The Production Possibility Model
I. Basics of the Model
Recall that one of the steps in building economic models by the scientific method is to make assumptions. Assumptions fill two basic purposes. Assumptions either reflect reality, increasing the ability of the model to make accurate predictions about the real world, or they serve to simplify the model, hopefully without the model losing the ability to predict. Thus, one of the assumptions of the production possibility model must be that resources are scarce, leading to scarcity of produced output as well. The model will also include some simplifying assumptions. For example, to make things simple, we'll assume that our economy produces only two goods, guns and butter. We will also assume, as implied by the name of the model (production possibilities) that we are interested in examining the implications that scarcity has upon decisions regarding production.
The main purpose of the simplifying assumption that our economy only produces two goods, guns and butter, is to allow the use of simple graphical analysis. Consider Graph 1 (follow the hyperlink to Graph 1.) The quantity produced for each of the two goods in the economy, guns and butter, is measured on the two axes. A single point on the graph can represent any combination of production for each good. For example, the production of 120 Guns and 100 pounds of butter is represented by point A. Similarly, any other combination of butter and gun production can be represented on the graph by a single point.
Recall that our model assumes scarcity of resources and, hence, scarcity of production. But how do we show scarcity in our simple graphical model? Scarcity is illustrated by the addition of what we will call a production possibility frontier (PPF) to our graph, as shown in Graph 2.
The PPF curve divides production space into 3 distinct areas, points on the PPF curve (points like B), points outside the curve (points like C), and points on the inside of the curve (points like A). Carefully consider the differences between the three types of points.
Scarcity is demonstrated by considering the difference between points like C, outside the frontier, and points like A and B, either on the frontier or on its interior. Points outside the frontier, like point C, are unattainable with the economy's current level of resources and technology. Points either on or inside the frontier, points like B and A, are attainable with the currently level of resources and technology.
The addition of the PPF curve thus illustrates scarcity by dividing production space into attainable and unattainable levels of production. However, not just any PPF curve illustrates scarcity. Consider, for example, the upward sloping PPF curve in Graph 3. For this PPF curve, the production of more of both goods is attained by moving upward along the frontier. Hence, it is only with a downward sloping, finite PPF curve, where producing more of one good on the PPF curve can only occur by producing less of the second good, that scarcity is illustrated.
As noted above, scarcity is illustrated by the existence of a downward sloping PPF curve, which divides production space into attainable and unattainable production combinations. However, what is the difference between the two types of attainable production combinations, points on the PPF curve (like point B in Graph 2) versus points inside the PPF curve (like point A)?
At a point on the frontier, like point B, the only way to produce more of one good, such as guns, is to produce less of the other good. Since the economy cannot produce more of both goods, clearly, it must be producing the maximum possible output given its resources and technology. But this is exactly the definition for technological efficiency that was discussed in the previous chapter. Hence, we can conclude that if an economy is producing on its PPF curve then it must be technologically efficient. Furthermore, in order to produce the maximum output on the frontier, the economy must clearly be utilizing all of their resources. In other words, resources like labor must be fully employed at points like B on the frontier.
What, then, is the difference between points on the frontier and points, like A, on the interior of the PPF curve? Clearly, since points on the PPF curve are possible, the economy could produce more of both goods. Hence, it is clearly not producing the maximum amount of output given its resources. There are three possible reasons for the economy's failure to produce the maximum possible output, either
As a result we can conclude that points on the frontier represent both technological efficiency and full employment of resources. However, points inside the frontier represent either technological inefficiency, unemployment of resources, or both inefficiency and unemployment.
Recall that opportunity cost is defined to equal the value of the next best alternative whenever a choice is made. Given scarcity, the PPF model demonstrates that choices must be made between the production of the two different goods, guns and butter, measured on the axes. This concept is illustrated by the PPF curve in Graph 4.
On the PPF curve, as is true of all downward-sloping PPF curves, this economy can only produce more of one good, such as guns, by decreasing the production of the other good, butter. But what is the opportunity cost of the decision to give up butter production in order to produce more guns?
