To determine the trading ratio for squash to carrots that is beneficial to both China and the United States, let's go through a detailed, step-by-step analysis:
1. Analyze China's production:
- Suppose China can produce 10 units of squash or 5 units of carrots in a given time period.
2. Analyze the United States' production:
- Suppose the United States can produce 8 units of squash or 4 units of carrots in the same time period.
3. Calculate the opportunity cost:
- For China, the opportunity cost of producing 1 unit of squash is [tex]\( \frac{5}{10} = 0.5 \)[/tex] units of carrots.
- For China, the opportunity cost of producing 1 unit of carrots is [tex]\( \frac{10}{5} = 2 \)[/tex] units of squash.
- For the United States, the opportunity cost of producing 1 unit of squash is [tex]\( \frac{4}{8} = 0.5 \)[/tex] units of carrots.
- For the United States, the opportunity cost of producing 1 unit of carrots is [tex]\( \frac{8}{4} = 2 \)[/tex] units of squash.
4. Establish mutually beneficial trading ratios:
- For China, to be beneficial, the trading ratio for squash to carrots should be lower than their own opportunity cost of producing carrots, which is 2 units of squash per 1 unit of carrots.
- For the United States, the trading ratio for squash to carrots should be lower than their own opportunity cost of producing carrots, which is also 2 units of squash per 1 unit of carrots.
5. Identify the congruent beneficial trading ratio:
- To be beneficial to both, the trading ratio should lie within the intersection of both opportunity costs. Since both countries have the same opportunity costs, the beneficial trading ratio should range anywhere between:
- [tex]\(\frac{1}{2}\)[/tex] squash to 1 carrot to [tex]\(\frac{2}{1}\)[/tex] squash to 1 carrot (0.5 to 2.0).
6. Compare the available options:
- Option A. 1 and 3: Falls outside the beneficial range (0.5 to 2.0).
- Option B. 0.5 and 1.33: Falls within the beneficial range (0.5 to 2.0).
- Option C. 0.75 and 1.33: Falls within the beneficial range (0.5 to 2.0).
- Option D. 0.5 and 0.75: Falls within the beneficial range (0.5 to 2.0).
Given this analysis, the only options are B, C, and D that align within a beneficial trading range.
Conclusively, the correct answer among provided options considering the true benefit criteria:
C. 0.75 and 1.33. This range ensures mutual benefit in trading squash for carrots between China and the United States.
