Although many decisions in economics are “either–or,” many others are “how much.” Not many people will give up their cars if the price of gasoline goes up, but many people will drive less. How much less? A rise in corn prices won’t necessarily persuade a lot of people to take up farming for the first time, but it will persuade farmers who were already growing corn to plant more. How much more?

Recall from our principles of microeconomics that “how much” is a decision at the margin. So to understand “how much” decisions, we will use an approach known as marginal analysis. Marginal analysis involves comparing the benefit of doing a little bit more of some activity with the cost of doing a little bit more of that activity. The benefit of doing a little bit more of something is what economists call its marginal benefit, and the cost of doing a little bit more of something is what they call its marginal cost.

Why is this called “marginal” analysis? A margin is an edge; what you do in marginal analysis is push out the edge a bit and see whether that is a good move. We will study marginal analysis by considering a hypothetical decision of how many years of school to complete. We’ll consider the case of Alex, who studies computer programming and design. Since there are many computer languages, app design methods, and graphics programs that can be learned one year at a time, each year Alex can decide whether to continue his studies or not. Unlike Maria, who faced an “either–or” decision of whether to get a social work degree, Alex faces a “how much” decision of how many years to study computer programming and design. For example, he could study one more year, or five more years, or any number of years in between. We’ll begin our analysis of Alex’s decision problem by defining Alex’s marginal cost of another year of study.

We’ll assume that each additional year of schooling costs Alex $10 000 in explicit costs—tuition, interest on a student loan, and so on. In addition to the explicit costs, he also has implicit costs—the income forgone by spending one more year in school. Unlike Alex’s explicit costs, which are constant (that is, the same each year), Alex’s implicit cost changes each year. That’s because each year he spends in school leaves him better trained than the year before; and the better trained he is, the higher the salary he can command. Consequently, the income he forgoes by not working rises each additional year he stays in school. In other words, the greater the number of years Alex has already spent in school, the higher his implicit cost of another year of school.

Table 9-4 contains the data on how Alex’s cost of an additional year of schooling changes as he completes more years. The second column shows how his total cost of schooling changes as the number of years he has completed increases. For example, Alex’s first year has a total cost of $30 000: $10 000 in explicit costs of tuition and the like as well as $20 000 in forgone salary.

The second column also shows that the total cost of attending two years is $70 000: $30 000 for his first year plus $40 000 for his second year. During his second year in school, his explicit costs have stayed the same ($10 000) but his implicit cost of forgone salary has gone up to $30 000. That’s because he’s a more valuable worker with one year of schooling under his belt than with no schooling. Likewise, the total cost of three years of schooling is $130 000: $30 000 in explicit cost for three years of tuition plus $100 000 in implicit cost of three years of forgone salary. The total cost of attending four years is $220 000, and $350 000 for five years.

The change in Alex’s total cost of schooling when he goes to school an additional year is his marginal cost of the one-year increase in years of schooling. In general, the marginal cost of producing a good or service (in this case, producing one’s own education) is the additional cost incurred by producing one more unit of that good or service. The arrows, which zigzag between the total costs in the second column and the marginal costs in the third column, are there to help you to see how marginal cost is calculated from total cost, and vice versa. As a formula, marginal cost, or MC, is:

where ΔTC is the change in total cost and ∆q is the change in quantity. For each step in Table 9-4, Δq = 1, so the marginal cost is simply the change in total cost.

As already mentioned, the third column of Table 9-4 shows Alex’s marginal costs of more years of schooling, which have a clear pattern: they are increasing. They go from $30 000, to $40 000, to $60 000, to $90 000, and finally to $130 000 for the fifth year of schooling. That’s because each year of schooling would make Alex a more valuable and highly paid employee if he were to work. As a result, forgoing a job becomes more and more costly as he becomes better educated. This is an example of what economists call increasing marginal cost, which occurs when each unit of a good costs more to produce than the previous unit.

Figure 9-1 shows a marginal cost curve, a graphic representation of Alex’s marginal costs. The height of each shaded bar corresponds to the marginal cost of a given year of schooling. The red line connecting the dots at the midpoint of the top of each bar is Alex’s marginal cost curve. Alex has an upward-sloping marginal cost curve because he has increasing marginal cost of additional years of schooling.

Although increasing marginal cost is a frequent phenomenon in real life, it’s not the only possibility. Constant marginal cost occurs when the cost of producing an additional unit is the same as the cost of producing the previous unit. Plant nurseries, for example, typically have constant marginal cost—the cost of growing one more plant is the same, regardless of how many plants have already been produced. With constant marginal cost, the marginal cost curve is a horizontal line.

