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Production possibility curve or production possibility frontier is concave to the origin because for producing  two kinds of goods,if one item is  increased the other item will have to be reduced because land is a fixed factor.that is ppc is concave to the origin. 

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Production Possibility Curve (PPC) is concave in shape it is due to the increase in the marginal rate of transformation(MRT). It shows that  when more and more units of a commodity are sacrificed in order to add an additional unit of another commodity.

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PPC Curve is concave towards the origin because of an increase in marginal opportunity cost, i.e., in order to produce more units of one good, few units of other goods need to be sacrificed.  

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Ppc curve shows all possible combinations of 2 goods which an economy can produce with full and efficient use of its given resources and available technology

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