To answer this question first consider how much butter one would have to give up if one went from producing only butter, point A on the PPF curve, to producing only guns, point B on the PPF curve. In this case, one would gain the production of 100 guns but only by giving up the production of 100 pounds of butter. Thus, the opportunity cost of the 100 guns that we chose to produce equals the production of 100 pounds of butter that was given up as a result. But how much would it cost us to produce just one more gun, rather than 100 more that we chose to produce? We can calculate this by using a simple equation. We already know that:
1. 100 G = 100 B
But we want to find out, not how much 100 guns cost in terms of foregone butter, but how much 1 gun costs. To find this simply divide both sides of the above equation by 100 to get:
2. 1 G = 1 B
Thus, we must give up 1 pound of butter for each extra gun we produce. The reverse is also true; we must give up 1 gun for each extra pound of butter we produce.
Now that we have the basics of determining opportunity cost for a PPF curve, let's try it again with a little more difficult PPF curve. Consider the PPF curve in Graph 5. Similar to the PPF curve in Graph 4 when all resources are devoted to producing butter, the maximum amount of butter that can be produced is 100 pounds. This is represented by point A on the graph. However, unlike Graph 4, the maximum number of guns that can be produced is only 50 guns, at point B. Thus, the production of each gun must require more productive resources in Graph 5.
In this situation, what happens to the opportunity cost of guns and butter? The easiest way to calculate opportunity costs is to follow the exact same procedure we used to calculate them for the PPF curve in Graph 4. That is, move from the intercept of the PPF curve on the butter axis, where only butter is being produced (point A), to the intercept of the PPF curve on the guns axis, where only guns are being produced. When we move from point A to point B, we gain 50 guns but give up 100 pounds of butter. Hence, we can say that the opportunity cost of 50 guns is 100 pounds of butter, or in equation form:
3. 50 G = 100 B
To get the opportunity cost of one gun, instead of 50 guns, divide both sides of the equation by 50 which yields: 1 G = 2 B. Hence, on the PPF curve in Graph 5 every time we wish to increase our production of guns by 1 we must decrease our production of butter by 2 pounds. What is the opportunity cost of butter? To find this divide both sides of equation 3 by 100 to obtain: 1 B = ½ G. Thus, on the PPF curve in Graph 5 it we must give up the production of ½ a gun every time we increase our butter production by 1 pound.
Notice that the opportunity costs are reciprocals (the reciprocal of x is 1/x.) This is always true for opportunity costs on linear PPF curves. Hence, if we had an additional PPF curve where we found that 1 gun cost 4 pounds of butter, we would know that 1 pound of butter must cost ¼ of a gun. Furthermore, along a linear PPF curve, the opportunity costs remain constant. Hence, in Graph 5, one extra gun always costs two pounds of butter.
Recall that the PPF model models the production of goods with an economy's limited resources and current level of technology. Hence, there exist two basic methods by which a PPF curve can shift: (1) a change in the amount of available resources or (2) a change in the level of technology.
- A Change in Resources
Changes in available resources have a fairly straightforward impact upon PPF curves. An increase in resources allows the economy to produce more output and, hence, will shift the PPF curve to the right, increasing the economy's production possibilities. Likewise, a decrease in the amount of resources available will have the impact of shifting the PPF to PPF1 the left. These two situations are illustrated in Graph 6.
- A Change in Technology
A change in technology is similar to a change in the amount of resources available in an economy. In fact, if the change in technology is general in nature, then the PPF curve will shift just as it does in Graph 6. A general increase or decrease in technology will change the ability of the economy to produce both goods on the axes. Hence, the PPF curve will shift to the right as illustrated by Graph 6 with a general increase in technology and to left with a general decrease in technology.
However, it is common for changes in technology to occur that are specific to the good. Suppose, for example, that the technology for producing butter improved but the technology for producing guns remained constant. How would the PPF curve change? In order to answer this question, it is useful to consider what would happen to the intercepts, where the economy is devoting all of its resources to producing either only butter or only guns.