There can also be decreasing marginal cost, which occurs when marginal cost falls as the number of units produced increases. With decreasing marginal cost, the marginal cost line is downward sloping. Decreasing marginal cost is often due to learning effects in production: for complicated tasks, such as assembling a new model of a car, workers are often slow and mistake-prone when assembling the earliest units, making for higher marginal cost on those units. But as workers gain experi ence, assembly time and the rate of mistakes fall, resulting in lower marginal cost for later units. As a result, overall production has decreasing marginal cost.

Finally, for the production of some goods and services the shape of the marginal cost curve changes as the number of units produced increases. For example, auto production is likely to have decreasing marginal costs for the first batch of cars produced as workers iron out kinks and mistakes in production. Then production has constant marginal costs for the next batch of cars as workers settle into a predictable pace. But at some point, as workers produce more and more cars, marginal cost begins to increase as they run out of factory floor space and the auto company incurs costly overtime wages. This gives rise to what we call a “swoosh”-shaped marginal cost curve—a topic we will discuss in more detail in Chapter 11. For now, we’ll stick to the simpler example of an increasing marginal cost curve.

Alex benefits from higher lifetime earnings as he completes more years of school. Exactly how much he benefits is shown in Table 9-5. Column 2 shows Alex’s total benefit according to the number of years of school completed, expressed as the value of the increase in lifetime earnings. The third column shows Alex’s marginal benefit from an additional year of schooling. In general, the marginal benefit of producing a good or service is the additional benefit earned from producing one more unit.

As in Table 9-4, the data in the third column of Table 9-5 show a clear pattern. However, this time the numbers are decreasing rather than increasing. The first year of schooling gives Alex a $300 000 increase in the value of his lifetime earnings. The second year also gives him a positive return, but the size of that return has fallen to $150 000; the third year’s return is also positive, but its size has fallen yet again to $90 000; and so on. In other words, the more years of school that Alex has already completed, the smaller the increase in the value of his lifetime earnings from attending one more year. Alex’s schooling decision has what economists call decreasing marginal benefit: each additional year of school yields a smaller benefit than the previous year. Or, to put it slightly differently, with decreasing marginal benefit, the benefit from producing one more unit of the good or service falls as the quantity already produced rises.

Just as marginal cost can be represented by a marginal cost curve, marginal benefit can be represented by a marginal benefit curve, shown in blue in Figure 9-2. Alex’s marginal benefit curve slopes downward because he faces decreasing marginal benefit from additional years of schooling.

Not all goods or activities exhibit decreasing marginal benefit. In fact, there are many goods for which the marginal benefit of production is constant—that is, the additional benefit from producing one more unit is the same regardless of the number of units already produced. In later chapters where we study firms, we will see that the shape of a firm’s marginal benefit curve from producing output has important implications for how that firm behaves within its industry. We’ll also see in Chapters 11 and 12 why constant marginal benefit is considered the norm for many important industries.

Now we are ready to see how the concepts of marginal benefit and marginal cost are brought together to answer the question of how many years of additional schooling Alex should undertake.

Table 9-6 shows the marginal cost and marginal benefit numbers from Tables 9-4 and 9-5. It also adds an additional column: the additional profit to Alex from staying in school one more year, equal to the difference between the marginal benefit and the marginal cost of that additional year in school. (Remember that it is Alex’s economic profit that we care about, not his accounting profit.) We can now use Table 9-6 to determine how many additional years of schooling Alex should undertake in order to maximize his total profit.

First, imagine that Alex chooses not to attend any additional years of school. We can see from column 4 that this is a mistake if Alex wants to achieve the highest total profit from his schooling—the sum of the additional profits generated by another year of schooling. If he attends one additional year of school, he increases the value of his lifetime earnings by $270 000, the profit from the first additional year attended.

Now, let’s consider whether Alex should attend the second year of school. The additional profit from the second year is $110 000, so Alex should attend the second year as well. What about the third year? The additional profit from that year is $30 000; so, yes, Alex should attend the third year as well. What about a fourth year? In this case, the additional profit is negative: it is –$30 000. Alex loses $30 000 of the value of his lifetime earnings if he attends the fourth year. Clearly, Alex is worse off by attending the fourth additional year rather than taking a job. And the same is true for the fifth year as well: it has a negative additional profit of –$80 000.

What have we learned? That Alex should attend three additional years of school and stop at that point. Although the first, second, and third years of additional schooling increase the value of his lifetime earnings, the fourth and fifth years diminish it. So three years of additional schooling lead to the quantity that generates the maximum possible total profit. It is what economists call the optimal quantity—the quantity that generates the maximum possible total profit.

