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.

a. Trade will be possible only when X is either greater than or less than 3 hours. Not when X = 3.

b. Germany will export cars and import wine only when X is less than 3.

Explanation:

Comparative advantage refers to the unit of A given up, that is the opportunity cost, in order to produce one unit of product B. Also, a country has a comparative advantage in the production of say product A if it has a lower opportunity cost than the other country.

There will be gains from trade when there is a comparative advantage.

Therefore, we need to compare opportunity cost.

Answer to question a.:

In Germany:

Opportunity Cost of producing a car = OCcarG = 400hour/2hours

                                                             = 200 cases of wine

Opportunity Cost of producing a wine case = OCwineG = 2hour/400hours

                                                                        = 1/200

                                                                        = 0.005 car

In France:

Opportunity Cost of producing a car = OCcarF = 600hour/Xhours

                                                             = 200 cases of wine

Opportunity Cost of producing a wine case = OCwineF = Xhour/600hours

Assuming X = 3, therefore:

OCcarF = 600hour/3hours

              = 200 cases of wine

OCwineF = 3hour/600hours

                = 1/200

                0.005 car

This shows neither Germany nor France has a comparative advantage in the two products since their opportunity costs for the goods are equal.

By implication, there will be trade when the value of X is either greater than or less than 3.

Answer to question b.:

Germany will export cars and import wine only if it has a comparative advantage in the car production, while France also will a comparative advantage in the production of wine.

This implies that Germany must have a lower opportunity cost in the production of car than France, i.e. OCcarG must be lower than OCcarF as given the a. above.

This can only happen when X is less than 3. For example, assume X = 2, we will have:

In France, when X = 2:

OCcarF = 600hour/2hours

              = 300 cases of wine

OCwineF = 2hour/600hours

                = 1/300

                 = 0.003 car

It can be seen that at X = 2, OCcarG (200 cases of wine) is less than OCcarF (300 cases of wine), while OCwineG (0.005 car) is greater than OCwineF (0.003).

This implies that Germany will have comparative advantage in the export of car when X = 2, while France a comparative advantage in wine export when X  = 2 again.

Therefore, Germany will export cars and import wine only when X is less than 3.