Shlieffen Making Decisions Essay
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>> Making
Decisions
A T A L E O F T W O I N VA S I O N S
O
6, 1944, ALLIED SOLDIERS
much should be used to defend Germany’s
stormed the beaches of Norman-
border with France? The original plan,
dy, beginning the liberation of
devised by General Alfred von Schlieffen,
France from German rule. Long before the
allocated most of the German army to the
assault, however, Allied generals had to
invasion force; on his deathbed, Schlieffen is
make a crucial decision: where would the
supposed to have pleaded, “Keep the right
soldiers land?
wing [the invasion force] strong!” But his
N JUNE
How economists model decision …show more content…
making by individuals and firms
➤
The importance of implicit as well as explicit costs in decision making ➤
➤
➤
The difference between accounting profit and economic profit, and why economic profit is the correct basis for decisions
The difference between
“either–or” and “how much” decisions The principle of marginal analysis “either–or” decision. Either the invasion
weakened the plan: he reallocated some of
force could cross the English Channel at its
the divisions that were supposed to race through Belgium to the defence. The weak-
the Germans expected—or it could try to
ened invasion force wasn’t strong enough:
surprise the Germans by landing farther west, in
Normandy. Since men and landing craft were in limited supply, the Allies could not do both. In fact, they chose to rely on surprise.
The German defences in
Normandy were too weak to stop the landings, and the
MGM/The Kobal Collection
➤
successor, General Helmuth von Moltke,
narrowest point, Calais—which was what
What you will learn in this chapter:
They had to make what we call an
Allies went on to liberate
France and win the war.
Thirty years earlier, at the beginning of World War I,
Decision: Attack here? Or there?
➤
What sunk costs are and why they should be ignored
German generals had to
make a different kind of decision. They, too,
the defending French army stopped it 30
How to make decisions in cases where time is a factor
planned to invade France, in this case via
miles from Paris. Most military historians
land, and had decided to mount that invasion
believe that by allocating too few men to the
through Belgium. The decision they had to
➤
attack, von Moltke cost Germany the war.
make was not an either–or but a “how much” decision: how much of their army should be
170
So Allied generals made the right decision in 1944; German generals made the
allocated to the invasion force, and how
wrong decision in 1914. The important
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point for this chapter is that in both cases
at the significance of opportunity cost for
the generals had to apply the same logic
economic decisions and the role it plays in
that applies to economic decisions, like
“either–or” decisions. Next we turn to the
production decisions by businesses and
problem of making “how much” decisions
consumption decisions by households.
and the usefulness of marginal analysis. We
In this chapter we will survey the princi-
then examine what kind of costs should be
ples involved in making economic deci-
ignored in making a decision—costs which
sions. These principles will help us under-
economists call sunk costs. We end by con-
stand how any individual—whether a con-
sidering the concept of present value and its
sumer or a producer—makes an economic
importance for making decisions when
decision. We begin by taking a deeper look
costs and benefits arrive at different times.
Opportunity Cost And Decisions
In Chapter 1 we introduced some core principles underlying economic decisions.
We’ve just seen two of those principles at work in our tale of two invasions. The first is that resources are scarce—the invading Allies had a limited number of landing craft, and the invading Germans had a limited number of divisions. Because resources are scarce, the true cost of anything is its opportunity cost—that is, the real cost of something is what you must give up to get it. When it comes to making decisions, it is crucial to think in terms of opportunity cost, because the opportunity cost of an action is often considerably more than the simple monetary cost.
Explicit versus Implicit Costs
Suppose that, upon graduation from university, you have two options: to go to school for an additional year to get an advanced degree or to take a job immediately. You would like to take the extra year in school but are concerned about the cost.
But what exactly is the cost of that additional year of school? Here is where it is important to remember the concept of opportunity cost: the cost of that year spent getting an advanced degree is what you forgo by not taking a job for that year.
This cost, like any cost, can be broken into two parts: the explicit cost of the year’s schooling and the implicit cost.
An explicit cost is a cost that requires an outlay of money. For example, the explicit cost of the additional year of schooling includes tuition. An implicit cost, on the other hand, does not involve an outlay of money; instead, it is measured by the value, in dollar terms, of all the benefits that are forgone. For example, the implicit cost of the year spent in school includes the income you would have earned if you had taken that job instead.
A common mistake, both in economic analysis and in real business situations, is to ignore implicit costs and focus exclusively on explicit costs. But often the implicit cost of an activity is quite substantial—indeed, sometimes it is much larger than the explicit cost.
Table 7-1 gives a breakdown of hypothetical explicit and implicit costs associated with spending an additional year in school instead of taking a job. The explicit cost consists of tuition, books, supplies, and a home computer for doing assignments—all of which require you to spend money. The implicit cost is the salary you would have earned if you had taken a job instead. As you can see, the forgone salary is $35,000 and the explicit cost is $9,500, making the implicit cost more than three times as much as the explicit cost. So ignoring the implicit cost of an action can lead to a seriously misguided decision.
An explicit cost is a cost that involves actually laying out money. An implicit cost does not require an outlay of money; it is measured by the value, in dollar terms, of the benefits that are forgone. 171
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TABLE
7-1
Opportunity Cost of an Additional Year of School
Explicit cost
Tuition
Implicit cost
$7,000
Books and supplies
Home computer
Total implicit cost
9,500
$35,000
35,000
1,500
Total explicit cost
Forgone salary
1,000
Total opportunity cost = Total explicit cost + Total implicit cost = $44,500
There is another, slightly different way of looking at the implicit cost in this example that can deepen our understanding of opportunity cost. The forgone salary is the cost of using your own resources—your time—in going to school rather than working.
The use of your time for more schooling, despite the fact that you don’t have to spend any money, is nonetheless costly to you. This illustrates an important aspect of opportunity cost: in considering the cost of an activity, you should include the cost of using any of your own resources for that activity. You can calculate the cost of using your own resources by determining what they would have earned in their next best use.
FOR
INQUIRING
MINDS
FAMOUS COLLEGE DROPOUTS
What do Bill Gates, Tiger Woods, and Sarah
Michelle Gellar (a.k.a. Buffy the Vampire
Slayer) have in common? None of them have a college degree.
Nobody doubts that all three are easily smart enough to have gotten their diplomas.
However, they all made the rational decision that the implicit cost of getting a degree would have been too high—by their late teens, each had a very promising career that would have had to be put on hold to get a college degree. Gellar would have had to postpone her acting career; Woods would have had to put off
winning one major tournament after another and becoming the world’s best golfer; Gates would have had to delay developing the most successful and most lucrative software ever sold, Microsoft’s computer operating system.
In fact, extremely successful people—especially those in careers like acting or athletics, where starting early in life is especially crucial—are often college dropouts. It’s a simple matter of economics: the opportunity cost of their time at that stage in their lives is just too high to postpone their careers for a college degree.
Accounting Profit versus Economic Profit
As the example of going to school suggests, taking account of implicit as well as explicit costs can be very important for individuals making decisions. The same is true of businesses.
