The productivity of a single resource in producing wheat and microchips in both Canada and Japan: One unit of resource produces: Canada 50 tons wheat, 20 micrchips and Japan 2 tons wheat, 12 microchips. (b) Suppose Canada is endowed with 2 units of this all-purpose resource while Japan is endowed with 10 units. If the resource productivities reported above remain constant at all levels of output, plot the straight-line production possibilities frontier (PPF) for each country. (c) Using the theory of comparative advantage, which country will produce wheat? How about microchips? Justify your answer.
To plot the production possibilities frontier (PPF) for each country, we need to calculate the maximum output combinations of wheat and microchips for each country given their resource endowments.
For Canada:
With 2 units of the all-purpose resource:
- Canada can produce 2 * 50 = 100 tons of wheat,
- Canada can produce 2 * 20 = 40 microchips.
For Japan:
With 10 units of the all-purpose resource:
- Japan can produce 10 * 2 = 20 tons of wheat,
- Japan can produce 10 * 12 = 120 microchips.
Now let's plot these output combinations on a graph, with wheat on the x-axis and microchips on the y-axis.
Canada's PPF:
- Point A: (100 tons of wheat, 0 microchips)
- Point B: (0 tons of wheat, 40 microchips)
Japan's PPF:
- Point C: (20 tons of wheat, 0 microchips)
- Point D: (0 tons of wheat, 120 microchips)
Connecting points A and B will give Canada's PPF, while connecting points C and D will give Japan's PPF.
The graph will show a straight line for Canada's PPF (A to B) and another straight line for Japan's PPF (C to D).
(c) Using the theory of comparative advantage, which country will produce wheat? How about microchips?
According to the theory of comparative advantage, a country should specialize in and produce the good in which it has a lower opportunity cost compared to other countries.
From the PPF graph, we can see that the opportunity cost of producing wheat is lower in Canada compared to Japan. Canada can produce 1 ton of wheat by giving up 0.4 microchips, while Japan needs to give up 6 microchips to produce 1 ton of wheat. Therefore, Canada has a comparative advantage in producing wheat.
On the other hand, the opportunity cost of producing microchips is lower in Japan compared to Canada. Canada needs to give up 2.5 tons of wheat to produce 1 microchip, while Japan needs to give up only 0.167 tons of wheat to produce 1 microchip. Therefore, Japan has a comparative advantage in producing microchips.
To summarize:
- Canada will produce wheat because it has a lower opportunity cost of producing wheat compared to Japan.
- Japan will produce microchips because it has a lower opportunity cost of producing microchips compared to Canada.
To plot the production possibilities frontier (PPF) for each country, we need to find the maximum quantities of wheat and microchips that each country can produce with their given resource endowments.
For Canada:
- With 2 units of the resource, Canada can produce 2 * 50 = 100 tons of wheat.
- With 2 units of the resource, Canada can produce 2 * 20 = 40 microchips.
For Japan:
- With 10 units of the resource, Japan can produce 10 * 2 = 20 tons of wheat.
- With 10 units of the resource, Japan can produce 10 * 12 = 120 microchips.
Now, let's plot the PPF for each country on a graph. The x-axis represents the quantity of wheat and the y-axis represents the quantity of microchips.
For Canada, the PPF would start at (0, 40) and connect to the point (100, 0). It is a downward sloping straight line.
For Japan, the PPF would start at (0, 120) and connect to the point (20, 0). It is also a downward sloping straight line, but steeper than Canada's PPF.
Next, let's determine which country will produce wheat and microchips based on the theory of comparative advantage.
Comparative advantage suggests that a country should specialize in producing the good in which it has a lower opportunity cost compared to its trading partner.
To find the opportunity cost, we can calculate the ratio of the two goods produced by each country.
For Canada, the opportunity cost of producing one ton of wheat is 40/100 = 0.4 microchips.
For Japan, the opportunity cost of producing one ton of wheat is 120/20 = 6 microchips.
Comparing the opportunity costs, we can see that Canada has a lower opportunity cost of producing wheat (0.4 microchips) compared to Japan (6 microchips). Therefore, Canada has a comparative advantage in producing wheat.
On the other hand, Japan has a lower opportunity cost of producing microchips (6 microchips) compared to Canada (0.4 microchips). Therefore, Japan has a comparative advantage in producing microchips.
In summary, based on the theory of comparative advantage, Canada will specialize in producing wheat while Japan will specialize in producing microchips.