At what price do they trade?

Now that we have confirmed that total output is higher with complete or incomplete specialization than under self-sufficiency, we know there must be a relative price at which trade makes both countries better off. The relative price for trade is such that both countries can buy wine or cloth at a lower cost than their opportunity cost of producing that good.

Opportunity costs

  Opportunity cost of cloth:
bottles of wine per meter of cloth
Opportunity cost of wine:
meters of cloth per bottle of wine
Portugal \(\dfrac{1,000}{2,000} = \dfrac{1}{2}\) \(\dfrac{2,000}{1,000} = 2\)
England \(\dfrac{1,250}{3,750} = \dfrac{1}{3}\) \(\dfrac{3,750}{1,250} = 3\)

For each bottle of wine, Portugal could produce two meters of cloth while England could produce three meters. Portugal has a comparative advantage in wine, so to be willing to trade, the price of wine must be higher than Portugal’s opportunity cost of producing wine. In other words, Portugal must receive more than two meters of cloth in exchange for a bottle of wine. Otherwise, Portugal would just decide to produce the cloth on its own, losing less wine in the process.

Conversely, for England to be willing to buy wine, the price of one bottle has to be below its opportunity cost to produce wine. England will only buy wine if the cost is below three meters of cloth; otherwise, it would be cheaper to make wine.

Therefore, the relative price at which wine trades must be between two and three meters of cloth. It is between the opportunity cost of both countries, so Portugal benefits from selling it, and England benefits from buying it.