The production possibility frontier (PPF) represents the quantity of output that can be obtained for a certain quantity of inputs using a given technology. Depending on the technology, the PPF will have a certain shape.
As you can see on the adjacent figure, this PPF (blue curve) slopes downwards. This slope, which equals the marginal rate of transformation between X and Y, shows us how, in order to increase the output X, the quantity of Y must decrease. In fact, the marginal rate of transformation measures the tradeoff of producing more X in terms of Y.
This frontier determines the maximum output (of both X and Y) that can be obtained given the technology. Production at point A will produce more quantity of Y and less of X than production at point B. However, both are technically efficient, since they maximize the output. For example, production at point C is technically inefficient because, at any point on the PPF, more combined output is produced using given the technology. Also, point D is unattainable given the technology, being this is the reason why it is outside the PPF.
The PPF can be derived from the contract curve on an Edgeworth box. In this box, we see the quantity of inputs (K, L) being used in the production of each good (X,Y). In fact, we can see how, for each quantity of each product, the quantity of each input can change. The isoquants (green curve for X, red for Y) determine how much a certain input has to increase in order to compensate the decrease in the other input, maintaining the quantity of output produced unaltered. The slope of these curves is given by the marginal rate of technical substitution of each output.
The points where the isoquants of different outputs combination intersect, which are Pareto-optimal, allow us to draw the contract curve, from which the PPF can be derived. Since the technology is given, only one PPF can be derived from the contract curve (as opposed to the case of the utility possibility frontier).
Video – Production possibility frontier: