We can use marginal benefit and marginal cost curves to show the total benefit, the total cost, and the net benefit of an activity. We will see that equating marginal benefit to marginal cost does, indeed, maximize net benefit. We will also develop another tool to use in interpreting marginal benefit and cost curves.
Panel (a) of Figure 6.4 shows the marginal benefit curve we derived in Panel (c) ofFigure 6.1. The corresponding point on the marginal benefit curve gives the marginal benefit of the first hour of study for the economics exam, 18 points. This same value equals the area of the rectangle bounded by 0 and 1 hour of study and the marginal benefit of 18. Similarly, the marginal benefit of the second hour, 14 points, is shown by the corresponding point on the marginal benefit curve and by the area of the shaded rectangle bounded by 1 and 2 hours of study. The total benefit of 2 hours of study equals the sum of the areas of the first two rectangles, 32 points. We continue this procedure through the fifth hour of studying economics; the areas for each of the shaded rectangles are shown in the graph.
Panel (a) shows the marginal benefit curve of Figure 6.1. The total benefit of studying economics at any given quantity of study time is given approximately by the shaded area below the marginal benefit curve up to that level of study. Panel (b) shows the marginal cost curve from Figure 6.3. The total cost of studying economics at any given quantity of study is given approximately by the shaded area below the marginal cost curve up to that level of study.
Two features of the curve in Panel (a) of Figure 6.4 are particularly important. First, note that the sum of the areas of the five rectangles, 50 points, equals the total benefit of 5 hours of study given in the table in Panel (a) of Figure 6.1. Second, notice that the shaded areas are approximately equal to the area under the marginal benefit curve between 0 and 5 hours of study. We can pick any quantity of study time, and the total benefit of that quantity equals the sum of the shaded rectangles between zero and that quantity. Thus, the total benefit of 2 hours of study equals 32 points, the sum of the areas of the first two rectangles.
Now consider the marginal cost curve in Panel (b) of Figure 6.4. The areas of the shaded rectangles equal the values of marginal cost. The marginal cost of the first hour of study equals zero; there is thus no rectangle under the curve. The marginal cost of the second hour of study equals 2 points; that is the area of the rectangle bounded by 1 and 2 hours of study and a marginal cost of 2. The marginal cost of the third hour of study is 6 points; this is the area of the shaded rectangle bounded by 2 and 3 hours of study and a marginal cost of 6.
Looking at the rectangles in Panel (b) over the range of 0 to 5 hours of study, we see that the areas of the five rectangles total 32, the total cost of spending all 5 hours studying economics. And looking at the rectangles, we see that their area is approximately equal to the area under the marginal cost curve between 0 and 5 hours of study.
We have seen that the areas of the rectangles drawn with Laurie Phan’s marginal benefit and marginal cost curves equal the total benefit and total cost of studying economics. We have also seen that these areas are roughly equal to the areas under the curves themselves. We can make this last statement much stronger. Suppose, instead of thinking in intervals of whole hours, we think in terms of smaller intervals, say, of 12 minutes. Then each rectangle would be only one-fifth as wide as the rectangles we drew in Figure 6.4. Their areas would still equal the total benefit and total cost of study, and the sum of those areas would be closer to the area under the curves. We have done this for Ms. Phan’s marginal benefit curve in Figure 6.5; notice that the areas of the rectangles closely approximate the area under the curve. They still “stick out” from either side of the curve as did the rectangles we drew in Figure 6.4, but you almost need a magnifying glass to see that. The smaller the interval we choose, the closer the areas under the marginal benefit and marginal cost curves will be to total benefit and total cost. For purposes of our model, we can imagine that the intervals are as small as we like. Over a particular range of quantity, the area under a marginal benefit curve equals the total benefit of that quantity, and the area under the marginal cost curve equals the total cost of that quantity.
When the increments used to measure time allocated to studying economics are made smaller, in this case 12 minutes instead of whole hours, the area under the marginal benefit curve is closer to the total benefit of studying that amount of time.