Consider the case of Kathy’s Copy Shop, a small business operating in a local shopping centre. Kathy makes copies for customers, who pay for her services. Out of that revenue, she has to pay her expenses: the cost of supplies and the rent for her store space. We suppose that Kathy owns the copy machines themselves. This year Kathy has $100,000 in revenues and $60,000 in expenses. Is her business profitable?
At first it might seem that the answer is obviously yes: she receives $100,000 from her customers and has expenses of only $60,000. Doesn’t this mean that she has a profit of $40,000? Not according to her accountant, who reduces the number by
$5,000, for the yearly depreciation (reduction in value) of the copy machines.
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Depreciation occurs because machines wear out over time. The yearly depreciation amount reflects what an accountant estimates to be the reduction in the value of the machines due to wear and tear that year. This leaves $35,000, which is the business’s accounting profit. Basically, the accounting profit of a company is its revenue minus its explicit costs and depreciation. The accounting profit is the number that
Kathy has to report on her income tax forms and that she would be obliged to report to anyone thinking of investing in her business.
Accounting profit is a very useful number, but suppose that Kathy wants to decide whether to keep her business going or to do something else. To make this decision, she will need to calculate her economic profit—the revenue she receives minus her opportunity cost, which may include implicit as well as explicit costs. In general, when economists use the simple term profit, they are referring to economic profit.
(We will adopt this simplification in later chapters of this book.)
Why does Kathy’s economic profit differ from her accounting profit? Because she may have implicit costs over and above the explicit cost her accountant has calculated. Businesses can face implicit costs for two reasons. First, a business’s capital—its equipment, buildings, tools, inventory, and financial assets—could have been put to use in some other way. If the business owns its capital, it does not pay any money for its use, but it pays an implicit cost because it does not use the capital in some other way. Second, the owner devotes time and energy to the business that could have been used elsewhere—a particularly important factor in small businesses, whose owners tend to put in many long hours.
If Kathy had rented her copy machines from the manufacturer, their rent would have been an explicit cost. But because Kathy owns her own machines, she does not pay rent on them and her accountant deducts an estimate of their depreciation in the profit statement. However, this does not account for the opportunity cost of the machines—what Kathy forgoes by owning them. Suppose that instead of using the machines for her own business, the best alternative Kathy has is to sell them for
$50,000 and put the money into a bank account where it would earn yearly interest of $3,000. This $3,000 is an implicit cost of running the business.
It is generally known as the implicit cost of capital, the opportunity cost of the capital used by a business; it reflects the income that could have been realized if the capital had been used in its next best alternative way. It is just as much a true cost as if Kathy had rented the machines instead of owning them.
Finally, Kathy should take into account the opportunity cost of her own time.
Suppose that instead of running her own shop, she could earn $34,000 as an office manager. That $34,000 is also an implicit cost of her business.
Table 7-2 summarizes the accounting for Kathy’s Copy Shop, taking both explicit and implicit costs into account. It turns out, unfortunately, that although the business makes an accounting profit of $35,000, its economic profit is actually negative.
TABLE
7-2
Profits at Kathy’s Copy Shop
Revenue
$100,000
Explicit cost
− 60,000
Depreciation
− 5,000
Accounting profit
35,000
Implicit cost of business
Income Kathy could have earned on capital in the next best way
Income Kathy could have earned as manager
Economic profit
− 3,000
− 34,000
–2,000
MAKING DECISIONS
173
The accounting profit of a business is the business’s revenue minus the explicit cost and depreciation.
The economic profit of a business is the business’s revenue minus the opportunity cost of its resources. It is usually less than the accounting profit.
The capital of a business is the value of its assets—equipment, buildings, tools, inventory, and financial assets.
The implicit cost of capital is the opportunity cost of the capital used by a business—the income the owner could have realized from that capital if it had been used in its next best alternative way. 500_12489_CH07_170-191
©The New Yorker Collection. 2000 William Hamilton from cartoonbank.com.
All Rights Reserved
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This means that Kathy would be better off financially if she closed the business and devoted her time and capital to something else.
In real life, discrepancies between accounting profits and economic profits are extremely common. As the following Economics in
Action explains, this is a message that has found a receptive audience among real-world businesses.
economics in action
Urban Sprawl and the Loss of Farmland in Canada
It seems irrational that some of the most fertile agricultural land in
Canada is buried under concrete and tarmac—a victim of urban sprawl.
Why does this occur and what, if anything, can be done about it?
“I’ve done the numbers, and I will marry you.”
The root cause is simple enough. Historically, people congregated in fertile areas, and villages and cities grew up in the middle of the most productive land, especially if there were also water routes nearby that facilitated trading.
Given these beginnings, city growth almost inevitably absorbs some of the best farmland.
The mechanics of urban growth work like this. As land prices increase on the edge of an urban area, so the implicit cost of farming increases. It doesn’t matter whether the farmer owns the land or not. Because land is a form of capital used to run the business, keeping one’s land as a farm instead of selling it to a developer constitutes an implicit cost of capital. Higher land prices increase the implicit cost of capital, which raises the cost of farming—even if the farmer owns the land. This puts intense pressure on farmers to generate incomes that are substantial enough to justify keeping the land in agriculture.
Eventually, these pressures become too great and the land is sold for development.
How great are these pressures? Well, farmland in Canada can sell for anything from $100 to $100,000 an acre, depending on its quality and location. Around small urban centres, one would expect to pay about $7000 an acre for good farmland in
2004, depending on the province. But around large metropolitan areas, prices are much higher. For example, a farm within 30 miles of the greater Toronto area, where urban development is foreseeable within the next 5 to 10 years, would command prices of about $100,000 an acre. It’s nearly impossible to operate a farm with such a high implicit cost of capital. That’s why developers succeed in buying up land where development is foreseen many years before the development takes place. They buy it and hold it as an investment—a so-called “land bank”.
Before we get too alarmed about urban sprawl, we should note that urban areas do need space to grow. We should be happy we’ve got it. Moreover, we should bear in mind that much of the decrease in the amount of land devoted to farming over the last 100 years has nothing to do with the growth of urban centres. Rather, it is due to the replacement of the horse with the tractor as the primary farm vehicle, which reduced the amount of land needed to produce hay and led to the abandonment of much pastureland.
Nevertheless, all provinces feel the need to control urban sprawl in various ways.
Most attempt to do this through zoning regulations and urban plans created by the municipality or local service district. The big drawback with this approach is that farmers comprise only about 3% of the rural population, so rural zoning laws may not offer much effective protection against urban development. Partly as a result of this problem, British Columbia set up an Agricultural Land Reserve in the 1970s. In essence, this took zoning decisions out of local hands and put them under provincial jurisdiction, and it has been very effective in preventing urban sprawl around southwestern BC and the Okanagan Valley.
But there are other options for controlling urban sprawl. For example, New
Brunswick has a farmland identification program under which provincial property taxes can be deferred indefinitely while the land remains farmland; but should the land be abandoned or developed, the last 15 years’ worth of property taxes (plus
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accrued interest) becomes due immediately. Another method, more common in the
U.S. than Canada, is to sell the development rights to a trust. Any developer must then not only buy the land from the farmer but also must buy the development rights from the trust. This insulates the farmer against increases in the implicit cost of capital due to higher land prices caused by impending development. Moreover, farmers benefit from the money they receive from selling the development rights to the land trust, but can meanwhile continue to use the land for agriculture.
