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The concave curve called production possibility frontier (PPF) is a curve that represents the comparison of two goods or services that can be produced.
The concave to origin curve case explains the fact that each additional unit of one good produced sacrifices one or more units of the other good produced: it compares "two production sectors." Hence, when one good is produced, the opportunity cost of that product increases "because we are using more and more resources that are less efficient in producing it."
You need to remember that the opportunity cost, in the case of the concave to origin curve, represents the benefits that are lost--through the costs that are increased--by selecting to produce one good over another good: "the cost of producing successive units of [one product] will increase as resources that are more and more specialized [for the other product] are moved into the [first product] industry."
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