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Sagot :
To analyze the opportunity costs for the United States and Italy, we need to understand the number of goods they can produce and how producing one good affects the production of the other. Let's break this down step by step.
### Step 1: Opportunity Cost in the United States
In the United States:
- 4 million tons of cheese can be produced per year.
- 2 million tons of tomatoes can be produced per year.
#### Opportunity Cost of Cheese in the United States:
To find the opportunity cost of producing 1 ton of cheese in terms of tomatoes, we calculate:
[tex]\[ \text{Opportunity cost of 1 ton of cheese} = \frac{\text{Tomatoes produced}}{\text{Cheese produced}} = \frac{2}{4} = 0.5 \text{ tons of tomatoes} \][/tex]
#### Opportunity Cost of Tomatoes in the United States:
To find the opportunity cost of producing 1 ton of tomatoes in terms of cheese, we calculate:
[tex]\[ \text{Opportunity cost of 1 ton of tomatoes} = \frac{\text{Cheese produced}}{\text{Tomatoes produced}} = \frac{4}{2} = 2 \text{ tons of cheese} \][/tex]
### Step 2: Opportunity Cost in Italy
In Italy:
- 1 million tons of cheese can be produced per year.
- 1 million tons of tomatoes can be produced per year.
#### Opportunity Cost of Cheese in Italy:
To find the opportunity cost of producing 1 ton of cheese in terms of tomatoes, we calculate:
[tex]\[ \text{Opportunity cost of 1 ton of cheese} = \frac{\text{Tomatoes produced}}{\text{Cheese produced}} = \frac{1}{1} = 1 \text{ ton of tomatoes} \][/tex]
#### Opportunity Cost of Tomatoes in Italy:
To find the opportunity cost of producing 1 ton of tomatoes in terms of cheese, we calculate:
[tex]\[ \text{Opportunity cost of 1 ton of tomatoes} = \frac{\text{Cheese produced}}{\text{Tomatoes produced}} = \frac{1}{1} = 1 \text{ ton of cheese} \][/tex]
### Step 3: Comparing Opportunity Costs
Now, let's compare the opportunity costs between the United States and Italy:
1. Opportunity Cost of Cheese:
- United States: 0.5 tons of tomatoes
- Italy: 1 ton of tomatoes
Italy has a higher opportunity cost in producing cheese because 1 ton of cheese in Italy costs 1 ton of tomatoes, while in the U.S. it costs only 0.5 tons of tomatoes.
2. Opportunity Cost of Tomatoes:
- United States: 2 tons of cheese
- Italy: 1 ton of cheese
Italy has a lower opportunity cost in producing tomatoes because 1 ton of tomatoes in Italy costs 1 ton of cheese, while in the U.S. it costs 2 tons of cheese.
### Conclusion
Based on the opportunity costs calculated:
- Italy has a higher opportunity cost than the United States in producing cheese.
- Italy has an equal opportunity cost with the United States in producing tomatoes.
Thus, the statement supported by the data table is:
Italy has a higher opportunity cost than the United States in producing cheese.
### Step 1: Opportunity Cost in the United States
In the United States:
- 4 million tons of cheese can be produced per year.
- 2 million tons of tomatoes can be produced per year.
#### Opportunity Cost of Cheese in the United States:
To find the opportunity cost of producing 1 ton of cheese in terms of tomatoes, we calculate:
[tex]\[ \text{Opportunity cost of 1 ton of cheese} = \frac{\text{Tomatoes produced}}{\text{Cheese produced}} = \frac{2}{4} = 0.5 \text{ tons of tomatoes} \][/tex]
#### Opportunity Cost of Tomatoes in the United States:
To find the opportunity cost of producing 1 ton of tomatoes in terms of cheese, we calculate:
[tex]\[ \text{Opportunity cost of 1 ton of tomatoes} = \frac{\text{Cheese produced}}{\text{Tomatoes produced}} = \frac{4}{2} = 2 \text{ tons of cheese} \][/tex]
### Step 2: Opportunity Cost in Italy
In Italy:
- 1 million tons of cheese can be produced per year.
- 1 million tons of tomatoes can be produced per year.
#### Opportunity Cost of Cheese in Italy:
To find the opportunity cost of producing 1 ton of cheese in terms of tomatoes, we calculate:
[tex]\[ \text{Opportunity cost of 1 ton of cheese} = \frac{\text{Tomatoes produced}}{\text{Cheese produced}} = \frac{1}{1} = 1 \text{ ton of tomatoes} \][/tex]
#### Opportunity Cost of Tomatoes in Italy:
To find the opportunity cost of producing 1 ton of tomatoes in terms of cheese, we calculate:
[tex]\[ \text{Opportunity cost of 1 ton of tomatoes} = \frac{\text{Cheese produced}}{\text{Tomatoes produced}} = \frac{1}{1} = 1 \text{ ton of cheese} \][/tex]
### Step 3: Comparing Opportunity Costs
Now, let's compare the opportunity costs between the United States and Italy:
1. Opportunity Cost of Cheese:
- United States: 0.5 tons of tomatoes
- Italy: 1 ton of tomatoes
Italy has a higher opportunity cost in producing cheese because 1 ton of cheese in Italy costs 1 ton of tomatoes, while in the U.S. it costs only 0.5 tons of tomatoes.
2. Opportunity Cost of Tomatoes:
- United States: 2 tons of cheese
- Italy: 1 ton of cheese
Italy has a lower opportunity cost in producing tomatoes because 1 ton of tomatoes in Italy costs 1 ton of cheese, while in the U.S. it costs 2 tons of cheese.
### Conclusion
Based on the opportunity costs calculated:
- Italy has a higher opportunity cost than the United States in producing cheese.
- Italy has an equal opportunity cost with the United States in producing tomatoes.
Thus, the statement supported by the data table is:
Italy has a higher opportunity cost than the United States in producing cheese.
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