Principles of Economics/PPF
The Production possibilities curve or frontier (PPF) is a graphical means of depicting the concept of diminishing returns and opportunity costs. The basic quandary here is how to use a limited (hence, skcarce) set of resources to satisfy infinite wants by as much as possible.
A single PPF curve is for an unchanging set of resources. If the resources change, so does the PPF. Insufficient resources for a second product mean a vertical/horizontal curve; insufficient resources for a single product means a curve that lies on the origin (these are trivial cases).
A two-dimensional PPF works with two products, each of them taking an axis (which one doesn't matter). The curve, or frontier, is formed from all the possible combinations of resources that produce the most products. The definition of most products is indeterminate due to the subjective value associated with both; hence, the curve of points. All points along the curve are productively efficient, but depending on society's goals, only one point will be allocatively efficient.
All points outside of the curve are unattainable (because they require more resources than are available) without trade with an external producer (such as is the case with international trade). All points within the curve are attainable but productively inefficient.
The basic frontier
For smaller entities such as individuals, the PPF curve will be almost exactly a straight line (at least for the majority of goods), which will reflect the budget constraints. However, for large entities that make a noticeable difference on the quantity of resources available, diminishing returns become apparent. Here is the PPF curve for such an entity. Note that at high values of either good, much of the other good must be sacrificed for a bit more of that one good.
Shifts in the frontier
When a change in the economy causes more or less of a good to be produced when others are held constant, that is considered a shift in the one good's production possibility. The positive version shifts the frontier outward along the axis the good is placed at, so here an increase in good 1's production possibility stretches the PPF along the x axis. It is possible for that to actually increase production of good 2, depending on how society apportions its resources.
Growth in the frontier
General economic growth increases all of the available goods (both in this case). The growth does not have to be proportionate, nor even hold the same shape, as this graph demonstrates.
Flattening of the PPF
When a technological advance makes it relatively easier to exchange between two goods, a flattening of the PPF occurs as is demonstrated in the graph. When a firm takes a smaller percentage of industry market share, its PPF also flattens because its actions have a less significant effect on the total resource/good supply to the point that it has to exert fewer and fewer sacrifices of one good to obtain the next unit of the other good. It should also be easy to imagine situations when the opposite is true.