The chart shows how many carrots or apples two countries could each grow if they devoted all of their farming resources to one product. Considering the comparative advantage each country has in this situation, which outcome would be most likely?

\begin{tabular}{|c|c|c|}
\hline
& \begin{tabular}{c}
Number of carrots grown \\
per day
\end{tabular} & \begin{tabular}{c}
Number of apples grown \\
per day
\end{tabular} \\
\hline
Country A & 40,000 & 10,000 \\
\hline
Country B & 20,000 & 10,000 \\
\hline
\end{tabular}

A. Country [tex]$B$[/tex] would have a greater trade deficit than country [tex]$A$[/tex].

B. Country [tex]$A$[/tex] would focus on growing carrots to trade with country [tex]$B$[/tex].

C. Country [tex]$B$[/tex] would focus on growing carrots to trade with country [tex]$A$[/tex].

D. Country [tex]$A$[/tex] would focus on growing apples to trade with country [tex]$B$[/tex].



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.