A German worker takes 400 hours to produce a car and 2 hours to produce a case of wine. A French worker takes X
 hours to produce a car and 3 hours to produce a case of wine.
For what values of X
 will gains from trade be possible? Check all that apply.

	1
	2
	650
	700

To determine the values of \( X \) (the time it takes a French worker to produce a car) that will allow for gains from trade, we can use the concept of comparative advantage. Gains from trade are possible when each country specializes in producing the good for which it has a comparative advantage, meaning it can produce that good at a lower opportunity cost than the other country.

### Calculating Opportunity Costs:

1. **German worker:**
   - **Opportunity cost of 1 car**: 
     - 1 car = 400 hours.
     - In 400 hours, a German worker could produce \( \frac{400 \text{ hours}}{2 \text{ hours per case}} = 200 \) cases of wine.
     - Opportunity cost of 1 car = 200 cases of wine.
   - **Opportunity cost of 1 case of wine**:
     - 1 case of wine = 2 hours.
     - In 2 hours, a German worker could produce \( \frac{2 \text{ hours}}{400 \text{ hours per car}} = 0.005 \) cars.
     - Opportunity cost of 1 case of wine = 0.005 cars.

2. **French worker:**
   - **Opportunity cost of 1 car**: 
     - 1 car = \( X \) hours.
     - In \( X \) hours, a French worker could produce \( \frac{X \text{ hours}}{3 \text{ hours per case}} \) cases of wine.
     - Opportunity cost of 1 car = \( \frac{X}{3} \) cases of wine.
   - **Opportunity cost of 1 case of wine**:
     - 1 case of wine = 3 hours.
     - In 3 hours, a French worker could produce \( \frac{3 \text{ hours}}{X \text{ hours per car}} \) cars.
     - Opportunity cost of 1 case of wine = \( \frac{3}{X} \) cars.

### Comparative Advantage:
- **Germany has a comparative advantage in cars** if the opportunity cost of a car is lower in Germany than in France.
  \[
  200 \text{ cases of wine} < \frac{X}{3} \text{ cases of wine}
  \]
  Simplifying:
  \[
  X > 600 \text{ hours}
  \]

- **France has a comparative advantage in wine** if the opportunity cost of wine is lower in France than in Germany.
  \[
  \frac{3}{X} \text{ cars} < 0.005 \text{ cars}
  \]
  Simplifying:
  \[
  X > 600 \text{ hours}
  \]

### Conclusion:
Gains from trade will be possible when \( X > 600 \) hours.

### Evaluating Given Options:
- \( X = 1 \): No gains from trade.
- \( X = 2 \): No gains from trade.
- \( X = 650 \): Gains from trade possible.
- \( X = 700 \): Gains from trade possible.

**Correct Values of \( X \) for Gains from Trade: 650, 700**

Would you like more details or have any questions?

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Here are five related questions:

1. How do you calculate opportunity cost in terms of another good?
2. What is the difference between absolute and comparative advantage?
3. Why are gains from trade possible when opportunity costs differ?
4. How would the analysis change if the French worker took 600 hours to produce a car?
5. What role does specialization play in gains from trade?

**Tip:** Comparative advantage focuses on the relative opportunity costs, not the absolute efficiency in production.

A German worker takes 400 hours to produce a car and 2 hours to produce a case of wine. A French worker takes X hours to produce a car and 3 hours to produce a case of wine. For what values of X will gains from trade be possible? Check all that apply.

1
2
650
700

Explore how comparative advantage determines gains from trade between German and French workers. Analyze the opportunity costs for producing cars and wine, and find out the values of X for which trade benefits both countries. This problem is ideal for undergraduate economics students.

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