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Sagot :
To answer the question, we need to analyze the provided data regarding the production capabilities of Country A and Country B. We will consider both the concepts of opportunity cost and comparative advantage, as well as absolute advantage.
### Step 1: Calculating Opportunity Costs
For Country A:
- Opportunity cost of producing one ship:
[tex]\[ \text{Opportunity Cost}_{\text{Ship}_A} = \frac{\text{Number of planes produced per day by Country A}}{\text{Number of ships produced per day by Country A}} = \frac{20}{60} = 0.333\ (\text{or}\ \frac{1}{3}) \][/tex]
- Opportunity cost of producing one plane:
[tex]\[ \text{Opportunity Cost}_{\text{Plane}_A} = \frac{\text{Number of ships produced per day by Country A}}{\text{Number of planes produced per day by Country A}} = \frac{60}{20} = 3 \][/tex]
For Country B:
- Opportunity cost of producing one ship:
[tex]\[ \text{Opportunity Cost}_{\text{Ship}_B} = \frac{\text{Number of planes produced per day by Country B}}{\text{Number of ships produced per day by Country B}} = \frac{50}{100} = 0.5 \][/tex]
- Opportunity cost of producing one plane:
[tex]\[ \text{Opportunity Cost}_{\text{Plane}_B} = \frac{\text{Number of ships produced per day by Country B}}{\text{Number of planes produced per day by Country B}} = \frac{100}{50} = 2 \][/tex]
### Step 2: Comparative Advantage
Comparative advantage is determined by the lower opportunity cost.
- For ships:
[tex]\[ \text{comparative advantage} \to \min \left( \text{Opportunity Cost}_{\text{Ship}_A}, \text{Opportunity Cost}_{\text{Ship}_B} \right) = \min \left( 0.333, 0.5 \right) = 0.333 \ (\text{Country A}) \][/tex]
- For planes:
[tex]\[ \text{comparative advantage} \to \min \left( \text{Opportunity Cost}_{\text{Plane}_A}, \text{Opportunity Cost}_{\text{Plane}_B} \right) = \min \left( 3, 2 \right) = 2 \ (\text{Country B}) \][/tex]
### Step 3: Absolute Advantage
Absolute advantage is determined by who can produce more of a good with the same resources.
- For ships:
[tex]\[ \text{Country A} \rightarrow 60 \, \text{ships/day}, \quad \text{Country B} \rightarrow 100 \, \text{ships/day} \quad \Rightarrow \quad \text{Country B has the absolute advantage in producing ships.} \][/tex]
- For planes:
[tex]\[ \text{Country A} \rightarrow 20 \, \text{planes/day}, \quad \text{Country B} \rightarrow 50 \, \text{planes/day} \quad \Rightarrow \quad \text{Country B has the absolute advantage in producing planes.} \][/tex]
### Conclusion
Using the analyses above, only the following statements are supported:
A. Country B has a comparative advantage producing planes.
Therefore, the correct conclusion supported by the data is:
A. Country B has a comparative advantage producing planes.
### Step 1: Calculating Opportunity Costs
For Country A:
- Opportunity cost of producing one ship:
[tex]\[ \text{Opportunity Cost}_{\text{Ship}_A} = \frac{\text{Number of planes produced per day by Country A}}{\text{Number of ships produced per day by Country A}} = \frac{20}{60} = 0.333\ (\text{or}\ \frac{1}{3}) \][/tex]
- Opportunity cost of producing one plane:
[tex]\[ \text{Opportunity Cost}_{\text{Plane}_A} = \frac{\text{Number of ships produced per day by Country A}}{\text{Number of planes produced per day by Country A}} = \frac{60}{20} = 3 \][/tex]
For Country B:
- Opportunity cost of producing one ship:
[tex]\[ \text{Opportunity Cost}_{\text{Ship}_B} = \frac{\text{Number of planes produced per day by Country B}}{\text{Number of ships produced per day by Country B}} = \frac{50}{100} = 0.5 \][/tex]
- Opportunity cost of producing one plane:
[tex]\[ \text{Opportunity Cost}_{\text{Plane}_B} = \frac{\text{Number of ships produced per day by Country B}}{\text{Number of planes produced per day by Country B}} = \frac{100}{50} = 2 \][/tex]
### Step 2: Comparative Advantage
Comparative advantage is determined by the lower opportunity cost.
- For ships:
[tex]\[ \text{comparative advantage} \to \min \left( \text{Opportunity Cost}_{\text{Ship}_A}, \text{Opportunity Cost}_{\text{Ship}_B} \right) = \min \left( 0.333, 0.5 \right) = 0.333 \ (\text{Country A}) \][/tex]
- For planes:
[tex]\[ \text{comparative advantage} \to \min \left( \text{Opportunity Cost}_{\text{Plane}_A}, \text{Opportunity Cost}_{\text{Plane}_B} \right) = \min \left( 3, 2 \right) = 2 \ (\text{Country B}) \][/tex]
### Step 3: Absolute Advantage
Absolute advantage is determined by who can produce more of a good with the same resources.
- For ships:
[tex]\[ \text{Country A} \rightarrow 60 \, \text{ships/day}, \quad \text{Country B} \rightarrow 100 \, \text{ships/day} \quad \Rightarrow \quad \text{Country B has the absolute advantage in producing ships.} \][/tex]
- For planes:
[tex]\[ \text{Country A} \rightarrow 20 \, \text{planes/day}, \quad \text{Country B} \rightarrow 50 \, \text{planes/day} \quad \Rightarrow \quad \text{Country B has the absolute advantage in producing planes.} \][/tex]
### Conclusion
Using the analyses above, only the following statements are supported:
A. Country B has a comparative advantage producing planes.
Therefore, the correct conclusion supported by the data is:
A. Country B has a comparative advantage producing planes.
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