Suppose that France and Denmark both produce oil and olives. Frances’s opportunity cost of producing a crate of olives is 4 barrels of oil, while Denmark’s opportunity cost of producing a crate of olives is 7 barrels of oil.

By comparing the opportunity cost of producing olives in the two countries, you can tell that _______has a comparative advantage in the production of olives and ______has a comparative advantage in the production of oil.

Suppose that France and Denmark consider trading olives and oil with each other. France can gain from specialization and trade as long as it receives more than _____ of oil for each crate of olives it exports to Denmark. Similarly, Denmark can gain from trade as long as it receives more than _____ of olives for each barrel of oil it exports to France.

Based on your answer to the last question, which of the following terms of trade (that is, price of olives in terms of oil) would allow both Denmark and France to gain from trade? Check all that apply.

__ 6 barrels of oil per crate of olives
__ 3 barrels of oil per crate of olives
__ 5 barrels of oil per crate of olives
__ 8 barrels of oil per crate of olives

France has a comparative advantage in the production of olives and Denmark has a comparative advantage in the production of oil. France can gain from specialization and trade as long as it receives more than 3 barrels of oil for each crate of olives it exports to Denmark. Similarly, Denmark can gain from trade as long as it receives more than 6 barrels of olives for each barrel of oil it exports to France.

Based on your answer to the last question, the following terms of trade would allow both Denmark and France to gain from trade: 3 barrels of oil per crate of olives, 5 barrels of oil per crate of olives, and 6 barrels of oil per crate of olives.

To determine which country has a comparative advantage in the production of olives and oil, we compare their opportunity costs. Opportunity cost refers to the cost of producing one unit of a good in terms of how much of another good must be given up to produce it.

In this case, France's opportunity cost of producing a crate of olives is 4 barrels of oil, while Denmark's opportunity cost of producing a crate of olives is 7 barrels of oil.

Since France's opportunity cost of producing olives is lower (4 barrels of oil) compared to Denmark's (7 barrels of oil), France has a comparative advantage in the production of olives. Conversely, since Denmark's opportunity cost of producing olives is higher, Denmark has a comparative advantage in the production of oil.

Now let's determine the terms of trade that would allow both countries to gain from trade. To do this, we need to consider the opportunity cost ratios before trade.

France's opportunity cost of producing a crate of olives is 4 barrels of oil, while Denmark's opportunity cost of producing a crate of olives is 7 barrels of oil. If France exports a crate of olives to Denmark, it would give up 4 barrels of oil. Therefore, for France to gain from trade, it should receive more than 4 barrels of oil for each crate of olives it exports to Denmark.

Denmark's opportunity cost of producing a crate of olives is 7 barrels of oil. If Denmark exports a barrel of oil to France, it would give up 7/4 (1.75) crates of olives. Therefore, for Denmark to gain from trade, it should receive more than 1.75 crates of olives for each barrel of oil it exports to France.

Based on the above analysis:
- France should receive more than 4 barrels of oil per crate of olives to gain from trade.
- Denmark should receive more than 1.75 crates of olives per barrel of oil to gain from trade.

Now let's check the given terms of trade options:
__ 6 barrels of oil per crate of olives
__ 3 barrels of oil per crate of olives
__ 5 barrels of oil per crate of olives
__ 8 barrels of oil per crate of olives

To benefit both France and Denmark from trade:
- France would benefit if it receives more than 4 barrels of oil per crate of olives. 6 barrels of oil per crate of olives satisfies this condition.
- Denmark would benefit if it receives more than 1.75 crates of olives per barrel of oil. None of the given options satisfy this condition.

Therefore, the only terms of trade that would allow both Denmark and France to gain from trade is 6 barrels of oil per crate of olives.

By comparing the opportunity cost of producing olives in the two countries, you can tell that Denmark has a comparative advantage in the production of olives and France has a comparative advantage in the production of oil.

France can gain from specialization and trade as long as it receives more than 4 barrels of oil for each crate of olives it exports to Denmark. Similarly, Denmark can gain from trade as long as it receives more than 7 crates of olives for each barrel of oil it exports to France.

Based on the answers to the last questions, the terms of trade (price of olives in terms of oil) that would allow both Denmark and France to gain from trade are:

- 6 barrels of oil per crate of olives
- 8 barrels of oil per crate of olives