Question

Suppose that in a year an American worker can produce 100 shirts or 20 computers and a Chinese worker can produce 100 shirts or 10 computers.   

1. For each country, graph the production possibilities frontier. Suppose that without trade the workers in each country spend half their time producing each good. Identify this point in your graphs.

2. Who has the comparative advantage in the production of shirts? What about for computers?

3. If these countries were open to trade, which country would export shirts? Give a specific numerical example and show it on your graphs. Which country would benefit from trade?

4. Explain at what price of computers (in terms of shirts) the two countries might trade.

Answer 1

1. 2. Opportunity Costs are:
   China - Computer - 20, So Shirts - 1/20.
America - Computer - 10, So Shirts - 1/10.
As we can see, China needs to give up a fewer number of computer than America to produce an additional shirt, China has a comparitive advantage in shirt production. America then must have a comparative advantage in producing the other good, ie. computers.

Production Possibility Frontiers for both the countries: 20 Computers 10 If half of the time spent producing each good. 50 Shirts 100 American Worker's Production Possibilities Frontier. Computers 10 f half of the time spent producing each good.] 50 100 Shirts Chinese Worker's Production Possibilities Frontier.

3. As China has comparitive advantage in shirt production, so China would export shirts. To understand it with numbers, suppose China has 100 workers, so total worker-hours available = 100 worker-years.
   Total Production of Shirts by China = 100*100 = 10,000 Shirts.
China would definitely benefit from trade as it can get more number of computers for the same working hours deployed. Let's say, China gives its 50% of produced shirts to America & in turn America gives 50% of produced computers to China. In this scenario, China will have 5000 of Shirts & 500 Computers, while without trade, it would have had 5000 shirts & only 250 computers with 50% of available working hours deployed to ecah production.

4. Suppose the terms of trade are 1 shirt = 0.15 computers (within the range above):

China specializes in shirts and produces 10,000 shirts and no computers.
Suppose she exports 5,000 of them to the US.
In return, she then imports (0.15*5,000) = 750 computers from the US.

∴ China produces (10,000 shirts, 0 computers) China consumes (5,000 shirts, 750 computers).

The US -- on the other hand – specializes in computer production, thus produces 0 shirts and 2,000 computers.
If she exports 750 computers to China, she gets 5000 shirts at the current terms of trade. This means she has (2000-750) =1250 computers left to consume domestically.

∴ The US produces (0 shirts, 2,000 computers) The US consumes (5,000 shirts, 1,250 computers).
Thus both China and the US are better off than before they specialized, since, recalling from (b) above, the autarky (no trade) production and consumption bundles were: China (5,000 shirts, 500 computers).  US (5,000 shirts, 1,000 computers) 