So, the main point is two-pronged: first, high implicit costs of capital put enormous pressure on farmers to sell their land to urban developers; and second, attempts to contain this pressure use zoning, farmland identification programs, and land trusts. ■
>>>>>>>>>>>>>>>>>>
>> CHECK YOUR UNDERSTANDING 7-1
Karma and Don run a furniture-refinishing business from their home. Which of the following represent an explicit cost of the business and which represent an implicit cost?
a. Supplies such as paint stripper, varnish, polish, sandpaper, and so on
b. Basement space that has been converted into a workroom
c. Wages paid to a part-time helper
d. A van that they inherited and use only for transporting furniture
e. The job at a larger furniture restorer that Karma gave up in order to run the business
Solutions appear at back of book.
Making “How Much” Decisions:
The Role Of Marginal Analysis
As the story of the two wars at the beginning of this chapter demonstrated, there are two types of decisions: “either–or” decisions and “how much” decisions. To help you get a better sense of that distinction, Table 7-3 offers some examples of each kind of decision.
TABLE
7-3
“How Much” versus “Either–Or” Decisions
“How much” decisions
“Either–or” decisions
How many days before you do your laundry?
Tide or Cheer?
How many miles do you go before an oil change in your car?
Buy a car or not?
How many jalapenos on your nachos?
An order of nachos or a sandwich?
How many workers should you hire in your company?
Run your own business or work for someone else?
How much should a patient take of a drug that generates side effects?
Prescribe drug A or drug B for your patients?
How many troops do you allocate to your invasion force?
Invade at Calais or in Normandy?
Although many decisions in economics are “either–or,” many others are “how much.” Not many people will stop driving if the price of gasoline goes up, but many people will drive less. How much less? A rise in wheat 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 wheat to plant more. How much more?
To understand “how much” decisions, we 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.
➤➤
➤
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➤
175
QUICK REVIEW
All costs are opportunity costs.
They can be divided into explicit costs and implicit costs.
Companies report their accounting profit, which is not necessarily equal to their economic profit.
Due to the implicit cost of capital, the opportunity cost of a company’s capital, and the opportunity cost of the owner’s time, economic profit is often substantially less than accounting profit.
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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 begin our study of marginal analysis by focusing on marginal cost, and we’ll do that by considering a hypothetical company called Felix’s Lawn-mowing
Service, operated by Felix himself with his tractor-mower.
Marginal Cost
Felix is a very hardworking individual; if he works continuously, he can mow 7 lawns in a day. It takes him an hour to mow each lawn. The opportunity cost of an hour of
Felix’s time is $10.00 because he could make that much in his next best job.
His one and only mower, however, presents a problem when Felix works this hard.
Running his mower for longer and longer periods on a given day takes an increasing toll on the engine and ultimately necessitates more—and more costly—maintenance and repairs.
The second column of Table 7-4 shows how the total daily cost of Felix’s business depends on the quantity of lawns he mows in a day. For simplicity, we assume that Felix’s only costs are the opportunity cost of his time and the cost of upkeep for his mower.
TABLE
7-4
Felix’s Marginal Cost of Mowing Lawns
Quantity of lawns mowed
Felix’s total cost
0
$0
1
10.50
2
21.75
3
35.00
4
50.50
5
68.50
6
89.25
7
Felix’s marginal cost of lawn mowed
$113.00
$10.50
11.25
13.25
15.50
18.00
20.75
23.75
The marginal cost of an activity is the additional cost incurred by doing one more unit of that activity.
There is increasing marginal cost from an activity when each additional unit of the activity costs more than the previous unit.
At only 1 lawn per day, Felix’s daily cost is $10.50: $10.00 for an hour of his time plus $0.50 for some oil. At 2 lawns per day, his daily cost is $21.75: $20 for 2 hours of his time and $1.75 for mower repair and maintenance. At 3 lawns per day, the daily cost has risen to $35.00: $30.00 for 3 hours of his time and $5.00 for mower repair and maintenance.
The third column of Table 7-4 contains the cost incurred by Felix for each additional lawn he mows, calculated from information in the second column. The 1st lawn he mows costs him $10.50; this number appears in the third column between the lines representing 0 lawn and 1 lawn because $10.50 is Felix’s cost of going from
0 to 1 lawn mowed. The next lawn, going from 1 to 2, costs him an additional $11.25.
So $11.25 appears in the third column between the lines representing the 1st and 2nd lawn, and so on.
The increase in Felix’s cost when he mows one more lawn is his marginal cost of lawn-mowing. In general, the marginal cost of any activity is the additional cost incurred by doing one more unit of that activity.
The marginal costs shown in Table 7-4 have a clear pattern: Felix’s marginal cost is greater the more lawns he has already mowed. That is, each time he mows a lawn, the additional cost of doing yet another lawn goes up. Felix’s lawn-mowing business has what economists call increasing marginal cost: each additional lawn costs
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Figure
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7-1
The Marginal Cost Curve
The height of each bar is equal to the marginal cost of mowing the corresponding lawn. For example, the 1st lawn mowed has a marginal cost of
$10.50, equal to the height of the bar extending from 0 to 1 lawn. The bars ascend in height, reflecting increasing marginal cost: each additional lawn is more costly to mow than the previous one.
As a result, the marginal cost curve (drawn by plotting points in the top center of each bar) is upward sloping.
Marginal cost of lawn mowed
$35
30
Marginal cost, MC
25
20
15
10
5
0
1
2
3
4
5
6
7
Quantity of lawns mowed
more to mow than the previous one. Or, to put it slightly differently, with increasing marginal cost, the marginal cost of an activity rises as the quantity already done rises.
Figure 7-1 is a graphical representation of the third column in Table 7-4. The horizontal axis measures the quantity of lawns mowed, and the vertical axis measures the marginal cost of a mowed lawn. The height of each shaded bar represents the marginal cost incurred by mowing a given lawn. For example, the bar stretching from 4 to 5 lawns is at a height of $18.00, equal to the cost of mowing the 5th lawn. Notice that the bars form a series of ascending steps, a reflection of the increasing marginal cost of lawn mowing. The marginal cost curve, the red curve in Figure 7-1, shows the relaThe marginal cost curve shows how the cost of undertaking one more unit of an tionship between marginal cost and the quantity of the activity already done. We draw activity depends on the quantity of that it by plotting a point in the center at the top of each bar and connecting the points. activity that has already been done.
The marginal cost curve is upward sloping, due to increasing marginal cost. Not all activities have increasing marginal cost; for example, it is possible for marginal cost to be the same regardless of the number of lawns already mowed. Economists call this case constant marginal cost. It is
PITFALLS
also possible for some activities to have a marginal cost that initially falls as we do more of the activity and then eventualincreasing total cost versus increasing ly rises. These sorts of activities involve gains from specializamarginal cost tion: as more output is produced, more workers are hired,
The concept of increasing marginal cost plays an important allowing each one to specialize in the task that he or she perrole in economic analysis, but students sometimes get conforms best. The gains from specialization yield a lower marfused about what it means. That’s because it is easy to wrongly conclude that whenever total cost is increasing, ginal cost of production. marginal cost must also be increasing. But the following
Now that we have established the concept of marginal cost, example shows that this conclusion is misguided. we move to the parallel concept of marginal benefit.