Clearly, when only butter technology has increased then this will have a positive impact on the intercept on the butter axis. Recall that when at this intercept all of the economy's resources are devoted to producing only butter. When butter technology increases, this will allow these resources to produce a larger amount of butter.
However, when only butter technology increases then the increased technology will have no impact upon the intercept on the gun axis. Again, recall that when at this intercept all of the economy's resources are devoted to producing only guns. When technology increases, since it is specific to producing butter and the economy is producing only guns, no more production can occur. Hence, the intercept on the gun axis will remain constant. As a result, an increase in butter technology will rotate the PPF out, as illustrated in Graph 7.
II. What Does the Model Show?
From the discussion in Section I above, it is clear that the model demonstrates a number of key concepts. Each student should be able to identify how the model demonstrates the following concepts:
However, the model can also be used to show additional important concepts.
In the previous chapter we discussed the Scientific Method. Recall that one of the steps in the scientific method was to test or compare the model to the actual world. Taking that step with the PPF model will yield some important insights. The PPF curves in all of the examples we presented in the graphs above were linear. As we discussed in Section I – E, opportunity costs are constant along linear PPF curves. That is, if it costs 4 pounds of butter to produce the first gun, it will also cost 4 pounds of butter to produce each successive pound of butter.
However, a crucial implicit assumption underlies the linear, constant opportunity cost PPF curves that needs to be examined for plausibility. Recall that, since PPF curves deal with production, whenever we shift from the production of one good, such as butter, to the production of another good, such as guns, resources must also be transferred. That is, in order to switch production one must first switch resources from the production of one good to the production of the other good.
Linear, constant opportunity cost, PPF curves assume that these resources are homogenous. Homogeneity of resources simply means that all resources are exactly the same. Hence, homogeneity denies the possibility that some resources are better suited to producing guns, say, than butter or the reverse. However, this implicit assumption does not seem particularly realistic as surely not all resources are homogenous. What happens to our PPF curve when resources are not homogenous but differ in their ability to produce different goods (i.e., the resources are heterogeneous)?
Consider the following example, where at least some resources are heterogeneous. To simplify, the example considers only one resource, labor. Suppose that there are three types of labor:
- Jill Machinist – Better at producing guns than butter.¬ heterogeneous resource
- Joe Farmer – Better at producing butter than guns. ¬ heterogeneous resource
- Jack Handyman – equally productive for either guns or butter. ¬ homogeneous resource
Now consider what happens when the economy is producing only butter initially and then begins to produce guns. If the economy is producing only butter, then it must be the case that all of the resources, all the Jills, Joes, and Jacks, are currently being employed in butter production. However, in order to begin producing guns, some of these resources must be switched from butter production to gun production. Consider the following two questions.
Clearly, it would make more sense to switch first those resources that are worse at producing butter and better at producing guns, such as the Jill Machinists. There are two advantages of using this type of labor first as the economy begins to produce guns.
- The loss of butter production is low because this type of labor is not very good at producing butter anyway.
- The gain in gun production will be high because this type of labor is most productive in gun production.
For both of the above reasons, that only a little butter production is lost for a large gain in gun production, the opportunity cost of producing guns must initially be low as gun production is increased. This is illustrated in Graph 8.
Initially, the economy is producing at point A, devoting all of its resources to efficiently produce 100 pounds of butter and no guns. Hence, point A is one point on the PPF curve. Following the above scenario, we begin to produce guns by shifting first those resources that are best able to produce guns and worst at producing butter. Hence, we get only a small decrease in butter production for a large increase in gun production. As noted above, this must mean that the opportunity cost for guns is small. In Graph 8, the increase in gun production is illustrated by a move from point A to point C.
Now consider what happens as we begin to increase the production of guns even more. As noted above, initially it makes sense to switch those resources that are best at producing guns and worst at producing butter. Once those types of resources are all switched into gun production, in order to continue to increase gun production then it makes sense to move those types of resources, the Jacks, which are homogenous. But eventually, as gun production continues to increase, it becomes necessary to begin to use those resources that are most productive in butter productive and least productive in gun production.
