Question

A German worker takes 400 hours to produce a car and 2 hours to produce a case of wine. A French worker takes 600 hours to produce a car and X hours to produce a case of wine.

a) For what values of X will gains from trade be possible? Explain.

b) For what values of X will Germany export cars and import wine? Explain.

Answer 1

a) The gains from trade will be possible for X values less than 8. b) Germany will export cars and import wine for X values greater than 0.01.

Step-by-step explanation:

a) The gains from trade will be possible when the opportunity cost of producing a case of wine is lower for the French worker than the German worker. The opportunity cost of producing a case of wine for the French worker is the number of hours it takes for them to produce a car divided by the number of hours it takes for them to produce a case of wine. So, the equation is X/600 < 2/400. Solving for X, we get X < 8. Therefore, gains from trade will be possible for X values less than 8.

b) Germany will export cars and import wine when the opportunity cost of producing a car is lower for the French worker than the German worker, and the opportunity cost of producing a case of wine is lower for the German worker than the French worker. The French worker's opportunity cost of producing a car is 600/400 = 1.5, while the German worker's opportunity cost is 400/600 = 0.67. The French worker's opportunity cost of producing a case of wine is X/2, while the German worker's opportunity cost is 2/400 = 0.005. Therefore, Germany will export cars and import wine when 0.67 < 1.5 and 0.005 < X/2. Solving for X, we get X > 0.01. Therefore, Germany will export cars and import wine for X values greater than 0.01.

Answer 2

Gains from trade will be possible if the opportunity cost of producing a case of wine in France is less than 2 hours. Germany will export cars and import wine if the opportunity cost of producing a case of wine in France is less than 2 hours.

Step-by-step explanation:

a) In order for gains from trade to be possible, there must be a difference in the opportunity costs of producing cars and producing wine between Germany and France. The opportunity cost of producing a car in Germany is 400 hours, while the opportunity cost of producing a car in France is 600 hours. The opportunity cost of producing a case of wine in Germany is 2 hours, while the opportunity cost of producing a case of wine in France is X hours. Therefore, gains from trade will be possible if the opportunity cost of producing a case of wine in France is less than 2 hours.

b) Germany will export cars and import wine if the opportunity cost of producing a case of wine in France is less than 2 hours. This is because Germany has a lower opportunity cost of producing cars compared to France, while France has a lower opportunity cost of producing wine. By specializing in the production of cars, Germany can produce more cars in the same amount of time, and by importing wine from France, they can obtain wine at a lower opportunity cost than producing it themselves.