Marginal Benefit
Felix’s business is in a town where some of the residents are very busy but others are not so busy. For people who are very busy, the opportunity cost of an hour of their time spent mowing the lawn is very high. So they are willing to pay Felix a fairly high sum to do it for them. People with lots of free time, however, have a lower opportunity cost of an hour of their time spent mowing the lawn. So they are willing to pay
Suppose that we change the numbers of our example: the marginal cost of mowing the 6th lawn is now $20, and the marginal cost of mowing the 7th lawn is now $15. In both instances total cost increases as Felix does an additional lawn: it increases by $20 for the 6th lawn and by $15 for the 7th lawn. But in this example marginal cost is decreasing: the marginal cost of the 7th lawn is less than the marginal cost of the 6th lawn. So we have a case of increasing total cost and decreasing marginal cost. What this shows us is that, in fact, totals and marginals can sometimes move in opposite directions.
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The marginal benefit from an activity is the additional benefit derived from undertaking one more unit of that activity. Felix only a relatively small sum. And between these two extremes lie other residents who are moderately busy and so are willing to pay a moderate price to have their lawns mowed.
We’ll assume that on any given day, Felix has one potential customer who will pay him $35 to mow her lawn, another who will pay $30, a third who will pay $26, a fourth who will pay $23, and so on. Table 7-5 lists what he can receive from each of his seven potential customers per day, in descending order according to price. So if
Felix goes from 0 to 1 lawn mowed, he can earn $35; if he goes from 1 to 2 lawns mowed, he can earn an additional $30; and so on. The third column of Table 7-5 shows us the marginal benefit to Felix of each additional lawn mowed. In general, marginal benefit is the additional benefit derived from undertaking one more unit of an activity. Because it arises from doing one more lawn, each marginal benefit value appears between the lines associated with successive quantities of lawns.
TABLE
7-5
Felix’s Marginal Benefit of Mowing Lawns
Quantity of lawns mowed
Felix’s total benefit
0
$0
1
35.00
2
65.00
3
91.00
4
114.00
5
135.00
6
154.00
7
Felix’s marginal benefit of lawn mowed
$172.00
$35.00
30.00
26.00
23.00
21.00
19.00
18.00
There is decreasing marginal benefit from an activity when each additional unit of the activity produces less benefit than the previous unit.
The marginal benefit curve shows how the benefit from undertaking one more unit of an activity depends on the quantity of that activity that has already been done. It’s clear from Table 7-5 that the more lawns Felix has already mowed, the smaller his marginal benefit from mowing one more. So Felix’s lawn-mowing business has what economists call decreasing marginal benefit: each additional lawn mowed produces less benefit than the previous lawn. Or, to put it slightly differently, with decreasing marginal benefit, the marginal benefit of an activity falls as the quantity already done rises.
Just as marginal cost could be represented with a marginal cost curve, marginal benefit can be represented with a marginal benefit curve, shown in blue in Figure 7-2.
The height of each bar shows the marginal benefit of each additional lawn mowed; the curve through the middle of each bar’s top shows how the benefit of each additional unit of the activity depends on the number of units that have already been undertaken.
Felix’s marginal benefit curve is downward sloping, because he faces decreasing marginal benefit from lawn-mowing. Not all activities have decreasing marginal benefit; in fact, there are many activities for which marginal benefit is constant—that is, it is the same regardless of the number of units already undertaken. 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 it behaves within its industry. We’ll also see in Chapters 10 and 11 why economists assume that declining marginal benefit is the norm when considering choices made by consumers. Like increasing marginal cost, decreasing marginal benefit is so common that for now we can take it as the norm.
Now we are ready to see how the concepts of marginal benefit and marginal cost can be brought together to answer the question of “how much” of an activity an individual should undertake.
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Figure
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7-2
The Marginal Benefit Curve
The height of each bar is equal to the marginal benefit of mowing the corresponding lawn. For example, the 1st lawn mowed has a marginal benefit of $35, equal to the height of the bar extending from 0 to 1 lawn. The bars descend in height, reflecting decreasing marginal benefit: each additional lawn produces a smaller benefit than the previous one. As a result, the marginal benefit curve (drawn by plotting points in the top center of each bar) is downward sloping. >web ...
Marginal benefit of lawn mowed
$35
30
25
Marginal benefit, MB
20
15
10
5
0
1
2
Marginal Analysis
Table 7-6 shows the marginal cost and marginal benefit numbers from Tables 7-4 and
7-5. It also adds an additional column: the net gain to Felix from one more lawn mowed, equal to the difference between the marginal benefit and the marginal cost.
We can use Table 7-6 to determine how many lawns Felix should mow. To see this, imagine for a moment that Felix planned to mow only 3 lawns today. We can immediately see that this is too small a quantity. If Felix mows an additional lawn, increasing the quantity of lawns mowed from 3 to 4, he realizes a marginal benefit of $23.00 and incurs a marginal cost of only $15.50—so his net gain would be $23 − $15.50 =
$7.50. But even 4 lawns is still too few: if Felix increases the quantity from 4 to 5, his marginal benefit is $21.00 and his marginal cost is only $18.00, for a net gain of
$21.00 − $18.00 = $3.00 (as indicated by the highlighting in the table).
But if Felix goes ahead and mows 7 lawns, that is too many. We can see this by looking at the net gain from mowing that 7th lawn: Felix’s marginal benefit is $18.00, but his marginal cost is $23.75. So mowing that 7th lawn would produce a net gain
TABLE
7-6
Felix’s Net Gain from Mowing Lawns
Quantity of Felix’s marginal benefit of lawn mowed lawns mowed
Felix’s marginal cost of lawn mowed
Felix’s net gain of lawn mowed
0
$35.00
$10.50
$24.50
30.00
11.25
18.75
26.00
13.25
12.75
23.00
15.50
7.50
21.00
18.00
3.00
19.00
20.75
−1.75
18.00
23.75
−5.75
1
2
3
4
5
6
7
3
4
5
6
7
Quantity of lawns mowed
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of $18.00 − $23.75 = −$5.75; that is, a net loss for his business. And even 6 lawns is too many: by increasing the quantity of lawns mowed from 5 to 6, Felix incurs a marginal cost of $20.75 compared with a marginal benefit of only $19.00. He is best off at mowing 5 lawns, the largest quantity of lawns at which marginal benefit is at least as great as marginal cost.
The upshot is that Felix should mow 5 lawns—no more and no less. If he mows fewer than 5 lawns, his marginal benefit from one more is greater than his marginal cost; he would be passing up a net gain by not mowing more lawns. If he mows more than 5 lawns, his marginal benefit from the last lawn mowed is less than his marginal cost, resulting in a loss for that lawn. So 5 lawns is the quantity that generates Felix’s maximum possible total net gain; it is what economists call the optimal quantity of lawns mowed.