Panel (a) of Figure 6.6 shows marginal benefit and marginal cost curves for studying economics, this time without numbers. We have the usual downward- sloping marginal benefit curve and upward-sloping marginal cost curve. The marginal decision rule tells us to choose D hours studying economics, the quantity at which marginal benefit equals marginal cost at point C. We know that the total benefit of study equals the area under the marginal benefit curve over the range from A to D hours of study, the area ABCD. Total cost equals the area under the marginal cost curve over the same range, or ACD. The difference between total benefit and total cost equals the area between marginal benefit and marginal cost between A and D hours of study; it is the green-shaded triangle ABC. This difference is the net benefit of time spent studying economics. Panel (b) of Figure 6.6 introduces another important concept. If an activity is carried out at a level less than the efficient level, then net benefits are forgone. The loss in net benefits resulting from a failure to carry out an activity at the efficient level is called a deadweight loss.
In Panel (a) net benefits are given by the difference between total benefits (as measured by the area under the marginal benefit curve up to any given level of activity) and total costs (as measured by the area under the marginal cost curve up to any given level of activity). Maximum net benefits are found where the marginal benefit curve intersects the marginal cost curve at activity level D. Panel (b) shows that if the level of the activity is restricted to activity level E, net benefits are reduced from the light-green shaded triangle ABC in Panel (a) to the smaller area ABGF. The forgone net benefits, or deadweight loss, is given by the purple-shaded area FGC. If the activity level is increased from D to J, as shown in Panel (c), net benefits declined by the deadweight loss measured by the area CHI.
Now suppose a person increases study time from D to J hours as shown in Panel (c). The area under the marginal cost curve between D and J gives the total cost of increasing study time; it is DCHJ. The total benefit of increasing study time equals the area under the marginal benefit curve between D and J; it is DCIJ. The cost of increasing study time in economics from D hours to J hours exceeds the benefit. This gives us a deadweight loss of CHI. The net benefit of spending J hours studying economics equals the net benefit of studying for D hours less the deadweight loss, or ABC minus CHI. Only by studying up to the point at which marginal benefit equals marginal cost do we achieve the maximum net benefit shown in Panel (a).
We can apply the marginal decision rule to the problem in Figure 6.6 in another way. In Panel (b), a person studies economics for E hours. Reading up to the marginal benefit curve, we reach point G. Reading up to the marginal cost curve, we reach point F. Marginal benefit at G exceeds marginal cost at F; the marginal decision rule says economics study should be increased, which would take us toward the intersection of the marginal benefit and marginal cost curves. Spending J hours studying economics, as shown in Panel (c), is too much. Reading up to the marginal benefit and marginal cost curves, we see that marginal cost exceeds marginal benefit, suggesting that study time be reduced.
This completes our introduction to the marginal decision rule and the use of marginal benefit and marginal cost curves. We will spend the remainder of the chapter applying the model.
Heads Up!
It is easy to make the mistake of assuming that if an activity is carried out up to the point where marginal benefit equals marginal cost, then net benefits must be zero. Remember that following the marginal decision rule and equating marginal benefits and costs maximizes net benefits. It makes the difference between total benefits and total cost as large as possible.
KEY TAKEAWAYS
- Economists assume that decision makers make choices in the way that maximizes the value of some objective.
- Maximization involves determining the change in total benefit and the change in total cost associated with each unit of an activity. These changes are called marginal benefit and marginal cost, respectively.
- If the marginal benefit of an activity exceeds the marginal cost, the decision maker will gain by increasing the activity.
- If the marginal cost of an activity exceeds the marginal benefit, the decision maker will gain by reducing the activity.
- The area under the marginal benefit curve for an activity gives its total benefit; the area under the marginal cost curve gives the activity’s total cost. Net benefit equals total benefit less total cost.
- The marginal benefit rule tells us that we can maximize the net benefit of any activity by choosing the quantity at which marginal benefit equals marginal cost. At this quantity, the net benefit of the activity is maximized.
TRY IT!
Suppose Ms. Phan still faces the exams in economics and in accounting, and she still plans to spend a total of 5 hours studying for the two exams. However, she revises her expectations about the degree to which studying economics and accounting will affect her scores on the two exams. She expects studying economics will add somewhat less to her score, and she expects studying accounting will add more. The result is the table below of expected total benefits and total costs of hours spent studying economics. Notice that several values in the table have been omitted. Fill in the missing values in the table. How many hours of study should Ms. Phan devote to economics to maximize her net benefit?
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Hours studying economics
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0
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1
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2
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3
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4
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5
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Total benefit
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0
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14
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24
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30
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32
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Total cost
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0
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2
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8
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32
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50
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Net benefit
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0
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12
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12
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0
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-18
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Now compute the marginal benefits and costs of hours devoted to studying economics, completing the table below.
