What are PPFs (production possibility frontiers)? And what does the slope of a PPF mean?

PPF is an acronym for a production possibility frontier.  This means that the associated graph shows the maximum combination of goods that can be produced in a given amount of time with a given amount of resources.  This graph is a good example of the concept of ceteris paribus, because the only thing you can change within the graph is the combination of goods that are produced (time frame, inputs, technology, and other shocks are assumed to be equal or not change).  The PPF also graphical shows the trade off between each of the goods in question because as we decide to produce more of one good, we see less of the other good being produced (also known as the opportunity cost).

Anything within the PPF (inside, down or left) is considered feasible, but inefficient.  It is inefficient because given the same amount of input resources, we can produce more of either good (by moving up and/or right).  An example of this occurs at point A.

Point B shows us an example of an efficient output decision.  This is because we are
on the PPF, we cannot make more of one good without giving up some of the other good.  In other words, there is no free lunch.

Finally, if we are outside of the PPF (up or right) then we in the unfeasible range.  This is because the PPF shows us the maximum we can produce, and producing beyond this isn’t possible given our current inputs.  This is shown with point C.

With respect to point C, it is possible to get there if we have changes outside of the system, for example, growth in capital/labor, better technology, or we can potentially consume at that point given trade.  An example of an economy that has experienced better technology, or capital or labor growth is shown below:

Important:  Probably the most difficult thing to understand about PPFs is that the slope of the curve is equal to the opportunity cost or trade off of changing which goods are produced.  The most basic PPF is a linear one, where the opportunity cost or trade off of switching between goods remains constant.  If you have a bowed out curve (shaped like the outside of a circle) then you have increasing opportunity costs as you specialize, or produce more of the same good.  The bowed out PPF means that production favors a mix of products produced, rather than specialization.  If you have a bowed in curve than the opportunity costs decline as you specialize in one good.  Examples of these three cases are shown below:
Increasing Opportunity Costs, your normal PPF
A linear PPF, constant Opportunity Costs

A PPF with decreasing opportunity costs, very rare

 Remember:  A PPF (production possibilities frontier) shows the different combinations of goods that can be produced in a certain amount of time given fixed inputs.  If any of these factors change, than the PPF will change as well.  A hint for possible questions, if something good happens, the PPF will move up and right (meaning we can produce more stuff), if something bad happens then the PPF will likely shift in (meaning we can produce less than before).  Also remember that the slope of the PPF shows the trade off or opportunity cost associated with the goods.

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