Graph 9 illustrates the situation that occurs as we finally get to the point of shifting the very last of these resources into gun production by finally moving to point B, where we are producing only guns. The last resources that we switch from producing butter to guns will, again, be those resources (the Jacks) that are most productive in butter production. Thus, we can see that:
- The loss of butter production is high because this type of labor is most productive in producing butter.
- The gain in gun production will be low because this type of labor is least productive in gun production.
For both of these reasons, the opportunity cost of producing guns will be high. This is illustrated in Graph 9 by a movement from point D to point B. Just as both points A and C are on the PPF curve, so must be both points B and D.
There are two important points to highlight. First, we demonstrated above that the opportunity cost of guns is initially low but eventually rises as production of guns occurs. Thus, rather than having constant opportunity costs, as do linear PPF curves, our new PPF curve will have increasing opportunity costs.
In fact, this is such an important point that economists refer to it as a law. Just as with physical laws, such as the law of gravity, economic laws refer to economic, rather than physical, phenomena that occur naturally in the real world. The law of gravity is considered a "law" because it has been tested so many times so as to be virtually sure that it is consistent. Likewise, economic laws are considered "laws" because they have been tested so many times as to be virtually sure that they occur. The above discussion develops one such economic law: the law of increasing (opportunity) cost.
Definition: The Law of Increasing Opportunity Cost - as the production of a good increases, ceteris paribus (holding all other variables constant,) the (opportunity) cost of that increased production must eventually increase.
Second, we developed four points, points A, B, C, and D, which are all on our new PPF curve. Graph 10 shows these four points connected, demonstrating how a PPF curve with increasing opportunity costs appears. Notice that the PPF curve in Graph 10 is bowed out from the origin, or concave, rather than linear as was the case for PPF curves with constant opportunity costs. Hence, the PPF model illustrates the law of increasing opportunity cost by using a concave PPF curve.
Definition: The Law of Diminishing Returns – as the production of a good increases, ceteris paribus, the increase in output for a fixed increase in resources must eventually become smaller.
The discussion of the law of increasing opportunity costs clearly identifies why the law of diminishing returns must also be correct. Essentially, what the law of diminishing returns says, in terms of the example used above, is that as we increase gun production we must switch resources from the production of butter to the production of guns. Again, assuming that these resources are heterogeneous, and we begin to move one unit of labor, one Jack, one Jill, or one Joe, into gun production at a time, eventually we must come to the point where doing so yields a smaller increase in gun production. Recall, that initially we would want to switch the Jills, because they are best a producing guns. But when we eventually ran out of this type of labor, we would have to begin using a type of labor that is less productive in gun production. It is at this point in our example that diminishing returns would begin.
Notice that these two laws, of diminishing returns and increasing opportunity costs, are inextricably connected. Why do we have increasing opportunity costs? Because, as was described in the previous section, diminishing returns exist. Without diminishing returns opportunity costs would not rise as the production of a good increased in the PPF model. Hence, it is fair to say that diminishing returns cause increasing opportunity costs in the model.
Recall that increasing opportunity costs are illustrated in the model by a concave PPF curve. Diminishing returns are not illustrated directly by the PPF model. However, because diminishing returns cause increasing opportunity costs, a concave PPF curve indirectly illustrates diminishing returns as well as directly showing increasing opportunity costs.
The PPF model can also be used to demonstrate how today's choices can affect our future production possibilities. However, for this the goods on the axes must change from guns and butter to more realistic, not to mention relevant, choices. Suppose, for example, that the goods on the axes are consumption goods (C) and investment goods (I).
What are investment goods? In this context, producing investment is to produce new capital. Capital, as we learned in the first chapter, is a resource that is itself an output from a production process. Investment as the term is being used here does not, however, refer to a financial investment. Hence, as an economy increases its production of investment goods it affects the resources that are available, not today before the completion of the new production, but in the future after the new capital begins being used as a resource.
