Answer :
To determine the most likely outcome based on the comparative advantage, we need to calculate the opportunity costs for each country in producing carrots and apples.
### 1. Calculating Opportunity Costs
For Country A:
- Opportunity cost of producing 1 carrot:
Country A can produce either 40,000 carrots or 10,000 apples. To find the opportunity cost of one carrot, we divide the maximum apples (10,000) by the maximum carrots (40,000):
[tex]\[ \text{Opportunity cost of 1 carrot} = \frac{10,000 \text{ apples}}{40,000 \text{ carrots}} = 0.25 \text{ apples per carrot} \][/tex]
- Opportunity cost of producing 1 apple:
Similarly, to find the opportunity cost of one apple, we take the maximum carrots (40,000) and divide by the maximum apples (10,000):
[tex]\[ \text{Opportunity cost of 1 apple} = \frac{40,000 \text{ carrots}}{10,000 \text{ apples}} = 4 \text{ carrots per apple} \][/tex]
For Country B:
- Opportunity cost of producing 1 carrot:
Country B can produce either 20,000 carrots or 10,000 apples. To find the opportunity cost of one carrot, we divide the maximum apples (10,000) by the maximum carrots (20,000):
[tex]\[ \text{Opportunity cost of 1 carrot} = \frac{10,000 \text{ apples}}{20,000 \text{ carrots}} = 0.5 \text{ apples per carrot} \][/tex]
- Opportunity cost of producing 1 apple:
Similarly, to find the opportunity cost of one apple, we take the maximum carrots (20,000) and divide by the maximum apples (10,000):
[tex]\[ \text{Opportunity cost of 1 apple} = \frac{20,000 \text{ carrots}}{10,000 \text{ apples}} = 2 \text{ carrots per apple} \][/tex]
### 2. Comparative Advantage Analysis
Next, we compare the opportunity costs to determine which country has a comparative advantage:
- Carrots: Country A's opportunity cost (0.25 apples per carrot) is lower than Country B's (0.5 apples per carrot).
- Apples: Country B's opportunity cost (2 carrots per apple) is lower than Country A's (4 carrots per apple).
### 3. Conclusion
Based on the principle of comparative advantage, each country should specialize in the product for which it has a lower opportunity cost and then trade to obtain the other product:
- Country A should specialize in growing carrots because it has a comparative advantage in carrots.
- Country B should specialize in growing apples because it has a comparative advantage in apples.
So, the most likely outcome is:
B. Country A would focus on growing carrots to trade with country B.
### 1. Calculating Opportunity Costs
For Country A:
- Opportunity cost of producing 1 carrot:
Country A can produce either 40,000 carrots or 10,000 apples. To find the opportunity cost of one carrot, we divide the maximum apples (10,000) by the maximum carrots (40,000):
[tex]\[ \text{Opportunity cost of 1 carrot} = \frac{10,000 \text{ apples}}{40,000 \text{ carrots}} = 0.25 \text{ apples per carrot} \][/tex]
- Opportunity cost of producing 1 apple:
Similarly, to find the opportunity cost of one apple, we take the maximum carrots (40,000) and divide by the maximum apples (10,000):
[tex]\[ \text{Opportunity cost of 1 apple} = \frac{40,000 \text{ carrots}}{10,000 \text{ apples}} = 4 \text{ carrots per apple} \][/tex]
For Country B:
- Opportunity cost of producing 1 carrot:
Country B can produce either 20,000 carrots or 10,000 apples. To find the opportunity cost of one carrot, we divide the maximum apples (10,000) by the maximum carrots (20,000):
[tex]\[ \text{Opportunity cost of 1 carrot} = \frac{10,000 \text{ apples}}{20,000 \text{ carrots}} = 0.5 \text{ apples per carrot} \][/tex]
- Opportunity cost of producing 1 apple:
Similarly, to find the opportunity cost of one apple, we take the maximum carrots (20,000) and divide by the maximum apples (10,000):
[tex]\[ \text{Opportunity cost of 1 apple} = \frac{20,000 \text{ carrots}}{10,000 \text{ apples}} = 2 \text{ carrots per apple} \][/tex]
### 2. Comparative Advantage Analysis
Next, we compare the opportunity costs to determine which country has a comparative advantage:
- Carrots: Country A's opportunity cost (0.25 apples per carrot) is lower than Country B's (0.5 apples per carrot).
- Apples: Country B's opportunity cost (2 carrots per apple) is lower than Country A's (4 carrots per apple).
### 3. Conclusion
Based on the principle of comparative advantage, each country should specialize in the product for which it has a lower opportunity cost and then trade to obtain the other product:
- Country A should specialize in growing carrots because it has a comparative advantage in carrots.
- Country B should specialize in growing apples because it has a comparative advantage in apples.
So, the most likely outcome is:
B. Country A would focus on growing carrots to trade with country B.
