Problem Set 5 - Soluciones del profesor de la magistral PDF

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Soluciones del profesor de la magistral...

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International Economics UC3M Problem Set 5

1. Thanks to proximity and industrial cooperation, France and Germany share the same technology for the production of mobile phones and champagne. These two european countries only differ in their respective factor endowments, where K F = 70 and LF = 110 while K G = 110 and LG = 70. 1/2 Both countries have the same utility function, which is represented by U (Cm , Cc ) = C m Cc1/2 where Cm represents the consumption of mobile phones and Cc represents the consumption of champagne. The production functions are: Qm = min{2Lm , Km } and Qc = min{Lc , 2Kc } where m represents the production of mobile phones. (a) i) Which industry is labor intensive and which is capital intensive? (HINT: As we mentioned in the Magistral session, when the production technology is of type Leontief, if a firm that does not wants to waste any resources (i.e. labor and capital) then it must be the case that 2Lm = Km in the mobile phone industry and that Lc = 2Kc in the champagne industry, from where you can deduct the number of machines per worker needed in each industry, therefore from this information you can deduct which industry is kapital intensive and which one is labor intensive). ii) Which country has a relative abundance in the capital intensive good? iii) Using the H-O Model, which is the pattern of trade that you predict if both economies start trading? ANSWER - i) Looking to the production function, we know that the mobile industry maximises profit when 2Lm = Km while the champagne industry when Lc = 2Kc , therefore Km /Lm = 2 and Kc /Lc = 1/2, which means that mobile phones are capital intensive, while champagne is labor intensive. ii) From the data provided we can see that K G /LG > K F /LF , therefore Germany has a relative abundance in Kapital. iii) The H-O theorem will predict the both countries will benefit from free trade if Germany exports mobile phones and France Champagne. (b) Find the close economy equilibrium allocation of capital and labor, and the equilibrium quantities. HINT: You will have to solve a linear system of 4 equations and 4 unknowns (you know how to do this: just substitute one equation inside the next one until you have only one unkown left). The four equations are this: two come from the efficiency use of resources (i.e 2Lm = Km and Lc = 2Kc ), and the other two come from the resources constraint. For example, the capital used in France in both industries must be equal to 70 units (i.e. Kc + Km = 70. You do the same for labor market and now you have a system of 4 equations and 4 unknowns. ANSWER - We start with German case. We know that in Germany it must be the case that Km + Kc = 110 and that Lm + Lc = 70, also Km /Lm = 2 and Kc /Lc = 1/2. Which is system of 4 unknown and 4 equation. Solving the system we get: Km = 100, Kc = 10 and that Lm = 50, Lc = 20. Then production is: Qm = min{2Lm , Km } = min{100, 100} = 100, Qm = 100. Similarly, replacing the data in the production function champagne, we see that of Qc = min{Lc , 2Kc } = min{20, 2 × 10} therefore Qc = 20. Is important to notice that in this resource allocation no resources are been wasted in production (firms maximize profit) since (Km /Lm = 2 and Kc /Lc = 1/2) and the we satisfy resource availability Km + Kc = 110 and Lm + Lc = 70. For France, since the data is symetrical, there is no need to make any calculations (if you want, you can do it in order to practice), the results are the same but reverse, where QFm = 20 and QcF = 100

