Explain how to derive a production possibility curve.

Production possibility curve, also called production-possibility frontier (PPF) is a graph showing the different combination of maximum quantities that can be produced by economy given its resources. Theoretically the PPF can be determined for any numbers of goods, but the limitation of two dimensional graphs permit representation of only two alternate goods.

Typically economist use the example of guns and butters to explain the concept of PPF. An economy has a choice of producing consumer goods for its people, represented by butter, or producing goods for waging war, represented by guns. We can draw a PPF for these two goods by representing quantity of butter produced on one axis (say x-axis) and quantity of guns produced on the other.

If all the resources of the economy are used for making only butter with no guns produced at all, this will be the maximum quantity of butter that the economy can produced. combination of maximum butter and no guns will be represented by a point on x-axis corresponding to maximum quantity of butter. Similarly the the combination of maximum numbers of guns and no butter will be represented by a point on y-axis.

Instead of producing only butter we can divert some of the resources to produce guns. Thus we can determine the quantities of guns that we can produce with different quantities of butter, giving us different point on the PPF graph. We continue this process, till we find the quantity of guns we ca produce with just a small quantity of butter. We can plot all these combinations of quantities of butter and guns on the PPF graph, and join them with a smooth curve to get PPF or production possibility curve.