 576,172. Substituting these values into production gives us QS = 502,315 and QF = 512,153. b) Compute the relative wage (wage relative to rental price of capital). Compute the real wage in terms of steel and in terms of furniture. The w/r ratio is equal to the ratio of the marginal product of labor to the marginal product of capital. It can be computed in the furniture or in the steel sector. In the steel sector it is equal to KS /LS , in the furniture industry it is 2KF /LF . Using the numbers from (a), both give an expression of 1.40. The real wage in terms of steel is the marginal product of labor in the steel sector, 1/2 −1/2 i.e., 1/2K S LS . This is equal to 0.59. The real wage in terms of furniture is the same because in this example both prices are the same. c) Now suppose the relative price of steel rises to pS /pF = 1,05. Compute the real wage in terms of steel and in terms of furniture. To start, you need to follow the same procedure as in (a). The only thing that changes is that when normalizing pF = 1, then pS = 1,05. The rest is the same. This gives the following numbers KF = 48,18, LF = 91,93, KS = 951,82 and LS = 908,07. The real wage in terms of steel is the marginal product of labor in the steel sector. This gives 0.51. The real wage in terms of furniture is the marginal product of labor in the furniture sector. This gives 0.54. d ) Compare the results in (b) and (c) and relate this to the Stolper-Samuelson theorem. The real wage goes down both in terms of steel and in terms of furniture. This is the result of Stolper-Samuelson. When the relative price of steel goes up (from 1 to 1.05), the real return to the factor that is used intensively in the steel industry (capital) increases, and the real return to the factor that is used intensively in the furniture industry (labour) decreases.

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4. When the EU-15 expanded towards the East of Europe, they decided to proceed in two phases : First, they introduced free trade and then later the free movement of labour.Using the Heckscher-Ohlin model discuss if it made sense to proceed in this manner. Use graphs and diagrams to illustrate your answer.

We can analyse the decisions of EU-15 on how to expand in East Europe by using the Heckscher-Ohlin theorem (see in figure above) and the factor price equalization theorem. In order to be applied the latter one needs three conditions to be satisfied: (1) same technologies across countries, (2) no full specialization and (3) no transport costs. We can see that only the second condition is satisfied across the countries of Europe. So only with free trade we don’t achieve convergence of relative and absolute wages of the factors in the economy. Then the free movement of workers can be used in order to achieve the convergence.

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