A Principle with Many Uses

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). Table 9-7 includes three examples of decisions that are suitable for marginal analysis.

The “how much” decision to be made

Applying marginal analysis

Arriving at the optimal quantity

The retaiiler PalMart must decide on the size of the new store it is constructing in Beijing.

PalMart must compare the marginal benefit of enlarging the store by 1 square foot (the value of the additional sales it makes from that additional square foot of floor space) to the marginal cost (the cost of constructing and maintaining the additional square foot).

The optimal store size for PalMart is the largest size at which marginal benefit is greater than or equal to marginal cost.

A physician must decide whether or not to increase the dosage of a drug in light of possible side effects.

The physician must consider the marginal cost, in terms of side effects, of increasing the dosage of a drug versus the marginal benefit of improving health by increasing the dosage.

The optimal dosage level is the largest level at which the marginal benefit of disease amelioration is greater than or equal to the marginal cost of side effects.

A farmer must decide how much fertilizer to apply.

More fertilizer increases crop yield but also costs more.

The optimal amount of fertilizer is the largest quantity at which the marginal benefit of higher crop yield is greater than or equal to the marginal cost of purchasing and applying more fertilizer.
Table :

TABLE 9-7 Making Decisions Using 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 tons of wheat—are not affected by income limitations. For example, in Alex’s case, he is not limited by income because he can always borrow to pay for another year of school. In the next chapter we will see how consumption decisions differ from—yet are similar to—production decisions.

!worldview! ECONOMICS in Action: The Cost of a Life

The Cost of a Life

What’s the marginal benefit to society of saving a human life? You might be tempted to answer that human life is infinitely precious. But in the real world, resources are scarce, so we must decide how much to spend on saving lives since we cannot spend infinite amounts. After all, we could surely reduce highway deaths by dropping the speed limit on interstates to 40 miles per hour, but the cost of a lower speed limit—in time and money—is more than most people are willing to pay.

Generally, people are reluctant to talk in a straightforward way about comparing the marginal cost of a life saved with the marginal benefit—it sounds too callous. Sometimes, however, the question becomes unavoidable.

For example, the cost of saving a life became an object of intense discussion in the United Kingdom after a horrible train crash near London’s Paddington Station killed 31 people. There were accusations that the British government was spending too little on rail safety. However, the government estimated that improving rail safety would cost an additional $4.5 million per life saved. But if that amount was worth spending—that is, if the estimated marginal benefit of saving a life exceeded $4.5 million—then the implication was that the British government was spending far too little on traffic safety.

In contrast, the estimated marginal cost per life saved through highway improvements was only $1.5 million, making it a much better deal than saving lives through greater rail safety.

Quick Review

  • A “how much” decision is made by using marginal analysis.

  • The marginal cost of producing a good or service is represented graphically by the marginal cost curve. An upward-sloping marginal cost curve reflects increasing marginal cost. Constant marginal cost is represented by a horizontal marginal cost curve. A downward-sloping marginal cost curve reflects decreasing marginal cost.

  • The marginal benefit of producing a good or service is represented by the marginal benefit curve. A downward-sloping marginal benefit curve reflects decreasing marginal benefit.

  • The optimal quantity, the quantity which generates the highest possible total profit, is found by applying the profit-maximizing principle of marginal analysis, according to which the optimal quantity is the largest quantity at which marginal benefit is greater than or equal to marginal cost. Graphically, it is the quantity at which the marginal cost curve intersects the marginal benefit curve.

9-2

  1. Question 9.4

    For each of the “how much” decisions listed in Table 9-3, describe the nature of the marginal cost and of the marginal benefit.

  2. Question 9.5

    Suppose that Alex’s school charges a fixed fee of $70,000 for four years of schooling. If Alex drops out before he finishes those four years, he still has to pay the $70,000. Alex’s total cost for different years of schooling is now given by the data in the accompanying table. Assume that Alex’s total benefit and marginal benefit remain as reported in Table 9-5.

    Use this information to calculate (i) Alex’s new marginal cost, (ii) his new profit, and (iii) his new optimal years of schooling. What kind of marginal cost does Alex now have—constant, increasing, or decreasing?

    Quantity of schooling (years)

    Total cost

    0

    $0

    1

    90,000

    2

    120,000

    3

    170,000

    4

    250,000

    5

    370,000

Solutions appear at back of book.