To determine the most efficient use of resources, we need to analyze the opportunity cost of producing fabric instead of yarn for both countries. The opportunity cost of producing fabric is the ratio of the time it takes to produce fabric to the time it takes to produce yarn.
Let's calculate the opportunity cost for each country.
For Country A:
- Time to produce yarn: 8 hours
- Time to produce fabric: 12 hours
- Opportunity cost of producing fabric instead of yarn: [tex]\( \frac{12 \text{ hours}}{8 \text{ hours}} = 1.5 \)[/tex] units of yarn.
For Country B:
- Time to produce yarn: 4 hours
- Time to produce fabric: 13 hours
- Opportunity cost of producing fabric instead of yarn: [tex]\( \frac{13 \text{ hours}}{4 \text{ hours}} = 3.25 \)[/tex] units of yarn.
Now that we have the opportunity costs:
- Country A: 1.5 units of yarn for fabric
- Country B: 3.25 units of yarn for fabric
To identify the most efficient use of resources, we should look at which country has the lower opportunity cost for each product. The country with the lower opportunity cost for a product should specialize in that product.
- For fabric, Country A has the lower opportunity cost (1.5 vs. 3.25).
- For yarn, we need to compare simply without given opportunity costs: Since Country B can produce yarn in 4 hours versus 8 hours for Country A, Country B should specialize in yarn production.
Therefore, the most efficient use of resources is:
- Country A produces fabric.
- Country B produces yarn.
This corresponds to the scenario:
Country B produces yarn, and Country A produces fabric.
So, the correct answer is:
Country B produces yarn, and Country A produces fabric.
