A PPF with Constant Opportunity Costs

Other Examples of Production Possibilities Frontiers (PPFs)

A PPF with Constant Opportunity Costs: Alternative Uses of Study Time

Suppose you are trying to decide how to spend the five hours between 7:00 p.m. and midnight. When you study economics, you can read 20 pages of your textbook each hour. By contrast, you can read 50 pages of your history textbook each hour. You could also spend part of the time reading magazines, watching television, talking on the telephone, or something else. A production possibilities frontier can be used to illustrate your options for spending these five hours. Let the vertical axis of a graph be used to measure the number of pages of your economics textbook you read. Let the horizontal axis measure the number of pages of your history textbook you read.

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Figure 3. A production possibilities frontier (PPF) for a student with five hours of study time. Straight-line PPFs illustrate constant opportunity costs.

If you spend all five hours reading your economics book, the maximum number of pages you could read is 100. (Five hours multiplied by 20 pages per hour equals 100 pages.) This is illustrated by point A in the graph. In this case, you cannot read any pages of your history book (because you are spending all five hours reading economics).

If you spend four hours reading your economics textbook and one hour reading your history book, you could read a maximum of 80 pages of economics and a maximum of 50 pages of history. This is illustrated by point B in the graph. Note that by reducing the amount of time spent reading your economics text, you lose the opportunity to read 20 pages of economics, but gain the opportunity to read 50 pages of history. The opportunity cost of reading 50 pages of history is the loss of the ability to read those additional 20 pages of economics.

If you spend three hours reading your economics book and two hours reading your history text, you could read a maximum of 60 pages of economics and a maximum of 100 pages of history. This is illustrated by point C in the graph. Note that by reducing the amount of time spent reading your economics book by one more hour, you lose the ability to read 20 pages of economics, but gain the opportunity to read 50 more pages of history. The opportunity cost of reading 50 additional pages of history is the loss of the ability to read 20 additional pages of economics.

If you spend two hours reading your economics textbook and three hours reading your history book, you could read a maximum of 40 pages of economics and a maximum of 150 pages of history. This is illustrated by point D in the graph. Again note that by reducing the amount of time spent reading your economics book by one more hour, you the lose the ability to read 20 pages of economics, but gain the opportunity to read 50 more pages of history. The opportunity cost of reading 50 additional pages of history is the loss of the ability to read 20 pages of economics.

If you only spend one hour reading your economics text and four hours reading your history book, you could read a maximum of 20 pages of economics and a maximum of 200 pages of history. This is illustrated by point E in the graph. By reducing the amount of time spent reading your economics book by one more hour, you lose the ability to read 20 pages of economics, but gain the opportunity to read 50 more pages of history. The opportunity cost of reading 50 additional pages of history is the loss of the ability to read 20 pages of economics.

If you spend all five hours reading your history book, the maximum number of pages you could read is 250. This is illustrated by point F in the graph. By reducing the amount of time spent reading your economics book by one more hour, you lose the ability to read 20 pages of economics, but gain the opportunity to read 50 more pages of history. The opportunity cost of reading 50 additional pages of history is the loss of the ability to read 20 pages of economics.

When these points are plotted on a graph, they can be connected to form a straight line that intersects the vertical axis at 100 pages of economics and intersects the horizontal axis at 250 pages of history. Any point on this line between the intercepts represents a possible combination of pages of economics and history which could be read if all five hours are devoted to reading economics and history. By spending more time reading history and less time reading economics, you can increase the number of pages of history you could read but must sacrifice some of the pages of economics you could read. Conversely, by spending more time reading economics and less time reading history, you can increase the number of pages of economics you could read but must sacrifice some of the pages of history you could read. This illustrates the concept of opportunity cost. If you choose to spend an hour reading 20 pages of economics, you forego the opportunity to spend that same hour reading 50 pages of history. The opportunity cost of reading 20 pages of economics is the 50 pages of history you forego reading. Similarly, if you spend an hour reading 50 pages of history, you forego the opportunity to spend that hour reading 20 pages of economics. The opportunity cost of reading 50 pages of history is the 20 pages of economics you forego reading.

In this simple example, there are constant opportunity costs. Constant opportunity costs occur when the quantity of one product that must be foregone to obtain a unit of another product is the same, regardless of how much has already been produced. Regardless of where you are on the PPF, the opportunity costs are the same. For each additional page of economics read, you forego the opportunity to read two and a half pages of history. (If you can spend one hour reading either 20 pages of economics or 50 pages of history, then you could spend 1/20 of an hour reading one page of economics (20/20 = 1) or two and a half pages of history (50/20 = 2 ½). Similarly, for each additional page of history read, you forego the opportunity to read 2/5 of a page of economics. (If you can spend one hour reading either 50 pages of history or 20 pages of economics, then you could spend 1/50 of an hour reading one page of history (50/50 = 1) or two-fifths of a page of economics (20/50 = 2/5). Graphically, constant opportunity costs are illustrated by a straight-line production possibilities frontier (PPF). The slope of the PPF, which measures the opportunity cost, is constant all along the PPF. Thus, any PPF that is a straight-line segment has constant opportunity costs.

It is impossible to produce at a point outside the production possibilities frontier. For example, you cannot read 80 pages of economics and 200 pages of history (point Z) in the same five hours. It is possible to produce at any point inside the PPF, however. For example, you could read 20 pages of economics and 50 pages of history (point S) and spend the other three hours doing something else. You could even produce at the origin (point W) and not read any economics or history.

A frontier is an edge or boundary. A production possibilities frontier separates attainable production points from those that are unattainable.

The points on the production possibilities frontier are efficient. Efficiency occurs when one achieves the largest possible output from a given set of resources. In this example, the set of resources is five hours of your time (i.e., labor). At any point on the PPF, it is impossible to read more pages of one subject without sacrificing pages of the other subject. Points inside the PPF are not efficient, however. For example, at point N, you spend two hours reading economics and one hour reading history. This point is not efficient because it would be possible to read more pages of economics or history simply by spending more of the five hours studying.

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Figure 4. An illustration of attainable, unattainable, and efficient points on a production possibilities diagram.