Q3. The following hypothetical produ... [FREE SOLUTION]

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Chapter 20: Q3. (page 432)

The following hypothetical production possibilities tables are for China and the United States. Assume that before specialization and trade the optimal product mix for China is alternative B and for the United States is alternative U.

China Production Alternatives
Product
A
B
C
D
E
F
Apparel (in thousands)
30
24
18
12
6
0
Chemicals (in tons)
0
6
12
18
24
30

U.S. Production Alternatives
Product
R
S
T
U
V
W
Apparel (in thousands)
10
8
6
4
2
0
Chemicals (in tons)
0
4
8
12
16
20
Are comparative-cost conditions such that the two areas should specialize? If so, what product should each produce?
What is the total gain in apparel and chemical output that would result from such specialization?
What are the limits of the terms of trade? Suppose that the actual terms of trade are 1 unit of apparel for 1陆 units of chemicals and that 4 units of apparel are exchanged for 6 units of chemicals. What are the gains from specialization and trade for each nation?

Short Answer

Expert verified

Yes, apparel should be produced by China, and the U.S. should produce chemicals.
The total gain in apparel will be 6000, and in chemical will be 2.
The limit to terms of trade will be 1000 units of apparel for 1 ton of chemicals and 1000 units of apparel for 2 tons of chemicals. The gain will be 2000 units of apparel and 2 tons of chemicals.

Step by step solution

Step 1. Explanation for part (a)

Two areas should indeed specialize.

The opportunity cost of producing apparel will be,

$C h i n a = \frac{30}{30} = 1 t o n C h e m i c a l s U . S . = \frac{20}{10} = 2 t o n c h e m i c a l s$

The opportunity cost for 1000 units of apparel will be 1 ton of chemicals in China, and 1000 units of apparel will be 2 tons of chemicals in U. S. Hence, China will specialize in the production of apparel asit has a lower opportunity cost.

The opportunity cost of producing chemicals will be,

$C h i n a = \frac{30}{30} = 1000 A p p a r e l U . S . = \frac{10}{20} = 500 A p p a r e l$

The opportunity cost for 1 ton of chemicals will be 1000 units of apparel in China, and 1 ton of chemicals will be 500 units of apparel in U. S. Hence, U. S. will specialize in the production of chemicals as it has a lower opportunity cost.

Step 2. Explanation for part (b)

China鈥檚 optimal product mix is B before the trade, and the U.S. optimal product mix will be U before. The total production of apparel will be 28000 units of apparel (=24000 China + 4000 U. S.), and chemicals will be 18 tons of chemicals (=6 China + 12 U. S.). The total production after specialization will be 30000 units of apparel and 20 tons of chemicals. The gains from specialization will be 2000 units of apparel (=30000 鈥� 28000) and 2 tons of chemicals (= 20 鈥� 18).

Step 3. Explanation for part (c)

The opportunity cost for China in production of 1000 units of apparel will be 1 ton of chemicals, and for the U.S. will be 1000 units of apparel will be 2 tons of chemicals. If the U.S. requires more apparel, then China will produce the chemical itself. If China requires more chemicals, then the U.S. will produce the apparel itself.

Thus, the limit to terms of trade will be 1000 units of apparel for 1 ton of chemicals and 1000 units of apparel for 2 tons of chemicals.

The actual terms of trade are 1 unit of apparel for 1陆 units of chemicals and that 4000 units of apparel are exchanged for 6 tons of chemicals.

The U.S. produces 20 tons of chemicals and trades 4000 units of apparel for 6 tons of chemicals; thus, after trade will be 14 (=20 鈥� 6) tons of chemicals and 4000 units of apparel.
China produces 30000 units of apparel and trade 6 tons of chemicals for 4000 units of apparel; thus, after trade will be 26000 (=30000 鈥� 4000) units of apparel and 6 tons of chemicals. The gains to China will be 2000 (=26000 鈥� 24000) apparel units, and the U.S. will gain 2 (=14 鈥� 12) tons of chemicals.