Figure 7-3 shows graphically how the optimal quantity can be determined. Felix’s marginal benefit and marginal cost curves are both shown. If Felix mows fewer than
5 lawns, the marginal benefit curve is above the marginal cost curve, so he can make himself better off by mowing more lawns; if he mows more than 5 lawns, the marginal benefit curve is below the marginal cost curve, so he would be better off mowing fewer lawns.
The table in Figure 7-3 confirms our result. The second column repeats information from Table 7-6, showing marginal benefit minus marginal cost—or the net gain— for each lawn. The third column shows total net gain according to the quantity of lawns mowed. The total net gain after doing a given lawn is simply the sum of numbers in the second column up to and including that lawn. For example, the net gain
The optimal quantity of an activity is the quantity that generates the maximum possible total net gain.
Figure
7-3
The Optimal Quantity
Marginal benefit, marginal cost of lawn mowed
Quantity of lawns mowed Felix's net gain of lawn mowed
0
Optimal point
$35
1
30
2
MC
25
3
20
4
MB
15
5
10
6
5
7
0
1
2
3
4
5
6
Felix's total net gain $0
$24.50
18.75
12.75
7.50
3.00
–1.75
–5.75
24.50
43.25
56.00
63.50
66.50
64.75
59.00
7
Optimal quantity
Quantity of lawns mowed
The optimal quantity of an activity is the quantity that generates the highest possible total net gain. It is the quantity at which marginal benefit is equal to marginal cost. Equivalently, it is the quantity at which the marginal benefit curve and the marginal cost curve intersect.
Here they intersect at approximately 5 lawns. The table beside the graph confirms that 5 is indeed the optimal quantity: the total net gain is maximized at 5 lawns, generating $66.50 in total net gain for Felix.
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MAKING DECISIONS
181
is $24.50 for the first lawn and $18.75 for the second. So the total net gain after doing the first lawn is $24.50, and the total net gain after doing the second lawn is
$24.50 + $18.75 = $43.25. Our conclusion that 5 is the optimal quantity is confirmed by the fact that the greatest total net gain, $66.50, occurs when the 5th lawn is mowed.
PITFALLS
The example of Felix’s lawn-mowing business shows how you go about finding the optimal quantity: increase the quantity as long as muddled at the margin the marginal benefit from one more unit is greater than the marginThe idea of setting marginal benefit equal to marginal cost sometimes confuses people. Aren’t al cost, but stop before the marginal benefit becomes less than the we trying to maximize the difference between marginal cost. benefits and costs? And don’t we wipe out our
In many cases, however, it is possible to state this rule more simply. gains by setting benefits and costs equal to each
When a “how much” decision involves relatively large quantities, the other? But what we are doing is setting marginal, rule simplifies to this: the optimal quantity is the quantity at which marnot total, benefit and cost equal to each other. ginal benefit is equal to marginal cost.
Once again, the point is to maximize the
To see why this is so, consider the example of a farmer who finds that total net gain from an activity. If the marginal her optimal quantity of wheat produced is 5,000 bushels. Typically, she benefit from the activity is greater than the will find that in going from 4,999 to 5,000 bushels, her marginal benefit marginal cost, doing a bit more will increase is only very slightly greater than her marginal cost—that is, the difference that gain. If the marginal benefit is less than between marginal benefit and marginal cost is close to zero. Similarly, in the marginal cost, doing a bit less will increase the total net gain. So only when the marginal going from 5,000 to 5,001 bushels, her marginal cost is only very slightbenefit and cost are equal is the difference ly greater than her marginal benefit—again, the difference between marbetween total benefit and cost at a maximum. ginal 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.
The principle of marginal analysis says
Economists call this rule the principle of marginal analysis. It says that the that the optimal quantity of an activity is optimal quantity of an activity is the quantity at which marginal benefit equals marthe quantity at which marginal benefit is ginal cost. Graphically, the optimal quantity is the quantity of an activity at which equal to marginal cost. the marginal benefit curve intersects the marginal cost curve. In fact, this graphical method works quite well even when the numbers involved aren’t that large. For example, in Figure 7-3 the marginal benefit and marginal cost curves cross each other at about 5 lawns mowed—that is, marginal benefit equals marginal cost at about 5 lawns mowed, which we have already seen is Felix’s optimal quantity.
A Principle with Many Uses
The principle of marginal analysis can be applied to just about any “how much” decision—including those decisions where the benefits and costs are not necessarily expressed in dollars and cents. Here are a few examples:
■
The number of traffic deaths can be reduced by spending more on highways, requiring better protection in cars, and so on. But these measures are expensive.
So we can talk about the marginal cost to society of eliminating one more traffic fatality. And we can then ask whether the marginal benefit of that life saved is large enough to warrant doing this. (If you think no price is too high to save a life, see the following Economics in Action.)
■
Many useful drugs have side effects that depend on the dosage. So we can talk about the marginal cost, in terms of these side effects, of increasing the dosage of a drug. The drug also has a marginal benefit in helping fight the disease. So the optimal quantity of the drug is the quantity that makes the best of this trade-off.
■
Studying for an exam has costs because you could have done something else with the time, such as studying for another exam or sleeping. So we can talk about the marginal cost of devoting another hour to studying for your chemistry final. The optimal quantity of studying is the level at which the marginal benefit in terms of a higher grade is just equal to the marginal cost.
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economics in action
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 major highways to 60 kilometres per hour, but the cost of such a lower speed limit—in time and money—is more than anyone is 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 in 1999, after a horrifying 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 way too little on traffic safety. 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 an activity is represented graphically by the marginal cost curve. An upward-sloping marginal cost curve reflects increasing marginal cost.
The marginal benefit of an activity is represented by the marginal benefit curve. A downward-sloping marginal benefit curve reflects decreasing marginal benefit.
The optimal quantity of an activity is found by applying the principle of marginal analysis. It says that the optimal quantity of an activity is the quantity at which marginal benefit is equal to marginal cost.
Equivalently, it is the quantity at which the marginal cost curve intersects the marginal benefit curve.
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7
Page 170
>> Making
Decisions
A T A L E O F T W O I N VA S I O N S
O
6, 1944, ALLIED SOLDIERS
much should be used to defend Germany’s
stormed the beaches of Norman-
border with France? The original plan,
dy, beginning the liberation of
devised by General Alfred von Schlieffen,
France from German rule. Long before the
allocated most of the German army to the
assault, however, Allied generals had to
invasion force; on his deathbed, Schlieffen is
make a crucial decision: where would the
supposed to have pleaded, “Keep the right
soldiers land?
wing [the invasion force] strong!” But his
N JUNE
How economists model decision …show more content…
making by individuals and firms
➤
The importance of implicit as well as explicit costs in decision making ➤
➤
➤
The difference between accounting profit and economic profit, and why economic profit is the correct basis for decisions
The difference between
“either–or” and “how much” decisions The principle of marginal analysis “either–or” decision. Either the invasion
weakened the plan: he reallocated some of
force could cross the English Channel at its
the divisions that were supposed to race through Belgium to the defence. The weak-
the Germans expected—or it could try to
ened invasion force wasn’t strong enough:
surprise the Germans by landing farther west, in
Normandy. Since men and landing craft were in limited supply, the Allies could not do both. In fact, they chose to rely on surprise.
