Question

Suppose in Vietnam a worker can produce either 16 units of cloth or 2 bicycles while in China a worker can produce either 20 units of cloth or 5 bicycles.

1. Suppose each country has 1,000 workers. Currently, each country devotes 40 percent of its labor force to cloth production and 60 percent to bicycle production. What is the output of cloth and bicycles for each country and what is the total output of cloth and bicycles between the two countries?   

2. Suppose each country specializes in the production of the good in which it has a comparative advantage. What is the total output of cloth and bicycles in the two countries?   

3. Provide a numerical example to show how Vietnam and China can both gain from trade. Assume that the terms of trade are established at 6 units of cloth for 1 bicycle.

Answer 1

a)

In Vietnam,

A worker can produce either 16 unit of cloth and 3 bicycles.

Total available labor = 1000

40% labor i.e. 1000× (40/100) = 400 labors are used in production of cloth .

400 labors can produce (16×400) = 6400 units of cloth.

60% labor i.e. 1000×(60/100) = 600 labors are used in production of bicycle.

600 labors can produce (3×600) = 1800 bicycle.

Hence in Vietnam 6400 units of cloth and 1800 bicycles will be produced.

In China,

A worker can produce 20 units of cloth or 5 bicycles.

Labor force available = 1000 labors.

40% labor i.e. 400 workers are engaged in production of cloth.

400 workers can produce (400×20) = 8000 units of cloth.

60% labors i.e. 600 labors are used in production of bicycles.

600 labors can produce (600×5) = 3000 bicycles.

Hence China produces 8000 units of cloth and 3000 bicycles.

b) Let us consider the Production Possibility Frontier of Vietnam and China.

Suppose Vietnam produces "C" units of cloth and "B" units of bicycles.

Now a worker in Vietnam can produce 16 units of cloth.

Hence 1 unit of cloth production requires (1/16) labors.

Thus, "C" units of cloth production requires { (1/16)×C } labors.

Now a worker in Vietnam can produce 2 bicycles.

Hence 1 bicycles production requires (1/2) labors.

Thus "B" units of bicycles production requires { (1/2)× B }.

Hence the PPF of Vietnam can be written as -

{(1/16)×C} + {(1/2)×B} = 1000

The absolute slope of Vietnam's PPF can be written as -

(1/16) ÷ (1/2) = (2/16) = (1/8) = 0.125

The slope of PPF of (1/8) can be interpreted as if Vietnam produces 1 more units of cloth it has to sacrifice (1/8) units of bicycles.

In similar way we can get the PPF of China in following way -

Suppose China produces 20 units of cloth or 5 bicycles.

Hence the PPF can be written as -

{(1/20)×C} + {(1/5)×B} = 1000

The absolute slope of China's PPF is -

(1/20) ÷ (1/5) = (5/20) = (1/4) = 0.25

Hence the absolute slope of China's PPF of (1/4) can be interpreted as if China produces 1 more units of cloth it has to sacrifice (1/4) units of computer.

Thus it seems the slope of China's PPF is higher than Vietnam which means for producing 1 more units of China has to sacrifice more units of Computers. Hence it can be stated that Vietnam has comparative advantage in production of cloth (since it has to sacrifice less amounts of computers for one more units of cloth production).

The theory of Comparative advantage suggests that, when Vietnam has comparative advantage in production of cloth we must have China has a comparative advantage in Bicycles production.

Hence Vietnam will specialize in production of Cloth and China will specialize in Bicycle production.

Thus the 1000 workers in Vietnam will produce (16×1000)= 16000 Cloth.

Thus the 1000 workers in China will produce (5×1000) = 5000 Bicycle.

Hence total output of cloth is given by 16000 cloth and total output of china 5000 bicycles.

C) The terms of trade (TOT) is given by 6 units of cloth for 1 bicycle.

The opportunity cost of Vietnam is given by 1 unit of cloth for (1/8) unit of bicycle.

Hence the opportunity cost of Vietnam can be rewritten as - 8 units of cloth for 1 bicycle.

Again the opportunity cost of China is given by 1 unit of cloth for (1/4) unit of bicycle.

Or, the opportunity cost of China can be rewritten is given by - 4 units of cloth for 1 bicycle.

Now we have seen that Vietnam has comparative advantage in production of cloth.

If Vietnam produces 1 units of less bicycle it can get 8 more units of Cloth. Now since the TOT is give by 6 units of cloth for 1 bicycle, with the additional 8 units of cloth which Vietnam got by producing 1 less unit of cloth can take more than 1 bicycle form market (since market TOT is 6 units of cloth for 1 bicycle). Thus under trade (with the given TOT) Vietnam by sacrificing 1 more unit of bicycle can take more than 1 unit of bicycle from market. Hence Vietnam is gaining from trade.

Similarly for China, if it produce 1 less unit of Cloth it can produce (1/4) more units if biclycle. Now the market TOT of 6 units of cloth for 1 bicycle can be rewritten as 1 units of cloth for (1/6) bicycle.

Thus while china can produce (1/4) more units of biclycle by sacrificing 1 unit of cloth production, with the given market TOT it can get 1 unit of cloth by using only (1/6) units of bicycles form market. Thus China in this case has not to use the total additional bicycles what it got by sacrificing 1 unit of cloth production [as (1/6) < (1/4)]. Thus using that (1/4) unit of bicycle china can take more than 1 units of cloth. Thus here china sacrificing 1units of cloth production can take more than 1 unit of cloth from market under trade. Hence China is gaining from trade.