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Is it possible to construct a Production Possibility Frontier (PPF) for 3 goods? Would this require a 3D graph and a part of a sphere, in one quadrant (as opposed to the usual 2D plot, with a part of a circle in one quadrant).

Is this something used in more complex analysis of production?

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It is possible. In fact you can construct PPF for arbitrary number of goods.

When it comes to plotting it for a case of 3 goods it is easy to make 2D projection of the 3D space. You can see the image below for an example.

enter image description here

Also note PPF is not necessary spherical or circular. The shape of PPF depends on the opportunity cost. In textbooks you might sometimes see it represented like a portion of a circle or elipse but it does not necessarily have to have that shape.

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