Question

Suppose Home has 2,000 units of labor available. It can produce two goods, clothing (C) and wheat (W). The unit labor requirement in clothing production is 5, while in wheat production it is 2.

Home is as described above. Now suppose there is another country, Foreign, with a labor force of 3,000. Foreign’s unit labor requirement in clothing production is 2, while in wheat production it is 4.

Please answer through a to d.

a. What and how much do Home and Foreign produce, respectively, when the world relative price of clothing is 0.5, i.e., p_C/p_W = 0.5.

b. What is the range for the relative price of clothing under free trade?

c. Suppose the world relative price of clothing under free trade is 2, i.e., p_C/p_W = 2. Describe the pattern of trade between Home and Foreign.

d. Show that both Home and Foreign gain from trade at p_C/p_W = 2.

Answer 1

a) Unit labor requirement in Home for Clothing production = 5

Unit labor requirement in Home for wheat production = 2

Opportunity cost of Clothing in Home = 5/2 = 2.5

Opportunity cost of Wheat in Home = 2/5 = 0.4

Unit labor requirement in Foreign for Clothing production = 2

Unit labor requirement in Foreign for wheat production = 4

Opportunity cost of Clothing in Foreign = 2/4 = 0.5

Opportunity cost of Wheat in Foreign = 4/2 = 2

Since Home has a lower opportunity cost in the production of wheat, it has a comparative advantage in the production of wheat and foreign has the comparative advantage in the production of clothing. So according to comparative advantage theory, Home should specialize in the production of only wheat and Foreign should specialize in the production of only clothing.

Production of wheat by Home = 2000/2 = 1000

Production of clothing by Foreign = 3000/2 = 1500

b) Range of relative price should lie between the opportunity cost of the Foreign and the opportunity cost of Home. Therefore, range for the relative price of clothing under free trade is between 0.5 and 2.5

c) If world relative price of clothing under free trade is 2, i.e., p_C/p_W = 2, then Home will produce only Wheat and Foreign will produce only clothing. Foreign will exchange 2 clothing for 1 wheat.

d) The maximum amount of Clothing that Home can produce given its labor constraint = 2000/5 = 400

The maximum amount of wheat that Home can produce given its labor constraint = 2000/2= 1000

The PPF of Home is drawn in panel a of figure 1 in blue color

The maximum amount of Clothing that Foreign can produce given its labor constraint = 3000/2 = 1500

The maximum amount of wheat that Foreign can produce given its labor constraint = 3000/4 = 750

The PPF of Foreign is drawn in panel b of figure 1 in blue color

Now Foreign specializes in production of Clothing and produces 1500 units. Now, it can trade 1500 units of clothing for 1500*2 = 3000 units of wheat, thus the new consumption possibility is given by red color in panel b of figure 1

Home produces 1000 units of wheat and can exchange 1000 units of wheat for 500 units of clothing, thus the new consumption possibility is given by red color in panel a of figure 1.

Figure 1

As we can clearly see, the consumption possibilities lies above the production possibilities that were there in autarky. Therefore, both the countries gain from trade.