Question
A country produces books and video games exclusively. In the same time it takes to produce one video game, the country could produce 4 books. If the country only focused on one of the goods to produce, the maximum amount the country can produce is either 200 video games or 800 books. They can create a combination of the two goods, but the opportunity cost for production will remain the same. If the country would like to consume a combination of 100 video games and 1,400 books, which of the following is true?(1 point)
Responses
This is only possible if the country produces 600 more books and 100 fewer video games itself.
This is only possible if the country produces 600 more books and 100 fewer video games itself.
It is impossible for the country to consume a combination of 100 video games and 1,400 books.
It is impossible for the country to consume a combination of 100 video games and 1,400 books.
The country might consume 100 video games and 1,400 books following trade.
The country might consume 100 video games and 1,400 books following trade.
The country can produce 600 more books and 100 fewer video games itself, or it can engage in trade.
Responses
This is only possible if the country produces 600 more books and 100 fewer video games itself.
This is only possible if the country produces 600 more books and 100 fewer video games itself.
It is impossible for the country to consume a combination of 100 video games and 1,400 books.
It is impossible for the country to consume a combination of 100 video games and 1,400 books.
The country might consume 100 video games and 1,400 books following trade.
The country might consume 100 video games and 1,400 books following trade.
The country can produce 600 more books and 100 fewer video games itself, or it can engage in trade.
Answers
GPT-4o mini
To determine whether the country can consume a combination of 100 video games and 1,400 books, we first need to analyze the production possibilities based on the information given.
1. **Production Possibility**:
- The country can produce **200 video games** or **800 books**.
- From the production capabilities, if the country focuses solely on one good, it produces 1 video game in the same time that it could produce 4 books.
We can also calculate how many books are equivalent to 100 video games:
- If producing 1 video game requires the same time as producing 4 books, then 100 video games require the same time as producing 400 books (since \(100 \text{ video games} = 100 \times 4 = 400 \text{ books}\)).
2. **Total Production Capacity**:
- To produce 100 video games and 1,400 books, we need to consider the opportunity cost.
- The production of 100 video games (which takes time equivalent to producing 400 books) means the country must allocate resources used to produce books as well.
- Therefore, the total equivalent in book terms for producing 100 video games and 1,400 books is \(400\) (equivalent books for the video games) + \(1400\) books = \(1800\) books.
3. **Conclusion**:
- The country has a maximum capacity of producing 800 books (if it focuses entirely on books) or 200 video games, which means it can only produce up to 800 books if it produces 0 video games.
- To produce any combination of books and video games, the country would need to stay within the limits set by these maximums.
Considering the calculation, the country can only produce a maximum of 800 books in any combination and therefore cannot reach the total consumption level of \(1800\) (400 equivalent for video games + 1400 books).
Thus, the correct answer is:
**It is impossible for the country to consume a combination of 100 video games and 1,400 books.**
1. **Production Possibility**:
- The country can produce **200 video games** or **800 books**.
- From the production capabilities, if the country focuses solely on one good, it produces 1 video game in the same time that it could produce 4 books.
We can also calculate how many books are equivalent to 100 video games:
- If producing 1 video game requires the same time as producing 4 books, then 100 video games require the same time as producing 400 books (since \(100 \text{ video games} = 100 \times 4 = 400 \text{ books}\)).
2. **Total Production Capacity**:
- To produce 100 video games and 1,400 books, we need to consider the opportunity cost.
- The production of 100 video games (which takes time equivalent to producing 400 books) means the country must allocate resources used to produce books as well.
- Therefore, the total equivalent in book terms for producing 100 video games and 1,400 books is \(400\) (equivalent books for the video games) + \(1400\) books = \(1800\) books.
3. **Conclusion**:
- The country has a maximum capacity of producing 800 books (if it focuses entirely on books) or 200 video games, which means it can only produce up to 800 books if it produces 0 video games.
- To produce any combination of books and video games, the country would need to stay within the limits set by these maximums.
Considering the calculation, the country can only produce a maximum of 800 books in any combination and therefore cannot reach the total consumption level of \(1800\) (400 equivalent for video games + 1400 books).
Thus, the correct answer is:
**It is impossible for the country to consume a combination of 100 video games and 1,400 books.**