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problem_set_1.pdf
ECO 441—Fall 2014 Prof. Miguel A. Iraola
Problem Set #1: Ricardian Model of Comparative Advantage
(Due date Monday, Sep. 22nd) Note: Please write your final answers in the spaces provided. You may show your work in the extra space provided here or attach extra pages if you need more room. 1. [20 points] Consider a world in which there are two countries: Big Industrialized Country (BIC) and Small Developing Country (SDC). BIC has a labor force of 500,000 and SDC has a labor force of 80,000. There are two types of goods in this world—food (F) and manufactures (M), and they are both produced using only labor. The technology for producing each of these goods in each country is described by the unit labor requirements in the following table:
Food Manufactures BIC 2 5 SDC 4 20
The world relative demand for food is given by: !! !!
= ! ! − !!
!!
(a) Sketch the production possibilities frontier (PPF) for each country here. Label the intercepts.
BIC QF
QM
SDC QF
QM
Name __________________________
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(b) Calculate the opportunity cost and relative autarky price of food in each country. Then determine the goods in which each country has an absolute and comparative advantage. Record your answers in the table below.
BIC SDC Opportunity CostF (PF/PM) in autarky Absolute Advantage in: Comparative Advantage in:
(c) On the graph below, construct the world relative supply curve describing the amount of food produced relative to the amount of manufactures. (Be clear about the intercepts, the points at which the RS curve is bent or kinked, and the point at which it intersects the relative demand curve RD).
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.1 0.2 0.3 0.4 0.5
𝑄! 𝑄!
𝑹𝑫: 𝑄! 𝑄!
= 1 2 − 𝑃! 𝑃!
𝑃! 𝑃!
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(d) Assuming the countries do trade, will they completely specialize? Using your answers from (b) and (c), briefly explain why or why not. • What will the pattern of specialization be? BIC produces ______________ SDC produces ______________ • What will the world relative price be? 𝑷𝑭 𝑷𝑴
𝑾𝒐𝒓𝒍𝒅 = ______________
(f) Sketch and label the consumption possibility frontiers after trade on the graphs in part (a). (g) Suppose BIC considers SDC’s ruling elite to be brutal dictators, and to punish them, BIC refuses to trade with SDC. Leaving aside the question of whether this would in fact weaken SDC’s rulers, would it reduce SDC’s consumption possibilities? Yes / No Would BIC sacrifice its own consumption in doing so? Yes / No
Name __________________________
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2. [14 points] Suppose that SDC from Problem 1 is able to increase its productivity in Food production and reduce its unit labor requirement to 2 labor-hours per unit of output. Assume all other technology and labor endowments in BIC and SDC remain the same as they were in Problem 1.
(a) Recalculate (if necessary):
BIC’s autarky price of food SDC’s autarky price of food BIC’s absolute advantage is in: SDC’s absolute advantage is in: BIC’s comparative advantage is in:
SDC’s comparative advantage is in:
QF under complete specialization QM under complete specialization World relative price of food
(b) Under these conditions, would BIC be sacrificing consumption if it refused to trade with SDC? Why or why not? (c) Is BIC better off after SDC’s productivity increase? (Argue intuitively, based on what happens to BIC’s range of choices.) (d) TRUE or FALSE (Explain your answer briefly). Problems 1 & 2 demonstrate that a country does not benefit from trade when it has an absolute advantage in all goods.
Name __________________________
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3. [10 points] In a Ricardian world, with labor the only paid factor of production, the following table gives the constant labor requirements per unit of producing different commodities in countries X and Z. Airplanes(A) Bicycles(B) Fertilizer(F) Radios (R) Shoes (S) T-Shirts(T) Country X
10,000 30 20 20 10 18
Country Z
120,000 45 225 180 15 18
(a) Suppose the wage rate in country X is wX =$10, in country Z is wZ =$2, and that there are no transportation costs. In a free-trade equilibrium: • Which goods are produced only by country X?
• Which goods are produced only by country Z?
• Which goods, if any, may be produced by both countries but may still be traded?
• Which goods, if any, are non-traded?
(b) Now suppose that it costs $1,000 to transport one airplane, and that it costs $40 to transport one unit of any other good from one country to the other. Now: • Which goods are produced only by country X?
• Which goods are produced only by country Z?
• Which goods, if any, may be produced by both countries but may still be traded?
• Which goods, if any, are non-traded?
Name __________________________
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4. [6 points] Assume that labor is the only factor in the production of electronics and clothing in the U.S. and Mexico. Suppose that unit labor requirements in each industry, for each country, is as shown in the following table:
Computer Chips
Shirts
U.S. 2 4 Mexico 20 10
Suppose that the wage rate in the U.S. is wUS = 5 $/hr. (a) For what range of Mexican wages will the two countries trade? (i.e. what is the range of possible equilibrium wages in Mexico under perfect competition and free trade?) (Express in terms of $.) Suppose that Mexican labor productivity doubles in both industries. (b) Now what is the range of Mexican wages under free trade and perfect competition? (c) TRUE OR FALSE (Explain your answer briefly). After the rise in Mexico’s productivity, Mexico will have a cost advantage in both industries, and therefore, the U.S. will not be able to export anything unless U.S. wages are reduced.
