One of the central principles of economics is that everyone faces tradeoffs because resources are limited. These tradeoffs are present both in individual choice and in the production decisions of entire economies.

The production possibilities frontier (PPF for short, also referred to as production possibilities curve) is a simple way to show these production tradeoffs graphically. Here is a guide to graphing a PPF and how to analyze it.

### Label the Axes

Since graphs are two-dimensional, economists make the simplifying assumption that the economy can only produce 2 different goods. Traditionally, economists use guns and butter as the 2 goods when describing an economy's production options, since guns represent a general category of capital goods and butter represents a general category of consumer goods.

The tradeoff in production can then be framed as a choice between capital and consumer goods, which will become relevant later. Therefore, this example will also adopt guns and butter as the axes for the production possibilities frontier. Technically speaking, the units on the axes could be something like pounds of butter and a number of guns.

### Plot the Points

The production possibilities frontier is constructed by plotting all of the possible combinations of output that an economy can produce. In this example, let's say the economy can produce:

- 200 guns if it produces only guns, as represented by the point (0,200)
- 100 pounds of butter and 190 guns, as represented by the point (100,190)
- 250 pounds of butter and 150 guns, as represented by the point (250,150)
- 350 pounds of butter and 75 guns, as represented by the point (350,75)
- 400 pounds of butter if it produces only butter, as represented by the point (400,0)

The rest of the curve is filled in by plotting all of the remaining possible output combinations.

### Inefficient and Infeasible Points

Combinations of output that are inside the production possibilities frontier represent inefficient production. This is when an economy could produce more of both goods (i.e. move up and to the right on the graph) by reorganizing resources.

On the other hand, combinations of output that lie outside the production possibilities frontier represent infeasible points, since the economy doesn't have enough resources to produce those combinations of goods.

Therefore, the production possibilities frontier represents all points where an economy is using all of its resources efficiently.

### Opportunity Cost and the Slope of the PPF

Since the production possibilities frontier represents all of the points where all resources are being used efficiently, it must be the case that this economy has to produce fewer guns if it wants to produce more butter, and vice versa. The slope of the production possibilities frontier represents the magnitude of this tradeoff.

For example, in moving from the top left point to the next point down the curve, the economy has to give up production of 10 guns if it wants to produce 100 more pounds of butter. Not coincidentally, the average slope of the PPF over this region is (190-200)/(100-0) = -10/100, or -1/10. Similar calculations can be made between the other labeled points:

- In going from the second to the third point, the economy must give up production of 40 guns if it wants to produce another 150 pounds of butter, and the average slope of the PPF between these points is (150-190)/(250-100) = -40/150, or -4/15.
- In going from the third to the fourth point, the economy must give up production of 75 guns if it wants to produce another 100 pounds of butter, and the average slope of the PPF between these points is (75-150)/(350-250) = -75/100 = -3/4.
- In going from the fourth to the fifth point, the economy must give up production of 75 guns if it wants to produce another 50 pounds of butter, and the average slope of the PPF between these points is (0-75)/(400-350) = -75/50 = -3/2.

Therefore, the magnitude, or absolute value, of the slope of the PPF represents how many guns must be given up in order to produce one more pound of butter between any 2 points on the curve on average.

Economists call this the** **opportunity cost of butter, given in terms of guns. In general, the magnitude of the PPF's slope represents how many of the things on the y-axis must be forgone in order to produce one more of the thing on the x-axis, or, alternatively, the opportunity cost of the thing on the x-axis.

If you wanted to calculate the opportunity cost of the thing on the y-axis, you could either redraw the PPF with the axes switched or just note that the opportunity cost of the thing on the y-axis is the reciprocal of the opportunity cost of the thing on the x-axis.

### Opportunity Cost Increases Along the PPF

You may have noticed that the PPF was drawn such that it is bowed out from the origin. Because of this, the magnitude of the slope of the PPF increases, meaning the slope gets steeper, as we move down and to the right along the curve.

This property implies that the opportunity cost of producing butter increases as the economy produces more butter and fewer guns, which is represented by moving down and to the right on the graph.

Economists believe that, in general, the bowed-out PPF is a reasonable approximation of reality. This is because there are likely to be some resources that are better at producing guns and others that are better at producing butter. If an economy is producing only guns, it has some of the resources that are better at producing butter producing guns instead. To start producing butter and still maintain efficiency, the economy would shift the resources that are best at producing butter (or worst at producing guns) first. Because these resources are better at making butter, they can make a lot of butter instead of just a few guns, which results in a low opportunity cost of butter.

On the other hand, if the economy is producing close to the maximum amount of butter produced, it's already employed all of the resources that are better at producing butter than producing guns. In order to produce more butter, then, the economy has to shift some resources that are better at making guns to making butter. This results in a high opportunity cost of butter.

### Constant Opportunity Cost

If an economy instead faces a constant opportunity cost of one producing one of the goods, the production possibilities frontier would be represented by a straight line. This makes intuitive sense as straight lines have a constant slope.

### Technology Affects Production Possibilities

If technology changes in an economy, the production possibilities frontier changes accordingly. In the example above, an advance in gun-making technology makes the economy better at producing guns. This means that, for any given level of butter production, the economy will be able to produce more guns than it did before. This is represented by the vertical arrows between the two curves. Thus, the production possibilities frontier shifts out along the vertical, or guns, axis.

If the economy were instead to experience an advance in butter-making technology, the production possibilities frontier would shift out along the horizontal axis, meaning that for any given level of gun production, the economy can produce more butter than it could before. Similarly, if technology were to decrease rather than advance, the production possibilities frontier would shift inward rather than outward.

### Investment Can Shift the PPF Over Time

In an economy, capital is used both to produce more capital and to produce consumer goods. Since capital is represented by guns in this example, an investment in guns will allow for increased production of both guns and butter in the future.

That said, capital also wears out, or depreciates over time, so some investment in capital is needed just to keep up the existing level of capital stock. A hypothetical example of this level of investment is represented by the dotted line on the graph above.

### Graphic Example of Effects of Investments

Let's assume that the blue line on the graph above represents today's production possibilities frontier. If today's level of production is at the purple point, the level of investment in capital goods (i.e. guns) is more than enough to overcome depreciation, and the level of capital available in the future will be greater than the level available today.

As a result, the production possibilities frontier will shift out, as evidenced by the purple line on the graph. Note that the investment doesn't have to affect both goods equally, and the shift illustrated above is just one example.

On the other hand, if today's production is at the green point, the level of investment in capital goods won't be enough to overcome depreciation, and the level of capital available in the future will be lower than today's level. As a result, the production possibilities frontier will shift in, as evidenced by the green line on the graph. In other words, focusing too much on consumer goods today will hinder an economy's ability to produce in the future.