Draw the marginal benefit and marginal cost curves for studying economics (remember to plot marginal values at the midpoints of the respective hourly intervals). Do your curves intersect at the “right” number of hours of study—the number that maximizes the net benefit of studying economics?
Case in Point: Preventing Oil Spills
Do we spill enough oil in our oceans and waterways? It is a question that perhaps only economists would ask—and, as economists, we should ask it.
There is, of course, no virtue in an oil spill. It destroys wildlife and fouls shorelines. Cleanup costs can be tremendous. However, Preventing oil spills has costs as well:
greater enforcement expenditures and higher costs to shippers of oil and, therefore, higher costs of goods such as gasoline to customers. The only way to prevent oil spills completely is to stop shipping oil. That is a cost few people would accept. But what is the right balance between environmental protection and the satisfaction of consumer demand for oil?
Vanderbilt University economist Mark Cohen examined the U.S. Coast Guard’s efforts to reduce oil spills through its enforcement of shipping regulations in coastal waters and on rivers. He focused on the costs and benefits resulting from the Coast Guard’s enforcement efforts in 1981. On the basis of the frequency of oil spills before the Coast Guard began its enforcement, Mr. Cohen estimated that the Coast Guard prevented 1,159,352 gallons of oil from being spilled in 1981.
Given that there was a total of 824,921 gallons of oil actually spilled in 1981, should the Coast Guard have attempted to prevent even more spillage? Mr. Cohen estimated that the marginal benefit of preventing one more gallon from being spilled was $7.27 ($3.42 in cleanup costs, $3 less in environmental damage, and $0.85 worth of oil saved). The marginal cost of preventing one more gallon from being spilled was $5.50. Mr. Cohen suggests that because the marginal benefit of more vigorous enforcement exceeded the marginal cost, more vigorous Coast Guard efforts would have been justified.
More vigorous efforts have, indeed, been pursued. In 1989, the Exxon oil tanker Exxon Valdez ran aground, spilling 10.8 million gallons of oil off the coast of Alaska. The spill damaged the shoreline of a national forest, four national wildlife refuges, three national parks, five state parks, four critical habitat areas, and a state game refuge. Exxon was ordered to pay $900 million in damages; a federal jury found Exxon and the captain guilty of criminal negligence and imposed an additional $5 billion in punitive damages. In 2008, The Supreme Court reduced the assessment of punitive damages to $507 million, with the majority arguing that the original figure was too high in comparison to the compensatory damages for a case in which the actions of the defendant, Exxon, were “reprehensible” but not intentional.
Perhaps the most important impact of the Exxon Valdez disaster was the passage of the Oil Pollution Act of 1990. It increased shipper liability from $14 million to $100 million. It also required double-hulled tankers for shipping oil.
The European Union (EU) has also strengthened its standards for oil tankers. The 2002 breakup of the oil tanker Prestige off the coast of Spain resulted in the spillage of 3.2 million gallons of oil. The EU had planned to ban single-hulled tankers, phasing in the ban between 2003 and 2015. The sinking of the Prestige led the EU to move up that deadline.
Spill crises have led both the United States and the European Union to tighten up their regulations of oil tankers. The result has been a reduction in the quantity of oil spilled, which was precisely what economic research had concluded was needed. By 2002, the amount of oil spilled per barrel shipped had fallen 30% from the level three decades earlier.
Sources: Mark A. Cohen, “The Costs and Benefits of Oil Spill Prevention and Enforcement,”Journal of Environmental Economics and Management 13(2) (June 1986): 167–188; Rick S. Kurtz, “Coastal Oil Pollution: Spills, Crisis, and Policy Change,” Review of Policy Research, 21(2) (March 2004): 201–219; David S. Savage, “Justices Slash Exxon Valdez Verdict,” Los Angeles Times, June 26, 2008, p. A1; and Edwin Unsworth, “Europe Gets Tougher on Aging Oil Tankers,”Business Insurance, 36(48) (December 2, 2002): 33–34.
ANSWER TO TRY IT! PROBLEM
Here are the completed data table and the table showing total and marginal benefit and cost.
Ms. Phan maximizes her net benefit by reducing her time studying economics to 2 hours. The change in her expectations reduced the benefit and increased the cost of studying economics. The completed graph of marginal benefit and marginal cost is at the far left. Notice that answering the question using the marginal decision rule gives the same answer.
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