In contrast to investment goods, consumption goods are those goods that cannot be used as a resource, but instead is consumed after production. Consumption may either be durable, in which case it takes a period of time before the good is consumed, or non-durable, in which case the consumption occurs more quickly. Oranges and apples are examples of non-durable consumption goods while refrigerators and furniture are examples of durable consumption goods.
Graph 11 shows a PPF curve with consumption goods and investment goods on the two axes. Notice that the graph has a certain level of investment labeled as IR. Recall that investment equals additions to the stock of a particular resource, capital. Capital is a durable good that lasts for a number of years. However, capital does eventually wear out and must be replaced or the total stock of capital available as a resource will fall. IR equals the replacement level of capital, that amount of new capital that must be produced in order to keep the stock of capital from falling.
Hence, if society chooses to produce investment less than IR then the amount of capital will fall. Likewise, if society chooses to produce more investment than IR then the amount of capital will rise. Finally, if society chooses to produce exactly IR then the amount of capital will remain constant. However, capital is itself a productive resource which is used to produce either investment or consumption goods. As explained above in Section I-F, changes in resources will move the production possibility frontier. In this case, the PPF curve will change in the future, not in the present. This is because investment goods are currently being produced in the present. It is only in the future that this production of resources will have an impact on the PPF curve.
Graph 12 illustrates how choices made today can affect future production possibilities. If this economy decides to produce at point B then investment equals IR, the replacement level and the PPF curve will not change in the future. However, if the economy chooses to produce at point A of the original PPF curve then investment will be set at less than its replacement level. This means that in the future the amount of capital available will fall and the PPF will decrease. This is shown in Graph 12 by a movement from the PPF curve labeled PPF to the one labeled PPFA.
Likewise, if the economy chooses to produce at point C of the original PPF curve, then investment will be set at more than its replacement level. Hence, in the future the amount of capital will rise and the PPF will increase. This is illustrated in Graph 12 by a shift from the curve labeled PPF to the one labeled PPFC.
Recall that we began a list above that included concepts that the PPF model demonstrated. Several concepts were then added to the list. The full list is included below. Each student should remember each item on the list and understand how the model demonstrates each concept.
Although the model can be used to illustrate a number of important economic concepts, there are some concepts that it does not illustrate. There is one concept in particular, allocative efficiency, that students often erroneously conclude is illustrated by the PPF model. Recall that allocative efficiency focuses on answering the basic economic questions of what to produce and who will receive those goods. That is, it focuses on the question of the efficient allocation of resources into different productive enterprises. In terms of the PPF model, allocative efficiency deals with the issue of which choice, out of all of the available choices, is the best choice for society.
However, the PPF model does not answer the question of which choice is the best, or most efficient, choice to make. It merely illustrates that choice must be made but does not offer any meaningful insight into which choice is best. This can be illustrated by the following true/false question, using Graph 13.
True or False - In Graph 13, point D on the PPF curve is a better (more allocatively efficient) choice for this economy than point C, because at point D the economy's production possibilities will increase more in the future.
Many students will answer True to this question because the last part of the statement is undoubtedly true
This can be easily illustrated simply by following the same logic used to conclude that the above statement is true to its logical conclusion. If point D is more efficient than point C, then it must be the case that point E is more efficient that point D for the same reason. In fact, by this logic point F is the most efficient choice of all, because production of investment goods are maximized, which maximizes future production possibilities. But at point F, the production of consumption goods is zero, meaning that everyone in the economy starves.
Clearly, a choice where the entire population dies cannot be efficient. Hence, the above True/False question is false. More specifically, any economy values both consumption and investment. It values investment goods because of the future production possibilities such investment generates. It values consumption goods because they generate satisfaction for individuals in the economy. The most allocatively efficient choice between consumption and investment goods depends upon how the society values each type of good. Our simple PPF model does simply not provide such information.
