Question

Suppose there are two countries, USA and Japan. USA is regarded as the home country and Japan is the foreign country. USA has 100 units of labor available and Japan has 80 units of labor. Both countries can produce only two goods, airplanes and cars. The output per hour of labor in the production of airplanes in the USA is 12, while in car production the output per hour of labor is 6. In Japan, the output per hour of labor in the production of airplanes is 2 and the output per hour of labor in the production of cars is 2. Using the Ricardian model:

(a) Construct a graph of the United States production possibility frontier (use the vertical axis to represent airplanes and the horizontal axis to represent cars).

(b) Construct a graph of Japan's production possibility frontier.

(c) Suppose the mutually beneficial terms of trade between USA and Japan is 1 airplane for ¾ car, draw the consumption possibility frontier for USA by superimposing it on the graph you constructed in (a) above.

(d) Using the inverse of the marginal product of labor, construct a table of the unit labor requirement?

(e) Derive the opportunity cost for both USA and Japan for both goods using the unit labor requirement table that you obtained in (c) above.

(f) Based on your results, determine which country should export airplane or cars.

Answer 1

a. USA, which is the home country, has 100 units of labor. If output per hour of labor in production of airplanes is 12 and if all labors are employed in the production of airplanes, then output = 12*100 = 1200 units.

Similarly, if output per hour of labor in production of cars is 6 and if all labors are employed in the production of cars, then output= 6*100 = 600 units.

With the information above,if we plot units of airplanes on the vertical axis and units of cars on the horizontal axis, the production possibility frontier curve for USA can be drawn as shown below in the diagram.

b. Japan, which is the foreign country, has 80 units of labor. If output per hour of labor in production of both airplanes and cars is 2 and if all labors are employed in production of airplanes, then output = 80*2 = 160 units. Similarly, if all labors are employed in production of cars, then output = 80*2 = 160 units.

With the information above, if we plot units of airplanes on the vertical axis and units of cars on the horizontal axis, the production possibility frontier curve for Japan can be drawn as shown below in the diagram.

c. In the diagram below, we have shown the consumption possibility curves for both the countries.

d. Now, unit labor requirement for airplanes in USA = 100/1200 = 0.08

and unit labor requirement for cars in USA = 100/600 = 0.16

Similarly, unit labor requirement for airplanes in Japan = 80/160 = 0.5

and unit labor requirement for cars in Japan = 80/160=0.5.

Hence, the required table is shown below:

e.Opportunity cost for production of airplanes in USA = (1/0.16) /(1/0.08) = 0.5

and opportunity cost for production of cars in USA = (1/0.5) / (1/0.5) = 1

As opportunity cost is lower in USA, it has comparative advantage in the production of airplanes.

Similarly, opportunity cost for production of airplanes in Japan = (1/0.08) / (1/0.16) = 2

and opportunity cost for production of cars in Japan = (1/0.5) / (1/0.5) = 1

As opportunity cost is lower in Japan, it has comparative advantage in the production of cars.

f. As USA has comparative advantage in production of airplanes, it will export airplanes and import cars.

As Japan has comparative advantage in production of cars, it will export cars and import airplanes.