Problem Set 1 Solutions PDF

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These are the solutions of problem sets I had to do as part of my course in international trade in Columbia University...

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Problem Set 1 Answer Key 1. Suppose there are only two countries in the world: France and Italy. Suppose further that there are only two goods in the world, bread (B) and cheese (C). Assume that the production possibilities frontier (PPF) for both countries is linear, and can be represented by the following equations: PPF Italy: 1000 = 10C + 2B PPF France: 200 = C + B a. Please draw each country’s PPF. What is the slope of each PPF if C is on the vertical axis? What does this slope measure? See below. The slope measures the opportunity cost of bread in terms of cheese. The opportunity cost is how many units of cheese the country must give up in order to produce an additional unit of bread.

b. What is the opportunity cost of producing a unit of Bread in France? What is the opportunity cost of producing Bread in Italy? The opportunity cost of producing one unit of bread in France is 1 unit of cheese. The opportunity cost of producing one unit of bread in Italy is 1/5th of a unit of cheese.

c. Which country has comparative advantage in Cheese? In Bread? France has a comparative advantage in the production of cheese (only costing 1 unit of bread to Italy’s 5) and Italy has a comparative advantage in the production of bread (only costing 1/5th of a unit of cheese to France’s 1). d. Find the interval between which the relative price of Cheese must fall for trade to be mutually beneficial. The relative price of cheese must fall between the two extremes of Italy and France’s opportunity costs for cheese. PCF < PC/PBW < PCI à. 1 < PC/PBW< 5. e. Under what condition is France indifferent to trade? Does Italy still benefit from trade in this case? Why or why not? France is indifferent to trade when PB/PC=1. This world relative price is the same as what France would face domestically under autarky. Therefore France can consume the same quantities of bread and cheese under autarky and under trade. Italy still benefits from trade because, under autarky, PB/PC=1/5. With the superior world relative price of 1, Italy will specialize in the production of bread which it can sell on the world market at the much more lucrative price of 1. As depicted below, Italy’s consumption possibilities frontier (CPF) is outside its PPF for every point other than the production point.

CPF is beyond PPF, allowing Italy to consume more under trade than under autarky.

CPF = PPF (France is indifferent to trade)

2. The following table shows the output per 400 days of labor input in each of the two commodities in each of the two counties:

Germany Brazil

Cars (C) 10 4

Airplanes (A) 2 1

a) Which country has absolute advantage in the production of cars? Airplanes? Germany has an absolute advantage in the production of both cars and airplanes (10>4 and 2>1). b) How many days of labor are needed to produce 1 car in Brazil? 400L can produce 4 cars à. 1 car can be produced by 100 days of labor input in Brazil.

c) What is the opportunity cost of producing 1 airplane in Germany? The opportunity cost of producing one airplane is 5 cars in Germany. d) Which country has comparative advantage in the production of cars? Airplanes? How does this compare with your answer in part “a”? Germany has a comparative advantage in the production of cars and Brazil has a comparative advantage in the production of airplanes. While Brazil has an absolute advantage in the production of neither cars nor airplanes, it has a comparative advantage in the production of airplanes. e) Assuming German consumers need both cars and airplanes, what is the relative price of planes (PA/PC) under autarky in Germany? PA/PC = 5 in autarky. f) Find the interval in which the relative price of cars must fall for trade to be mutually beneficial. Discuss in detail, why countries gain from trade in this case. 4 < PA/PC < 5. At any world relative price between 4 and 5, both Germany and Brazil can specialize in the good they enjoy a comparative advantage and trade on the world market for the other good at a superior relative price than their opportunity cost under autarky. In so doing, both countries are able to separate their CPF from their PPF, gaining from trade by consuming more while producing the same. 3. (Adapted from Krugman 7th Edition, Ch. 3: #1-3) Home has 200 units of labor in its economy. It can produce only two goods, milk (M) and wool (W). The unit labor requirement in milk production is 2, while in wool production the unit labor requirement is 4. a) Graph Home's PPF.

b) What is the opportunity cost of milk? To produce 1 unit of milk, Home must give up ½ unit of wool.

c) Assume that Home is closed to trade (i.e., in autarky). Furthermore, assume Home consumers' derive no utility if only one good is produced. What would the relative price of milk be? How do we know for certain that this is the autarky price? The relative price of milk would be the same as the opportunity cost of milk under autarky: ½. We know this must be the case because it is given that consumers demand a combination of both goods. The relative price of PM/PW represents the consumption abilities of the population while the unit factor requirements (aLM/aLW) represent the production abilities (as well as the opportunity cost). If the relative price and opportunity cost are not equal (say the relative price is 4 and the opportunity cost is 2), only milk will be produced and everyone will be trying to trade it for 4 wool. But no one will be producing wool because they can only trade it for ¼ of a milk instead of the ½ milk it would cost in production. Since the economy demands both goods but only milk is being produced, the relative price of milk will decline until it matches the opportunity cost. d) Now assume that an adventurous citizen of Home sails off on a raft and discovers another economy, Foreign. After meeting with the tribal leaders of Foreign, the sailor informs the Home government that Foreign has a work force of 100. As it turns out, Foreign's economy also only produces milk and wool. The unit labor requirement for milk in Foreign is 4 and for wool it is 5. Graph Foreign's PPF.

e) Given this information for Home and Foreign, graph the world relative supply curve. Clearly label both axes and intercepts.

f) The world relative demand curve takes the following form: The relative demand for milk in terms of wool = 2 - (price of milk / price of wool). Graph the relative demand curve.

In red above. g) What is the equilibrium relative price of milk? PM/PW = ½; QM/QW = 2 – ½ = 3/2 h) Describe the pattern of trade. Home will produce milk and wool; Foreign will produce only wool. While Foreign will specialize in wool, it cannot meet world demand and so Home will produce both goods. If Home does not do this, the market will experience an under-supply of wool and the relative price will adjust accordingly. Home firms will react to the changing prices and produce more wool. In so doing, the relative price of wool will decline (the relative price of milk will increase) until the market reaches equilibrium. Foreign will export wool and home will export milk. i)

Demonstrate graphically the gains from trade for Home and Foreign....