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Unformatted text preview: ECON‐ENVECON C181 – International Trade Problem Set 2 Due Tuesday March 15 Problem Set 2: DUE AT THE BEGINING OF LECTURE TUESDAY, March 15th Consider two countries that differ only in the composition of their labor force (the share of skilled to unskilled labor). In country “A”, 45% of the labor force is skilled, while in country “B”, only 25% of the labor force is skilled. The two categories of labor are the only factors of the economy. Note that in this simplified model, we consider that it is not possible to train and increase the share of skilled workers. The shares are thus fixed. There are only two goods: cloth (C) and microchips (M). Both countries have the same technology: It takes 10 hours of skilled labor (LS) and 10 hours of unskilled labor (LU) to produce a ton of microchip. You need 5 hours of unskilled labor and one hour of skilled labor to produce one ton of cloth. The production factors are not substitutable. Assume there are 10,000 inhabitants in each country, and that the whole population is part of the labor force. a) Graph an isoquant of the microchip industry. Remember that the factors are not substitutable: LS Qm = 2 20 10 Qm = 1 10 20 LU ECON‐ENVECON C181 – International Trade Problem Set 2 Due Tuesday March 15 b) Draw the production possibility frontier for each country. Make sure to identify the intersection points and kinks. Country A Country B ‐ 4,500 skilled workers (LS) ‐ 2,500 skilled workers ‐ 5,500 unskilled workers (LU) ‐ 7,500 unskilled workers Qc Qc 2,500 4,500 1,500 1,100 Q m Qm 450 550 250 750 Legend: Skilled labor constraint Production possibility frontier Unskilled labor constraint Qc Qc 2,500 4,500 Qm = 125 Qc = 1,250 Qm = 425 1,500 Qc = 250 1,100 Qm Q m 250 450 550 750 c) Assuming that both countries locate at the kink of their PPFs (nice and well behaved social utility curves), give an interval for the price of microchips in terms of cloth. Qc The PPF is kinked since both factors are limiting production at some point. The price of microchips in terms of 1,500 cloth will lie between the values of the two slopes (that is between 2 and 10) in both countries. Qm 250 ECON‐ENVECON C181 – International Trade Problem Set 2 Due Tuesday March 15 d) Assuming preferences are identical in both countries, in which country would you expect the price of microchips in terms of cloth to be higher? Why? The kink on A’s PPF is lower and to the right of B’s. If social indifference curves are the same in both countries, we would expect them to hit the kink with a greater slope (in absolute value) in B than in A. Hence we suspect that the relative price of microchips is higher in B. e) From now on, assume that the resulting price of microchips in terms of cloth in country B is 8 (this should be coherent with your answer to question d) and that it is only 4 in A. Calculate the wage of qualified workers relative to unskilled workers in both countries. (You can use assumptions we made in studying the Heckscher‐Ohlin model – please state the ones you use). As we assumed in class, labor is perfectly mobile between industries, and the factor markets work perfectly. We can calculate the wage ratio in each country between the skilled and unskilled workers, using the fact that in different industries the same level of skills should receive the same salary. In country A: ‐ We know that Pm = 4 x Pc ‐ In a competitive market, the price of a good equals the marginal cost of production ‐ Producing a unit of microchips costs 10 units of skilled labor (each paid ws) and 10 units of unskilled labor (each paid wu). Producing a unit of cloth costs 5 units of unskilled labor and 1 unit of unskilled labor. ‐ Hence Pm = 10 x ws + 10 x wu ‐ Pc = 1 x ws + 5 x wu ‐ We can therefore solve: 10 x ws + 10 x wu = 4 x (1 x ws + 5 x wu) . ‐ In country B: ‐ 10 x ws + 10 x wu = 8 x (1 x ws + 5 x wu) ‐ 2 ws = 30 wu 15 ‐ f) When both countries open up to trade, the price of microchips in terms of cloth should equalize to some intermediate level. Assume the world price of microchips relative to cloth is 6. What is now the wage of skilled workers relative to unskilled workers? ws 5 wu g) Who benefits from trade? Who loses? (Hint: note that for this question, you cannot simply look at the new relative wages: indeed, wages changed, but prices changed as well! You must look at the purchasing power of the new wages). What theorem does this exemplify? Take shirts as the numéraire. A’s production before trade was 425 units of microchips and 250 units of cloth, and the relative price of microchips was 4. Hence the production of A was worth 250 + 425*4 = 1950 units of cloth. This income was distributed among the workers, skilled and unskilled. 5,500 1950 4500 We solve the system: 3 5 ECON‐ENVECON C181 – International Trade ⇔ .15 .25 Problem Set 2 Due Tuesday March 15 Similarly, in country B, the production before trade was 125 tons of microchips for 1250 tons of cloth, with a relative price of microchips equal to 8. The production was worth 1250 + 8*125 = 2250 tons of cloth. This income was distributed among workers: 2500 7,500 2250 15 .05 ⇔ .75 With trade now, the world production is 550 tons microchips and 1500 tons of cloth, and the world price is 6 tons of cloth for one ton of microchips. The world production is thus worth 1500 + 550*6 = 4800. The relative wage is 5. 13000 4800 7000 5 .10 ⇔ .50 As indicated in the Stopler‐Samuelson theorem, the owners of the abundant factor gain from trade while the owners of the other factor loose. Exercise 2: Assume France is producing only wine and cheese, which both necessitate labor but different kinds of capital (vine for wine and goats for cheese). Labor is perfectly mobile between both sectors. A disease (phylloxera) spreads and destroys 50% of the French vines (oh, no!!!). Explain what happens to the repartition of the labor force and to the wages (use a graph and write a short explanation). Y=f(K0,L) Wine Y=f(K0/2,L) Labor ECON‐ENVECON C181 – International Trade Problem Set 2 Due Tuesday March 15 The reduction in capital (goats) led to a sharp fall in the marginal productivity of labor for every level of labor used (the slope of the production function). MPL cheese MPL wine Labor There are now fewer workers in the wine production sector (they are moving to the cheese sector). At the same time, the wage of the workers is reduced (as the equilibrium MPL is lower). Exercise 3: Go back to the preceding exercise. Now, France is a relatively goat‐abundant country. It decides to engage in trade with the rest of the world. Which of the following sentences seem true to you? A. Workers earn less, vine owners earn more, goat owners earn less B. 50% of the goats are slaughtered to restore the proportions with the vines C. Workers earn more, vine owners earn less, goat owners earn more D. France exports cheese and wine. E. France exports its students to promote French wine in the PSs they write in the US F. France exports wine G. Workers earn less, vine owners earn less, goat owners earn more H. France exports cheese I. Workers earn more, vine owners earn more, goat owners earn less J. French wine is still bought all over the world because it tastes incredibly good Exercise 4: In two lines, explain the main difference between the Ricardian Model and the Heckscher‐Ohlin model? The Ricardian model assumes differences in technology between countries. The Heckscher‐Ohlin model relies on differences in factor endowment to explain trade. ...
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This note was uploaded on 03/18/2011 for the course ECON 162 taught by Professor Hanemann during the Spring '07 term at Berkeley.
- Spring '07