The German defences in
Normandy were too weak to stop the landings, and the
MGM/The Kobal Collection
➤
successor, General Helmuth von Moltke,
narrowest point, Calais—which was what
What you will learn in this chapter:
They had to make what we call an
Allies went on to liberate
France and win the war.
Thirty years earlier, at the beginning of World War I,
Decision: Attack here? Or there?
➤
What sunk costs are and why they should be ignored
German generals had to
make a different kind of decision. They, too,
the defending French army stopped it 30
How to make decisions in cases where time is a factor
planned to invade France, in this case via
miles from Paris. Most military historians
land, and had decided to mount that invasion
believe that by allocating too few men to the
through Belgium. The decision they had to
➤
attack, von Moltke cost Germany the war.
make was not an either–or but a “how much” decision: how much of their army should be
170
So Allied generals made the right decision in 1944; German generals made the
allocated to the invasion force, and how
wrong decision in 1914. The important
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point for this chapter is that in both cases
at the significance of opportunity cost for
the generals had to apply the same logic
economic decisions and the role it plays in
that applies to economic decisions, like
“either–or” decisions. Next we turn to the
production decisions by businesses and
problem of making “how much” decisions
consumption decisions by households.
and the usefulness of marginal analysis. We
In this chapter we will survey the princi-
then examine what kind of costs should be
ples involved in making economic deci-
ignored in making a decision—costs which
sions. These principles will help us under-
economists call sunk costs. We end by con-
stand how any individual—whether a con-
sidering the concept of present value and its
sumer or a producer—makes an economic
importance for making decisions when
decision. We begin by taking a deeper look
costs and benefits arrive at different times.
Opportunity Cost And Decisions
In Chapter 1 we introduced some core principles underlying economic decisions.
We’ve just seen two of those principles at work in our tale of two invasions. The first is that resources are scarce—the invading Allies had a limited number of landing craft, and the invading Germans had a limited number of divisions. Because resources are scarce, the true cost of anything is its opportunity cost—that is, the real cost of something is what you must give up to get it. When it comes to making decisions, it is crucial to think in terms of opportunity cost, because the opportunity cost of an action is often considerably more than the simple monetary cost.
Explicit versus Implicit Costs
Suppose that, upon graduation from university, you have two options: to go to school for an additional year to get an advanced degree or to take a job immediately. You would like to take the extra year in school but are concerned about the cost.
But what exactly is the cost of that additional year of school? Here is where it is important to remember the concept of opportunity cost: the cost of that year spent getting an advanced degree is what you forgo by not taking a job for that year.
This cost, like any cost, can be broken into two parts: the explicit cost of the year’s schooling and the implicit cost.
An explicit cost is a cost that requires an outlay of money. For example, the explicit cost of the additional year of schooling includes tuition. An implicit cost, on the other hand, does not involve an outlay of money; instead, it is measured by the value, in dollar terms, of all the benefits that are forgone. For example, the implicit cost of the year spent in school includes the income you would have earned if you had taken that job instead.
A common mistake, both in economic analysis and in real business situations, is to ignore implicit costs and focus exclusively on explicit costs. But often the implicit cost of an activity is quite substantial—indeed, sometimes it is much larger than the explicit cost.
Table 7-1 gives a breakdown of hypothetical explicit and implicit costs associated with spending an additional year in school instead of taking a job. The explicit cost consists of tuition, books, supplies, and a home computer for doing assignments—all of which require you to spend money. The implicit cost is the salary you would have earned if you had taken a job instead. As you can see, the forgone salary is $35,000 and the explicit cost is $9,500, making the implicit cost more than three times as much as the explicit cost. So ignoring the implicit cost of an action can lead to a seriously misguided decision.
An explicit cost is a cost that involves actually laying out money. An implicit cost does not require an outlay of money; it is measured by the value, in dollar terms, of the benefits that are forgone. 171
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TABLE
7-1
Opportunity Cost of an Additional Year of School
Explicit cost
Tuition
Implicit cost
$7,000
Books and supplies
Home computer
Total implicit cost
9,500
$35,000
35,000
1,500
Total explicit cost
Forgone salary
1,000
Total opportunity cost = Total explicit cost + Total implicit cost = $44,500
There is another, slightly different way of looking at the implicit cost in this example that can deepen our understanding of opportunity cost. The forgone salary is the cost of using your own resources—your time—in going to school rather than working.
The use of your time for more schooling, despite the fact that you don’t have to spend any money, is nonetheless costly to you. This illustrates an important aspect of opportunity cost: in considering the cost of an activity, you should include the cost of using any of your own resources for that activity. You can calculate the cost of using your own resources by determining what they would have earned in their next best use.
FOR
INQUIRING
MINDS
FAMOUS COLLEGE DROPOUTS
What do Bill Gates, Tiger Woods, and Sarah
Michelle Gellar (a.k.a. Buffy the Vampire
Slayer) have in common? None of them have a college degree.
Nobody doubts that all three are easily smart enough to have gotten their diplomas.
However, they all made the rational decision that the implicit cost of getting a degree would have been too high—by their late teens, each had a very promising career that would have had to be put on hold to get a college degree. Gellar would have had to postpone her acting career; Woods would have had to put off
winning one major tournament after another and becoming the world’s best golfer; Gates would have had to delay developing the most successful and most lucrative software ever sold, Microsoft’s computer operating system.
In fact, extremely successful people—especially those in careers like acting or athletics, where starting early in life is especially crucial—are often college dropouts. It’s a simple matter of economics: the opportunity cost of their time at that stage in their lives is just too high to postpone their careers for a college degree.
Accounting Profit versus Economic Profit
As the example of going to school suggests, taking account of implicit as well as explicit costs can be very important for individuals making decisions. The same is true of businesses.
Consider the case of Kathy’s Copy Shop, a small business operating in a local shopping centre. Kathy makes copies for customers, who pay for her services. Out of that revenue, she has to pay her expenses: the cost of supplies and the rent for her store space. We suppose that Kathy owns the copy machines themselves. This year Kathy has $100,000 in revenues and $60,000 in expenses. Is her business profitable?
At first it might seem that the answer is obviously yes: she receives $100,000 from her customers and has expenses of only $60,000. Doesn’t this mean that she has a profit of $40,000? Not according to her accountant, who reduces the number by
$5,000, for the yearly depreciation (reduction in value) of the copy machines.
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Depreciation occurs because machines wear out over time. The yearly depreciation amount reflects what an accountant estimates to be the reduction in the value of the machines due to wear and tear that year. This leaves $35,000, which is the business’s accounting profit. Basically, the accounting profit of a company is its revenue minus its explicit costs and depreciation. The accounting profit is the number that
Kathy has to report on her income tax forms and that she would be obliged to report to anyone thinking of investing in her business.
Accounting profit is a very useful number, but suppose that Kathy wants to decide whether to keep her business going or to do something else. To make this decision, she will need to calculate her economic profit—the revenue she receives minus her opportunity cost, which may include implicit as well as explicit costs. In general, when economists use the simple term profit, they are referring to economic profit.
(We will adopt this simplification in later chapters of this book.)