Figure 9-3 shows how the optimal quantity can be determined graphically. Alex’s marginal benefit and marginal cost curves are shown together. If Alex chooses fewer than three additional years (that is, 0, 1, or 2 years), he will choose a level of schooling at which his marginal benefit curve lies above his marginal cost curve. He can make himself better off by staying in school. If instead he chooses more than three additional years (4 or 5 years), he will choose a level of schooling at which his marginal benefit curve lies below his marginal cost curve. He can make himself better off by not attending the additional year of school and taking a job instead.

The table in Figure 9-3 confirms our result. The second column repeats information from Table 9-6, showing Alex’s marginal benefit minus marginal cost—the additional profit per additional year of schooling. The third column shows Alex’s total profit for different years of schooling. The total profit for each possible year of schooling is simply the sum of numbers in the second column up to and including that year. For example, Alex’s profit from additional years of schooling is $270 000 for the first year and $110 000 for the second year. So the total profit for two additional years of schooling is $270 000 + $110 000 = $380 000. Similarly, the total profit for three additional years is $270 000 + $110 000 + $30 000 = $410 000. Our claim that three years is the optimal quantity for Alex is confirmed by the data in the table in Figure 9-3: at three years of additional schooling, Alex reaps the greatest total profit, $410 000.

Alex’s decision problem illustrates how you go about finding the optimal quantity when the choice involves a small number of quantities (in this example, one through five years). With small quantities, the rule for choosing the optimal quantity is: Increase the quantity as long as the marginal benefit from one more unit is greater than the marginal cost, but stop before the marginal benefit becomes less than the marginal cost.

In contrast, when a “how much” decision involves relatively large quantities, the rule for choosing the optimal quantity simplifies to this: The optimal quantity is the quantity at which marginal benefit is equal to marginal cost.

To see why this is so, consider the example of a farmer who finds that her optimal quantity of wheat produced is 5000 bushels. Typically, she will find that in going from 4999 to 5000 bushels, her marginal benefit is only very slightly greater than her marginal cost—that is, the difference between marginal benefit and marginal cost is close to zero. Similarly, in going from 5000 to 5001 bushels, her marginal cost is only very slightly greater than her marginal benefit—again, the difference between marginal cost and marginal benefit is very close to zero. So a simple rule for her in choosing the optimal quantity of wheat is to produce the quantity at which the difference between marginal benefit and marginal cost is approximately zero—that is, the quantity at which marginal benefit equals marginal cost.

Now we are ready to state the general rule for choosing the optimal quantity—one that applies for decisions involving either small quantities or large quantities. This general rule is known as the profit-maximizing principle of marginal analysis: When making a profit-maximizing “how much” decision, the optimal quantity is the largest quantity at which marginal benefit is greater than or equal to marginal cost.

Graphically, the optimal quantity is the quantity of an activity at which the marginal benefit curve intersects the marginal cost curve. For example, in Figure 9-3 the marginal benefit and marginal cost curves cross each other at three years—that is, marginal benefit equals marginal cost at the choice of three additional years of schooling, which we have already seen is Alex’s optimal quantity.

A straightforward application of marginal analysis explains why so many people went back to school in 2009 through 2012: in the depressed job market, the marginal cost of another year of school fell because the opportunity cost of forgone wages had fallen.

Simple applications of marginal analysis can explain many facts, such as why restaurant portion sizes in the United States and, to some extent, Canada are typically larger than those in other countries (as was just discussed in the Global Comparison).

The profit-maximizing principle of marginal analysis can be applied to just about any “how much” decision in which you want to maximize the total profit for an activity. It is equally applicable to production decisions, consumption decisions, and policy decisions. Furthermore, decisions where the benefits and costs are not expressed in dollars and cents can also be made using marginal analysis (as long as benefits and costs can be measured in some type of common units). Here are a few examples of decisions that are suitable for marginal analysis:

A Preview: How Consumption Decisions Are Different We’ve established that marginal analysis is an extraordinarily useful tool. It is used in “how much” decisions that are applied to both consumption choices and to profit maximization. Producers use it to make optimal production decisions at the margin and individuals use it to make optimal consumption decisions at the margin. But consumption decisions differ in form from production decisions. Why the difference? Because when individuals make choices, they face a limited amount of income. As a result, when they choose more of one good to consume (say, new clothes), they must choose less of another good (say, restaurant dinners). In contrast, decisions that involve maximizing profit by producing a good or service —such as years of education or tonnes of wheat—are not affected by income limitations. For example, in Alex’s case, we assume he is not limited by income because he can always borrow to pay for another year of school. In Chapter 10 we we will see in greater detail how consumption decisions differ from production decisions—but also how they are similar.