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(c) Find the autarchy equilibrium relative prices, and prove that at those prices the economy is at equilibrium. HINT: Find GDP and give all that income to a representative consumer (just as we did in Ricardo), now we to derive the demand, but we know (as we also knew from the Ricardo Model exercise) that for this utility function, demand of good x is equal to income divided by two times the price (Dx = Y /(2Px ). The last thing you have to find is the relative prices that make supply equal to demand (supply was already calculated in question a)) ANSWER - Find first GDP (we are assuming a representative consumer), where Y = GDP = Pm 100 + Pc 20, we know that demand for mobile phones is equal to Dm = Y /2Pm , we also know that Qm = 100. Therefore, equating supply with demand, where Dm = (Pm 100 + Pc 20)/(2Pm ) = Qm = 100 and solving for the equilibrium relative prices, we find that the equilibrium price Pm /Pc = 1/5. If there is equilibrium in the mobile market then there is also an equilibrium in the champagne market. In any case, it is easy to verify that indeed Pm /Pc = 1/5 is an autarchy equilibrium price in both markets. For France, because of symmetry, the result is Pm /Pc = 5, but if you want to do it, you can verify that these is indeed the case. (d) Find the equilibrium relative prices if both countries engaged in free trade. Notice that for this question you must find the equilibrium relative PRICE. To find it you have to make exports equal to imports and solve por Pm /Pc (not be surprisingly you will find that at equilibrium Pm /Pc = 1). Find the equilibrium quantities (in production and consumption) and describe the pattern of trade. HINT: Exports is production minus consumption, where data for production you know it already: is the same that in autarchy, which might seem surprising, but look to the PPF when there is a Leontief technology (look to the slides from last class), besides that we know that the set of 4 equations that determine production remain the same under free trade or autarchy, thus the production levels will not change. Consumption you know: is the formula for demand that depends on prices. ANSWER - By symmetry, it must be the case that in France Qc = 100 and Qm = 20. Now we proceed to calculate the open economy case, where it must be the case that exports are equal to imports. Choose the price Pm /Pc = 1 as a CANDIDATE for free trade equilibrium price . Substitute into the demand function and we find that for both countries Dm = 60 and Dc = 60. The production levels are the same under close economy and free trade since the system of 4 equations and 4 unknowns does not changes with prices (in class we say the PPF is like a square where both country maximize GDP in the same corner). Thus is easy to verify that Pm /Pc = 1 is a free trade equilibrium where the pattern of trade is: Germany exports 40 mobile phones and imports 40 bottles of champagne. Notice that the question is asking to calculate the equilibrium, which is easy: just makes exports equal to imports and solve for Pm /Pc . For example, in the mobile phone industry it must be the case that: Xm = Mm where, G − DG F F − QF which means that 100 − DG Qm m M = D m − 20 now substitute the M = Dm demand functions for both countries and solve for the relative price. (e) Do both countries are better off under free trade? HINT: Substitute the data for consumption in the Utility function and verify if the utility increases when the economy opens to trrade. ANSWER - Yes, with countries benefit form free trade. Before trade U (Cm , Cc ) = 1001/2 201/2 = 20001/2 , and under free trade U (Cm , Cc ) = 601/2 601/2 = 36001/2 . Also is important to notice that we have produced a welfare improvement with free trade in the following scenario: same technologies, same preferences, and only a difference in relative abundance of factors of production, which was our objective.

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(f) Are these results consistent with what the H-O Model might predict? ANSWER - Yes, the results are consistent. Both countries are benefit for free trade while exporting the good which is intensive in the factor of production where they have a relative abundance. That is, Germany has a relative abundance in capital and is exporting mobile phones. (g) For this economy (Germany vs France), who is better off and who is worst off under international Trade? Explain this interesting result. ANSWER - Notice that production does not changes with FREE TRADE. This result is not very surprising since the PPF is not concave, neither a straight line like Ricardo, is something very close to a square It is not exactly a square, but it has a corner and when maximizing GDP, they do it in the same corner under open or closed economy.. In any case, from the previous question we know that the system of 4 equations has as unique solution, regardless of the price level. Well, since production does not changes, demand for labor (or capital) does not changes, therefore the RELATIVE returns the should not change. Then, if production has not change, how is possible that in both countries agents are better off ? It is because the terms of TRADE have improve. The mobile phone industry will receive more champagne for one phone, in that sense they are better off, and viceversa with champagne (they receive less phones). In any case, the GDP in terms of champagne has increased.

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