Why does Kathy’s economic profit differ from her accounting profit? Because she may have implicit costs over and above the explicit cost her accountant has calculated. Businesses can face implicit costs for two reasons. First, a business’s capital—its equipment, buildings, tools, inventory, and financial assets—could have been put to use in some other way. If the business owns its capital, it does not pay any money for its use, but it pays an implicit cost because it does not use the capital in some other way. Second, the owner devotes time and energy to the business that could have been used elsewhere—a particularly important factor in small businesses, whose owners tend to put in many long hours.
If Kathy had rented her copy machines from the manufacturer, their rent would have been an explicit cost. But because Kathy owns her own machines, she does not pay rent on them and her accountant deducts an estimate of their depreciation in the profit statement. However, this does not account for the opportunity cost of the machines—what Kathy forgoes by owning them. Suppose that instead of using the machines for her own business, the best alternative Kathy has is to sell them for
$50,000 and put the money into a bank account where it would earn yearly interest of $3,000. This $3,000 is an implicit cost of running the business.
It is generally known as the implicit cost of capital, the opportunity cost of the capital used by a business; it reflects the income that could have been realized if the capital had been used in its next best alternative way. It is just as much a true cost as if Kathy had rented the machines instead of owning them.
Finally, Kathy should take into account the opportunity cost of her own time.
Suppose that instead of running her own shop, she could earn $34,000 as an office manager. That $34,000 is also an implicit cost of her business.
Table 7-2 summarizes the accounting for Kathy’s Copy Shop, taking both explicit and implicit costs into account. It turns out, unfortunately, that although the business makes an accounting profit of $35,000, its economic profit is actually negative.
TABLE
7-2
Profits at Kathy’s Copy Shop
Revenue
$100,000
Explicit cost
− 60,000
Depreciation
− 5,000
Accounting profit
35,000
Implicit cost of business
Income Kathy could have earned on capital in the next best way
Income Kathy could have earned as manager
Economic profit
− 3,000
− 34,000
–2,000
MAKING DECISIONS
173
The accounting profit of a business is the business’s revenue minus the explicit cost and depreciation.
The economic profit of a business is the business’s revenue minus the opportunity cost of its resources. It is usually less than the accounting profit.
The capital of a business is the value of its assets—equipment, buildings, tools, inventory, and financial assets.
The implicit cost of capital is the opportunity cost of the capital used by a business—the income the owner could have realized from that capital if it had been used in its next best alternative way. 500_12489_CH07_170-191
©The New Yorker Collection. 2000 William Hamilton from cartoonbank.com.
All Rights Reserved
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This means that Kathy would be better off financially if she closed the business and devoted her time and capital to something else.
In real life, discrepancies between accounting profits and economic profits are extremely common. As the following Economics in
Action explains, this is a message that has found a receptive audience among real-world businesses.
economics in action
Urban Sprawl and the Loss of Farmland in Canada
It seems irrational that some of the most fertile agricultural land in
Canada is buried under concrete and tarmac—a victim of urban sprawl.
Why does this occur and what, if anything, can be done about it?
“I’ve done the numbers, and I will marry you.”
The root cause is simple enough. Historically, people congregated in fertile areas, and villages and cities grew up in the middle of the most productive land, especially if there were also water routes nearby that facilitated trading.
Given these beginnings, city growth almost inevitably absorbs some of the best farmland.
The mechanics of urban growth work like this. As land prices increase on the edge of an urban area, so the implicit cost of farming increases. It doesn’t matter whether the farmer owns the land or not. Because land is a form of capital used to run the business, keeping one’s land as a farm instead of selling it to a developer constitutes an implicit cost of capital. Higher land prices increase the implicit cost of capital, which raises the cost of farming—even if the farmer owns the land. This puts intense pressure on farmers to generate incomes that are substantial enough to justify keeping the land in agriculture.
Eventually, these pressures become too great and the land is sold for development.
How great are these pressures? Well, farmland in Canada can sell for anything from $100 to $100,000 an acre, depending on its quality and location. Around small urban centres, one would expect to pay about $7000 an acre for good farmland in
2004, depending on the province. But around large metropolitan areas, prices are much higher. For example, a farm within 30 miles of the greater Toronto area, where urban development is foreseeable within the next 5 to 10 years, would command prices of about $100,000 an acre. It’s nearly impossible to operate a farm with such a high implicit cost of capital. That’s why developers succeed in buying up land where development is foreseen many years before the development takes place. They buy it and hold it as an investment—a so-called “land bank”.
Before we get too alarmed about urban sprawl, we should note that urban areas do need space to grow. We should be happy we’ve got it. Moreover, we should bear in mind that much of the decrease in the amount of land devoted to farming over the last 100 years has nothing to do with the growth of urban centres. Rather, it is due to the replacement of the horse with the tractor as the primary farm vehicle, which reduced the amount of land needed to produce hay and led to the abandonment of much pastureland.
Nevertheless, all provinces feel the need to control urban sprawl in various ways.
Most attempt to do this through zoning regulations and urban plans created by the municipality or local service district. The big drawback with this approach is that farmers comprise only about 3% of the rural population, so rural zoning laws may not offer much effective protection against urban development. Partly as a result of this problem, British Columbia set up an Agricultural Land Reserve in the 1970s. In essence, this took zoning decisions out of local hands and put them under provincial jurisdiction, and it has been very effective in preventing urban sprawl around southwestern BC and the Okanagan Valley.
But there are other options for controlling urban sprawl. For example, New
Brunswick has a farmland identification program under which provincial property taxes can be deferred indefinitely while the land remains farmland; but should the land be abandoned or developed, the last 15 years’ worth of property taxes (plus
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accrued interest) becomes due immediately. Another method, more common in the
U.S. than Canada, is to sell the development rights to a trust. Any developer must then not only buy the land from the farmer but also must buy the development rights from the trust. This insulates the farmer against increases in the implicit cost of capital due to higher land prices caused by impending development. Moreover, farmers benefit from the money they receive from selling the development rights to the land trust, but can meanwhile continue to use the land for agriculture.
So, the main point is two-pronged: first, high implicit costs of capital put enormous pressure on farmers to sell their land to urban developers; and second, attempts to contain this pressure use zoning, farmland identification programs, and land trusts. ■
>>>>>>>>>>>>>>>>>>
>> CHECK YOUR UNDERSTANDING 7-1
Karma and Don run a furniture-refinishing business from their home. Which of the following represent an explicit cost of the business and which represent an implicit cost?
a. Supplies such as paint stripper, varnish, polish, sandpaper, and so on
b. Basement space that has been converted into a workroom
c. Wages paid to a part-time helper
d. A van that they inherited and use only for transporting furniture
e. The job at a larger furniture restorer that Karma gave up in order to run the business
Solutions appear at back of book.
Making “How Much” Decisions:
The Role Of Marginal Analysis
As the story of the two wars at the beginning of this chapter demonstrated, there are two types of decisions: “either–or” decisions and “how much” decisions. To help you get a better sense of that distinction, Table 7-3 offers some examples of each kind of decision.
TABLE
7-3
“How Much” versus “Either–Or” Decisions
“How much” decisions
“Either–or” decisions
How many days before you do your laundry?
Tide or Cheer?
How many miles do you go before an oil change in your car?
