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Answer 1

Because, even if one country is a more efficient producer of both goods, there will be a difference in how much more efficient. And it pays the country which has a greater comparative advantage in one good to produce more of that good and less of the other. The relative advantage and resource constraints will determine how much of products A and B each country should produce.

This process will maximise the total of goods A and B produced and will (in theory) maximise utility - the benefit of the two countries.

Unfortunately for economic theory, the world is not a perfect market place: it is often not transparent, producers and consumers do not have perfect knowledge, political factors interfere and so on.

Answer 2

Typically, there will be a different ratio of effeciency between the production of goods A and B depending on the country. For example, imagine that the United States could produce 30 As or 6 Bs in a week, whereas Japan could produce 15As or 5Bs in a week. This means that for the Americans each B is worth 5As because in order to produce a B, 5As must be forgone. For the Japanese, each B is worth 3As for the same reason. As a result, the Japanese would be willing to produce a B and sell it to the Americans for 4As because that would give them a profit of 1A. Conversely, the Americans would be willing to buy a B for 4As because it would have cost them 5As to make their own B. This will naturally lead to America producing As and Japan producing Bs because each is more efficient in the production of that product than the other and the exchange rate will likely hover around 4As per B since it is beneficial to both the USA and Japan, but it must be 3>x>5 otherwise there is no benefit to trading.

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Q: Why should the US and Japan trade products A and B even if they can both produce the products individually?
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