pcecon.com Class Notes

Production Possibilities Curve

The efficient production possibilities for a single producer or group of producers can be shown graphically. Such a graph is called the production possibilities curve. It is based on this idea: for any amount of one good that is produced, there is one efficient (maximum) amount of another good that could also be produced, given the resources and technology we have to use. For example, if we wish to produce a particular amount of good X, there is a maximum amount of good Y that could also be produced.

In class, we used examples from your study guide, but here is another:
Suppose we have three producers, Red, Purple and Blue.
Red can produce 5 X or 5 Y (so each X costs 1 Y and each Y costs 1 X).
Purple can produce 10 X or 30 Y (so each X costs 3 Y and each Y costs 1/3 X)
Blue can produce 5 X or 20 Y (so each X costs 4Y and each Y costs 1/4 X)

To find the efficient possible combinations of X and Y that the available resources can produce, we must remember to use them in the order of comparative cost advantage. The producer or resource that can produce X at the lowest cost (in terms of Y given up or not produced) should be used to produce the first few units of X. Then, the second-lowest cost X producer should be used, and so on.

What do the possibilities look like? One possibility would be to have all three producers produce Y (and no one produce X). If we did this, the total output would be 55 Y and 0 X. This would be efficient (and is possible). It is shown as the first combination on the table below.
If we want any X produced, the comparative advantages (costs) would require that Red produce the X, since Red is the lowest cost producer. Each X that Red produces would require giving up one Y, so we could get 1X and 54Y, or 2X and 53Y, or 3X and 52Y, etc. If we want more than 5 X produced, we would then have Purple produce them (at a cost of 3Y each). Only if we want more X than Red and Purple could produce would we have Blue make any X.
Following this line of thinking, we get the table below:

Here, the red numbers represent Red switching from making Y to making X (the first five Xs must be made by Red in order to be efficient). The trade-off or cost of Red doing this is that each X costs one Y. The purple numbers represent Purple then switching from Y to X, at a cost of three Y per X. The blue numbers represent Blue switching from Y to X, at a cost of four Y per X.

If we graph these efficient possibilities, we get a diagram called the production possibilities curve, which shows all of the combinations of flats and lubes that are possible and efficient. The segments' colors correspond to which producer is being switched from Y to X (red for Red, purple for Purple, and blue for Blue):

This graph is the production possibilities curve (PPC for short).
While you won't have to make a PPC, there are a few things you should know about it:

First, the slopes of the three segments making up the PPC indicate the costs of having the producers make X. That is why Red's segment is flattest (Red's costs of making X are least), Purple's is steeper than Red's, (because of Purple's higher cost of making X). Blue's segment is the steepest, because Blue's cost of making X is the highest. These costs dictate the bowed or bent shape of the production possibilities curve (PPC). Most PPCs will be flatter at the top than at the bottom, indicating that the cost of making X (the good on the horizontal axis) increases as more of it is being made. This also means that the cost of making Y (the good on the vertical axis) is decreasing as less of it is made.

Second, all of the combinations on the PPC are possible and efficient. If we are producing a combination of X and Y that is on the PPC, and is thus efficient, more of one good can be produced only by producing less of the other good. For example, if we are producing 5X and 50Y and wish to produce more X, we can do so only by reducing the production of Y. We could thus have 6X produced along with 47Y, but we could not produce 6X and 50Y together. The fact that producing an additional X requires us to produce fewer Ys indicates that the original combination (of 5X and 50Y) was efficient. So, for that matter, would be producing 6X and 47Y; there are many efficient combinations.

Third, all of the combinations below the PPC (which are also described as being inside or to the left of the PPC) are possible, but not efficient. For example, it is possible to produce 1 X and 51 Y (shown on the diagram), but it is not efficient to do so, since it is possible to produce 1X and more than 51Y (in fact, we can produce 1X and 54 Y). An inefficient combination might be produced if resources (producers) are used in a way that does not consider or exploit their comparative advantages, such as if Blue (rather than Red) is used to make the first X. If a combination is inefficient, it is possible to produce more of one of the goods without producing less of the other good. 1X and 51Y is inefficient because it is possible to produce more Y without producing fewer X (we can produce 1X and 54Y just by changing which producer is making the X).

Fourth, points to the right of the PPC, (which could also be described as being outside or above the PPC) represent combinations of X and Y that are not possible using the resources or producers available. Such a combination of X and Y is shown at 12X and 50Y on the diagram.

In addition, if new resources are employed, or if other things change, combinations which are now impossible might be made possible in the future.
In addition to having more resources, the possibilities might be expanded by having better technology, education (training), weather, or infrastructure (such as communications or transportation of parts and the like). If such changes make greater production possible, a new production possibilities curve must be drawn, as is shown below.

The curves shown above are smoother than the Red, Purple, and Blue curve, reflecting the shape we would expect if there were many more resources or producers (actually, the smooth curves are made up of many tiny segments put together instead of only three). These might reflect the production possibilities of X and Y for a large factory, a large city with lots of producers, or a whole country.

The PPC does not have to show two relatively specific goods. We could designate that X is "pizza" and Y is "everything else," for example. For that matter, we can use it to show any two good that could be produced with a given set of resources
Copyright 2006 by Ray Bromley. For economics information, and other information about Ray Bromley, visit www.raybromley.com. Permission to copy for educational use is granted, provided this notice is retained. All other rights reserved.
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