III. Application of the Model - The Vicious Circle of Poverty
The general utility of the PPF model is illustrated by an example known as "the vicious circle of poverty." The vicious circle example compares the choices faced by two types of countries: (1) developed countries like the U.S. and (2) developing countries, like many of those in Central and South America. Two of the main differences between developed and developing countries deal with resources and technology with developed countries having both more resources and much better technology. As a result, a developed country's PPF curve will be much larger relative to its population. Graph 14 illustrates this comparison for two countries, one developed and one developing, which both have similar population. Notice that the Developing Country has a much smaller PPF curve than the Developed Country, which reflects its fewer resources and lower level of technology.
Recall from Section II-C that the replacement level of investment (IR) represents that level of production that would just exactly replace the capital worn out in the current period. Consumption also has a similar concept, the subsistence level of consumption (CS), which equals that level of the production of consumption goods just sufficient to feed a country's population without starvation. If consumption production is less than CS, then famine occurs.
Graph 15 illustrates the vicious circle of poverty many developing countries face by including both the replacement level of investment and the subsistence level of consumption for both a representative developed and developing country. The developed country has the enviable ability to choose to both feed its population at or above the subsistence level and replace or expand its stock of capital. That is, the country can choose to produce on its PPF curve anywhere between points A and B. In this area, the country has the ability to both feed its population and expand its production possibilities in the future.
The developing country, however, has a lower technology base and fewer resources, but still a similar population. Hence, it is faced with the choice of either feeding its population (C³ CS) or expanding its production possibilities (I > IR). This country cannot do both. Graph 16 illustrates what happens if the country decides to feed its population at the expense of replacing worn out capital. In order to feed its population, even at the subsistence level of CS, the country must produce less than the replacement level of investment (I < IR). As a result, in the future the country's PPF curve will shift back, making the decision even more difficult. Now, feeding its population requires an even lower level of production for investment goods. Which will, in turn, lead to an even more severe decrease in the country's PPF curve. Eventually, if the country continues to choose to feed its population, the PPF curve will shift back so far (because of the decline in productive resources brought about by not replacing worn out capital) that the country will be unable to either replace its capital or feed its population. This result is illustrated in Graph 16 by a movement over time to production possibility frontier P2.
What are the possible solutions to this vicious circle, where simply trying to feed one's population leads to ever more poverty? Clearly, one of the solutions is for the country to decide to set its production of investment at more than the replacement level. From the perspective of the future, this choice has two advantages. First, it will expand the country's PPF curve in the future, reducing the poverty problem in the future. In fact, eventually the PPF will shift out enough so that the developing country will become like the developed country in Graph 15, able to both feed its population and expand its production possibilities in the future.
Second, choosing to allow some of their population to starve will also move the country in the direction of being able to both feed its population and increase its PPF curve. This is true because some people will die through starvation, presumably those who are least productive. In the future, since the population is lower, the subsistence level of consumption will fall. Because it is the least productive who will starve, their deaths will not have a large adverse effect upon the PPF curve.
Of course, few would argue that starvation is the ideal choice for a country. It is just the only internal choice that results in the fewest deaths and the most future productive growth. Do or have countries behaved like this in the past? Unfortunately, the answer is yes. (Can you think of examples?)
Another, more palatable, option does exist. However, this option requires outside intervention. The vicious circle of poverty can be avoided if the country either has more resources or better technology. Foreign aid from developed countries like the U.S. can give developing countries either or both of these, allowing them to avoid the unpalatable choices discussed above. But what, you might ask, incentive does the U.S. have to offer such foreign aid? Aside from humanitarian concerns, there exist real economic reasons for offering such aid. Not only do starving people tend to start wars in an attempt to take the resources necessary to avoid the vicious circle, but helping a country develop will also develop markets for U.S. goods and services.
Notice, then, that the PPF model has been used to:
One of the major uses of economics and economic theory is in just such applications as this one, leading to public policy proposals or analysis. Hence, economics can and is used to help us in our formulation of public policy. (That's why the U.S. President has a council of economic advisors.)
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