When a production possibilities frontier is bowed outward, the opportunity cost of the first good

We see in Figure 2.4 "The Combined Production Possibilities Curve for Alpine Sports" that, beginning at point A and producing only skis, Alpine Sports experiences higher and higher opportunity costs as it produces more snowboards. The fact that the opportunity cost of additional snowboards increases as the firm produces more of them is a reflection of an important economic law. The law of increasing opportunity cost holds that as an economy moves along its production possibilities curve in the direction of producing more of a particular good, the opportunity cost of additional units of that good will increase.

We have seen the law of increasing opportunity cost at work traveling from point A toward point D on the production possibilities curve in Figure 2.4 "The Combined Production Possibilities Curve for Alpine Sports". The opportunity cost of each of the first 100 snowboards equals half a pair of skis; each of the next 100 snowboards has an opportunity cost of 1 pair of skis, and each of the last 100 snowboards has an opportunity cost of 2 pairs of skis. The law also applies as the firm shifts from snowboards to skis. Suppose it begins at point D, producing 300 snowboards per month and no skis. It can shift to ski production at a relatively low cost at first. The opportunity cost of the first 200 pairs of skis is just 100 snowboards at Plant 1, a movement from point D to point C, or 0.5 snowboards per pair of skis. We would say that Plant 1 has a comparative advantage in ski production. The next 100 pairs of skis would be produced at Plant 2, where snowboard production would fall by 100 snowboards per month. The opportunity cost of skis at Plant 2 is 1 snowboard per pair of skis. Plant 3 would be the last plant converted to ski production. There, 50 pairs of skis could be produced per month at a cost of 100 snowboards, or an opportunity cost of 2 snowboards per pair of skis.

The bowed-out shape of the production possibilities curve illustrates the law of increasing opportunity cost. Its downwards slope reflects scarcity.

Figure 2.5 "Production Possibilities for the Economy" illustrates a much smoother production possibilities curve. This production possibilities curve in Panel (a) includes 10 linear segments and is almost a smooth curve. As we include more and more production units, the curve will become smoother and smoother. In an actual economy, with a tremendous number of firms and workers, it is easy to see that the production possibilities curve will be smooth. We will generally draw production possibilities curves for the economy as smooth, bowed-out curves, like the one in Panel (b). This production possibilities curve shows an economy that produces only skis and snowboards. Notice the curve still has a bowed-out shape; it still has a negative slope. Notice also that this curve has no numbers. Economists often use models such as the production possibilities model with graphs that show the general shapes of curves but that do not include specific numbers.

Figure 2.5 Production Possibilities for the Economy

As we combine the production possibilities curves for more and more units, the curve becomes smoother. It retains its negative slope and bowed-out shape. In Panel (a) we have a combined production possibilities curve for Alpine Sports, assuming that it now has 10 plants producing skis and snowboards. Even though each of the plants has a linear curve, combining them according to comparative advantage, as we did with 3 plants in Figure 2.4 "The Combined Production Possibilities Curve for Alpine Sports", produces what appears to be a smooth, nonlinear curve, even though it is made up of linear segments. In drawing production possibilities curves for the economy, we shall generally assume they are smooth and "bowed out," as in Panel (b). This curve depicts an entire economy that produces only skis and snowboards.

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The production possibility frontier (PPF) is a curve on a graph that illustrates the possible quantities that can be produced of two products if both depend upon the same finite resource for their manufacture. The PPF is also referred to as the production possibility curve.

PPF also plays a crucial role in economics. For example, it can demonstrate that a nation's economy has reached the highest level of efficiency possible.

• When producing goods, opportunity cost is what is given up when you take resources from one product to produce another. The maximum amount that can be produced is illustrated by a curve on a graph.
• The production possibility frontier (PPF) is above the curve, illustrating impossible scenarios given the available resources.
• The PPF demonstrates that the production of one commodity may increase only if the production of the other commodity decreases.
• The PPF is a decision-making tool for managers deciding on the optimum product mix for the company.

The PPF is the area on a graph representing production levels that cannot be obtained given the available resources; the curve represents optimal levels. Here are the assumptions involved:

• A company/economy wants to produce two products
• There are limited resources
• Technology and techniques remain constant
• All resources are fully and efficiently used

If a company is deciding how much of each product to produce, it can plot points on a graph representing the number of products made using variables based on amounts of available resources. Keeping in mind that resources are limited, if the desire is to produce more of one product, resources must be taken away from the other.

As resources are taken from one product and allocated to the other, another point can be plotted on the curve. When you plot the points where more of X will be produced by taking resources from Y or vice versa, a curve is generated representing the maximum amount of each product that can be produced as resources are reallocated.

For example, if a non-profit agency provides a mix of textbooks and computers, the curve may show that it can provide either 48 textbooks and six computers or 72 textbooks and two computers. This results in a ratio of about six textbooks to one computer.

The agency's leadership must determine which item is more urgently needed. In this example, the opportunity cost of providing an additional 30 textbooks equals five more computers, so it would only be able to give out one computer with 78 textbooks. If it wanted more computers, it would need to reduce the number of textbooks by six for every computer.

