A PPF with Increasing Opportunity Costs

A PPF with Increasing Opportunity Costs: Alternative Uses of Farmland in the United States

Consider an extreme use of farmland in the United States. Pretend all U.S. farmland is used to grow oranges. Orange trees are planted in the tropical areas, such as Florida and California. In areas less suited to growing oranges, green houses are built to create a tropical environment in which to grow oranges. There is a maximum quantity of oranges that can be produced with the finite amount of farmland and other resources in the United States. This point is illustrated by point A in the graph below. Now suppose the United States considers using some of the farmland to grow wheat instead of oranges. It makes sense to stop growing oranges and begin growing wheat on the farmland that is not well suited for growing oranges but is well suited for growing wheat (perhaps Kansas or Nebraska). In order to gain a billion bushels of wheat, the U.S. must sacrifice a relatively small amount of orange production (2 million tons). It is a relatively small amount of oranges because the land was not well suited for orange production anyway.


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Figure 3-5. A production possibilities frontier (PPF) for U.S. farmland.
Curved PPFs illustrate increasing opportunity costs.

If the U.S. continues to switch farmland out of orange production and into wheat production, then the quantity of oranges produced will go down and the quantity of wheat produced will increase. For each additional ton of wheat produced, however, the sacrifice (in terms of reduced orange production) increases. Land that was a little bit better at growing oranges (such as Oklahoma) will be used to grow wheat. So in order to gain an additional thousand tons of wheat, the U.S. must sacrifice a relatively larger amount of orange production.

Suppose this process continues until the entire country is planted in wheat (point E). This implies bulldozing orange groves in Florida and California to build greenhouses to grow wheat. To obtain those last billion bushels of wheat (moving from point D to point E), the U.S. must sacrifice a relatively large amount of orange production (10 million tons).

In this example, the opportunity cost of producing additional wheat increases as wheat production increases. The amount of orange production that must be foregone in order to produce additional wheat increases as wheat production increases. Thus, this is an example of increasing opportunity costs. Increasing opportunity costs occur when the quantity of one product that must be foregone to obtain a unit of another product increases as more is produced.
Graphically, increasing opportunity costs are illustrated by a production possibilities frontier that is convex to the origin. The slope of the PPF, which represents the opportunity costs, increases as the production point moves down the curve.

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.

The Economic Perspective on Costs

Economists also have a different perspective on costs than many other people. Most people consider the cost of something to be the amount of money paid to acquire it. Economists prefer to consider opportunity costs. The opportunity cost of something is what is sacrificed or foregone when a choice is made.

Most people consider the costs of attending college to be the amounts paid for tuition, books, and similar expenses. When economists consider the costs of college, however, they think about the opportunity costs. The opportunity costs of college include everything that is foregone, sacrificed, or given up in order to attend college. The monies paid for tuition and books are certainly given up when one goes to college. Yet there are many other sacrifices, too. The time devoted to college could have been spent at a job. Whatever income could have been earned at that job is also given up when one attends college full-time.

If the annual cost of tuition and books is $20,000 and a person quits a job that pays $30,000 per year in order to attend college, then economists would say the true costs, or opportunity costs, are $50,000 rather than the $20,000 most people consider.

A similar argument can be made about the costs of war. Most people think about the bombs, missiles, and other munitions used. It is also expensive to transport troops and equipment to the battleground, particularly if it is halfway around the world. When calculating the costs of war, however, economists also include the sacrifice of what else military personnel could do with their time and effort. This is especially relevant to the men and women who lose their lives and reservists who, in the absence of war, would be productive in the civilian sector of the economy.

The Opportunity Cost of War in Iraq

The August 31, 2007 article "The Opportunity Cost of War in Iraq," provides data and links to estimate the U.S. opportunity cost of the war in Iraq.