Production Possibilities

How are trade-offs and opportunity cost related?

Production Possibilities, p
. 21

Scarcity implies the existence of tradeoffs. These tradeoffs can be illustrated quite nicely by a production possibilities frontier.
For simplicity, it is assumed that a firm (or an economy) produces only two goods (this assumption is needed only to make the representation feasible on a two-dimensional surface -- such as a graph on paper or on a computer screen). When a production possibilities curve is drawn, the following assumptions are also made:

1. there is a fixed quantity and quality of available resources,
2. technology is fixed, and
3. there are no unemployed nor underemployed resources

Very shortly, we'll also see what happens when these assumptions are relaxed.

For now, though, let's consider a simple example. Suppose that a student has four hours left to study for exams in two classes: introductory microeconomics and introductory calculus. The output in this case is the exam score in each class. The assumption of a fixed quantity and quality of available resources means that the individual has a fixed supply of study materials such as textbooks, study guides, notes, etc. to use in the available time. A fixed technology suggests that the individual has a given level of study skills that allow him or her to translate the review materials into exam scores. A resource is unemployed if it is not used. Idle land, factories, and workers are unemployed resources for a society. Underemployed resources are not used in the best possible way. Society would have underemployed resources if the best brain surgeons were driving taxis while the best taxi drivers were performing brain surgery.... The use of an adjustable wrench as a hammer or the use of a hammer to pound a screw into wood provide additional examples of underemployed resources. If there are no unemployed or underemployed resources, efficient production is said to occur. 

The table below represents possible outcomes from each various combination of time studying each subject: 

Notice that each additional hour spent studying either calculus or economics results in smaller marginal improvements in the grade. The reason for this is that the first hour will be spent studying the most essential concepts. Each additional hour is spent on the "next-most" important topics that have not already been mastered. (It is important to note that a good grade on an economics examination requires substantially more than four hours of study time.) This is an example of a general principle known as the law of diminishing returns. The law of diminishing returns states that output will ultimately increase by progressively smaller amounts as additional units of a variable input (time in this case) are added to a production process in which other inputs are fixed (the fixed inputs here include the stock of existing subject matter knowledge, study materials, etc.).

To see how the law of diminishing returns works in a more typical production setting, consider the case of a restaurant that has a fixed quantity of capital (grills, broilers, fryers, refrigerators, tables, etc.). As the level of labor use increases, output may initially rise fairly rapidly (since additional workers allow more possibilities for specialization and reduces the time spent switching from task to task). Eventually, however, the addition of more workers will result in progressively smaller increases in output (since there is a fixed amount of capital for these workers to use). It is even possible that beyond some point workers may start getting in each others way and output may decline ("too many cooks may spoil the broth...." sorry.... I couldn't resist).

In any case, the law of diminishing returns explains why your grade will increase by fewer points with each additional hour that you spend studying.

The points in the table above can be represented by a production possibilities curve (PPC) such as the one appearing in the diagram below. Each point on the production possibilities curve represents the best grades that can be achieved with the existing resources and technology for each alternative allocation of study time. 

Let's consider why the production possibilities curve has this concave shape. As the diagram below indicates, a relatively large improvement in economics grade can be achieved by giving up relatively few points on the calculus exam. A movement from point A to point B results in a 30-point increase in economics grade and only a 10-point reduction in calculus grade. The marginal opportunity cost of a good is defined to be the amount of another good that must be given up to produce an additional unit of the first good. Since the opportunity cost of 30 points on the economics test is a 10-point reduction in the score on the calculus test, we can say that the marginal opportunity cost of one additional point on the economics test is approximately 1/3 of a point on the calculus test. (If in doubt, note that if 30 points on the economics exam have an opportunity cost of 10 points, each point on the economics test must cost approximately 1/30th of 10 points on the calculus test -- approximately 1/3 of a point on the calculus test). 

Now, let's see what happens a second hour is transferred to the study of economics. The diagram below illustrates this outcome (a movement from point B to C). As this diagram indicates, transferring a second hour from the study of mathematics to the study of economics results in a smaller increase in economics grade (from 30 to 45 points) and a larger reduction in calculus grade (from 75 to 55). In this case, the marginal opportunity cost of a point on the economics exam has increased to approximately 4/3 of a point on the calculus exam. 

The increase in the marginal opportunity cost of points on the economics exam as more time is devoted to studying economics is an example of the law of increasing cost. This law states that the marginal opportunity cost of any activity rises as the level of the activity increases. This law can also be illustrated using the table below. Notice that the opportunity cost of additional points on the calculus exam rises as more time is devoted to studying calculus. Reading from the bottom of the table up to the top, you can also see that the opportunity cost of additional points on the economics exam rises as more time is devoted to the study of economics. 

One of the reasons for the law of increasing cost is the law of diminishing returns (as in the example above). Each extra hour devoted to the study of economics results in a smaller increase in the economics grade and a larger reduction in the calculus grade because of diminishing returns to time spent on either activity.
A second reason for the law of increasing cost is the fact that resources are specialized. Some resources are better suited for some some types of productive activities than for other types of production. Suppose, for example, that a farmer is producing both wheat and corn. Some land is very well suited for growing wheat, while other land is relatively better suit for growing corn. Some workers may be more adept at growing wheat than corn. Some farm equipment is better suited for planting and harvesting corn.

The diagram below illustrates the PPC curve for this farmer. 

At the top of this PPC, the farmer is producing only corn. To produce more wheat, the farmer must transfer resources from corn production to wheat production. Initially, however, he or she will transfer those resources that are relatively better suited for wheat production. This allows wheat production to increase with only a relatively small reduction in the quantity of corn produced. Each additional increase in wheat production, however, requires the use of resources that are relatively less well suited for wheat production, resulting in a rising marginal opportunity cost of wheat.

Now, let's suppose that this farmer either does not use all of the available resources, or uses them in a less than optimal manner (i.e., either unemployment or underemployment occurs). In this case, the farmer will produce at a point that lies below the production possibilities curve (as illustrated by point A in the diagram below). 

In practice, all firms and all economies operate below their production possibilities frontier. Firms and economies, however, generally attempt to get as close to the frontier as possible.

Points above the production possibilities cannot be produced using current resources and technology. In the diagram below, point B is not obtainable unless more or higher quality resources become available or technological change occurs. 

An increase in the quantity or quantity of resources will cause the production possibilities curve to shift outward (the curve should shift outwards for both wheat and corn). This type of outward shift could also be caused by technological change that increases the production of both goods.
Thus, for the production of both goods: an increase in the quantity or quantity of resources will cause the production possibilities curve to shift outward.

Cf. http://www.oswego.edu/~economic/eco101/chap2/chap2.htm

In some cases, however, technological change will only increase the production of a specific good. The diagram below illustrates the effect of a technological change in wheat production that does not affect corn production.