comparative advantage and the gains from trade
There are potentially many gains in economic welfare to be achieved through free trade:
Greater choice of products for consumers
Increased competition for producers
Other countries can supply certain products more efficiently
Trade speeds up the pace of technological progress and innovation
Businesses are better placed to exploit economies of scale
Political benefits from expansion of global trade
The theory of comparative advantage can show these gains from trade: The diagrams below take you through an example:
Establishing the comparative advantage:

With half their economic resources allocated to each product, Germany can produce more of both freezers and dishwashers than Italy. But Italy is closest to Germany in producing freezers. The opportunity cost of each extra freezer for Italy is 1/4 dishwasher, whereas for Germany the opportunity cost is 1/2 of a dishwasher. Italy should therefore specialise in the production of freezers. Germany has a comparative advantage in freezers.
The effects of specialisation

Specialisation has led to an increase in output of both goods (pre specialisation output is shown in brackets at the bottom of the table)
Gains from trade between the two countries

For mutually beneficial trade to take place an acceptable terms of trade between freezers and dishwashers has to be established. Both countries stand to gain from a swap of 3 freezers for 1 dishwasher. The allocation of output after trade has taken place is shown in the table above.
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