When this is plotted, the area below the curve represents computers and textbooks that are not being used, and the area above the curve represents donations that cannot happen with the available resources. The area above the curve is called the production possibility frontier, and the curve (the line itself) is sometimes called the opportunity cost curve. The entire graph is sometimes referred to as the production possibility curve.

The non-profit could provide 10 textbooks and 10 computers, but this is not using all of its resources. This would be represented by a plot beneath the curve. A plot would be placed above the curve in the frontier area if the company wanted to give more than its resources provided, such as 85 textbooks and no computers or 42 textbooks and 10 computers—it simply can't do it based on available resources.

This technique can be used by economists to determine the set of points at which a country’s economy is most efficiently allocating its resources to produce as many goods as possible. If the production level is on the curve, the country can only produce more of one good if it produces less of some other good.

If the economy is producing less than the quantities indicated by the curve, this signifies that resources are not being used to their full potential. In this case, it is possible to increase the production of some goods without cutting production in other areas.

The production possibility frontier demonstrates that there are limits on production, given that the assumptions hold. Therefore, each economy must decide what combination of goods and services should be produced to attain maximum resource efficiency.

Imagine a national economy that can produce only two things: wine and cotton. If points A, B, and C are plotted on a curve, it represents the economy's most efficient use of resources.

For instance, producing five units of wine and five units of cotton (point B) is just as attainable as producing three units of wine and seven units of cotton. Point X represents an inefficient use of resources, while point Y represents a goal that the economy simply cannot attain with its present levels of resources.

As we can see, for this economy to produce more wine, it must give up some of the resources it is currently using to produce cotton (point A). If the economy starts producing more cotton (represented by points B and C), it would need to divert resources from making wine and, consequently, it will produce less wine than it is producing at point A.

Moreover, by moving production from point A to B, the economy must decrease wine production by a small amount in comparison to the increase in cotton output. But if the economy moves from point B to C, wine output will be reduced by about 50%, while the cotton output only increases by about 75%.

Keep in mind that A, B, and C all represent the most efficient allocation of resources for the economy. The nation must decide how to achieve the PPF and which combination to use. For example, if more wine is in demand, the cost of increasing its output is proportional to the cost of decreasing cotton production. Markets play an important role in telling the economy what the PPF should look like.

Consider point X in the figure above. If a country is producing at point X, it means its resources are not being used efficiently—that is, the country is not producing enough cotton or wine, given the potential of its resources. On the other hand, point Y, as we mentioned above, represents an unattainable output level.

An economy can only be produced on the PPF curve in theory. Economies constantly struggle to reach an optimal production capacity. Scarcity always forces an economy to forgo some choice in favor of another.

The only way for the curve to move outward to point Y is if there were an improvement in cotton and grape harvesting technology because the available resources—land, labor, and capital—generally remain constant. As output increased, the PPF curve would be pushed outwards. A new curve, represented in the figure on which Y would fall, would show the new optimal allocation of resources.

When the PPF shifts outwards, it implies growth in an economy. When it shifts inwards, the economy is shrinking due to a failure to allocate resources and optimal production capability. A shrinking economy could result from a decrease in supplies or a deficiency in technology.

The Pareto Efficiency, a concept named after Italian economist Vilfredo Pareto, measures the efficiency of the commodity allocation on the PPF. The Pareto Efficiency states that any point within the PPF curve is inefficient because the total output of commodities is below the output capacity.

Conversely, any point outside the PPF curve is impossible because it represents a mix of commodities that will require more resources to produce than are currently obtainable.

Therefore, in situations with limited resources, the only efficient commodity mixes lie along the PPF curve, with one commodity on the X-axis and the other on the Y-axis.

An economy may be able to produce all of the goods and services it needs to function using the PPF as a guide. However, this may lead to an overall inefficient allocation of resources and hinder future growth when the benefits of trading with other countries are considered.

There are four common assumptions in the model:

1. The economy is assumed to have only two goods that represent the market
2. The supply of resources is fixed or constant
3. Technology and techniques remain constant
4. All resources are efficiently and fully used

The PPF demonstrates whether resources are being used efficiently and fully when everything else remains constant. Thus, the variables can be changed to see how the curve reacts, letting you observe different outcomes.

The simplest method is to use Excel or Google Sheets. Fill two columns with two variable values, highlight the data, and use the chart wizard. Create an XY scatter plot chart and label the X and Y axes.

Because the PPF is a curve based on the data of two variables representing resources between two goods, the data can be manipulated to observe how scarcity, growth, inefficiency, efficiency, and other factors can affect production.

The PPF identifies the options when making a decision. When you decide on one action, you lose the opportunity the other action provides. Thus, there is an opportunity cost; the PPF curve plots this.

The production possibilities curve illustrates the maximum possible output for two products when there are limited resources. It also illustrates the opportunity cost of making decisions about allocating resources.

Businesses and economists use the PPF to consider possible production scenarios by changing resource variables. The PPF allows businesses to learn how variables influence production or decide which products to manufacture. Economists can use it to learn how much of a specific good can be produced in a country while not producing another good to analyze economic efficiency levels and growth.