Buy a car or not?
How many jalapenos on your nachos?
An order of nachos or a sandwich?
How many workers should you hire in your company?
Run your own business or work for someone else?
How much should a patient take of a drug that generates side effects?
Prescribe drug A or drug B for your patients?
How many troops do you allocate to your invasion force?
Invade at Calais or in Normandy?
Although many decisions in economics are “either–or,” many others are “how much.” Not many people will stop driving if the price of gasoline goes up, but many people will drive less. How much less? A rise in wheat 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 wheat to plant more. How much more?
To understand “how much” decisions, we 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.
➤➤
➤
➤
➤
175
QUICK REVIEW
All costs are opportunity costs.
They can be divided into explicit costs and implicit costs.
Companies report their accounting profit, which is not necessarily equal to their economic profit.
Due to the implicit cost of capital, the opportunity cost of a company’s capital, and the opportunity cost of the owner’s time, economic profit is often substantially less than accounting profit.
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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 begin our study of marginal analysis by focusing on marginal cost, and we’ll do that by considering a hypothetical company called Felix’s Lawn-mowing
Service, operated by Felix himself with his tractor-mower.
Marginal Cost
Felix is a very hardworking individual; if he works continuously, he can mow 7 lawns in a day. It takes him an hour to mow each lawn. The opportunity cost of an hour of
Felix’s time is $10.00 because he could make that much in his next best job.
His one and only mower, however, presents a problem when Felix works this hard.
Running his mower for longer and longer periods on a given day takes an increasing toll on the engine and ultimately necessitates more—and more costly—maintenance and repairs.
The second column of Table 7-4 shows how the total daily cost of Felix’s business depends on the quantity of lawns he mows in a day. For simplicity, we assume that Felix’s only costs are the opportunity cost of his time and the cost of upkeep for his mower.
TABLE
7-4
Felix’s Marginal Cost of Mowing Lawns
Quantity of lawns mowed
Felix’s total cost
0
$0
1
10.50
2
21.75
3
35.00
4
50.50
5
68.50
6
89.25
7
Felix’s marginal cost of lawn mowed
$113.00
$10.50
11.25
13.25
15.50
18.00
20.75
23.75
The marginal cost of an activity is the additional cost incurred by doing one more unit of that activity.
There is increasing marginal cost from an activity when each additional unit of the activity costs more than the previous unit.
At only 1 lawn per day, Felix’s daily cost is $10.50: $10.00 for an hour of his time plus $0.50 for some oil. At 2 lawns per day, his daily cost is $21.75: $20 for 2 hours of his time and $1.75 for mower repair and maintenance. At 3 lawns per day, the daily cost has risen to $35.00: $30.00 for 3 hours of his time and $5.00 for mower repair and maintenance.
The third column of Table 7-4 contains the cost incurred by Felix for each additional lawn he mows, calculated from information in the second column. The 1st lawn he mows costs him $10.50; this number appears in the third column between the lines representing 0 lawn and 1 lawn because $10.50 is Felix’s cost of going from
0 to 1 lawn mowed. The next lawn, going from 1 to 2, costs him an additional $11.25.
So $11.25 appears in the third column between the lines representing the 1st and 2nd lawn, and so on.
The increase in Felix’s cost when he mows one more lawn is his marginal cost of lawn-mowing. In general, the marginal cost of any activity is the additional cost incurred by doing one more unit of that activity.
The marginal costs shown in Table 7-4 have a clear pattern: Felix’s marginal cost is greater the more lawns he has already mowed. That is, each time he mows a lawn, the additional cost of doing yet another lawn goes up. Felix’s lawn-mowing business has what economists call increasing marginal cost: each additional lawn costs
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7-1
The Marginal Cost Curve
The height of each bar is equal to the marginal cost of mowing the corresponding lawn. For example, the 1st lawn mowed has a marginal cost of
$10.50, equal to the height of the bar extending from 0 to 1 lawn. The bars ascend in height, reflecting increasing marginal cost: each additional lawn is more costly to mow than the previous one.
As a result, the marginal cost curve (drawn by plotting points in the top center of each bar) is upward sloping.
Marginal cost of lawn mowed
$35
30
Marginal cost, MC
25
20
15
10
5
0
1
2
3
4
5
6
7
Quantity of lawns mowed
more to mow than the previous one. Or, to put it slightly differently, with increasing marginal cost, the marginal cost of an activity rises as the quantity already done rises.
Figure 7-1 is a graphical representation of the third column in Table 7-4. The horizontal axis measures the quantity of lawns mowed, and the vertical axis measures the marginal cost of a mowed lawn. The height of each shaded bar represents the marginal cost incurred by mowing a given lawn. For example, the bar stretching from 4 to 5 lawns is at a height of $18.00, equal to the cost of mowing the 5th lawn. Notice that the bars form a series of ascending steps, a reflection of the increasing marginal cost of lawn mowing. The marginal cost curve, the red curve in Figure 7-1, shows the relaThe marginal cost curve shows how the cost of undertaking one more unit of an tionship between marginal cost and the quantity of the activity already done. We draw activity depends on the quantity of that it by plotting a point in the center at the top of each bar and connecting the points. activity that has already been done.
The marginal cost curve is upward sloping, due to increasing marginal cost. Not all activities have increasing marginal cost; for example, it is possible for marginal cost to be the same regardless of the number of lawns already mowed. Economists call this case constant marginal cost. It is
PITFALLS
also possible for some activities to have a marginal cost that initially falls as we do more of the activity and then eventualincreasing total cost versus increasing ly rises. These sorts of activities involve gains from specializamarginal cost tion: as more output is produced, more workers are hired,
The concept of increasing marginal cost plays an important allowing each one to specialize in the task that he or she perrole in economic analysis, but students sometimes get conforms best. The gains from specialization yield a lower marfused about what it means. That’s because it is easy to wrongly conclude that whenever total cost is increasing, ginal cost of production. marginal cost must also be increasing. But the following
Now that we have established the concept of marginal cost, example shows that this conclusion is misguided. we move to the parallel concept of marginal benefit.
Marginal Benefit
Felix’s business is in a town where some of the residents are very busy but others are not so busy. For people who are very busy, the opportunity cost of an hour of their time spent mowing the lawn is very high. So they are willing to pay Felix a fairly high sum to do it for them. People with lots of free time, however, have a lower opportunity cost of an hour of their time spent mowing the lawn. So they are willing to pay
Suppose that we change the numbers of our example: the marginal cost of mowing the 6th lawn is now $20, and the marginal cost of mowing the 7th lawn is now $15. In both instances total cost increases as Felix does an additional lawn: it increases by $20 for the 6th lawn and by $15 for the 7th lawn. But in this example marginal cost is decreasing: the marginal cost of the 7th lawn is less than the marginal cost of the 6th lawn. So we have a case of increasing total cost and decreasing marginal cost. What this shows us is that, in fact, totals and marginals can sometimes move in opposite directions.
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The marginal benefit from an activity is the additional benefit derived from undertaking one more unit of that activity. Felix only a relatively small sum. And between these two extremes lie other residents who are moderately busy and so are willing to pay a moderate price to have their lawns mowed.
We’ll assume that on any given day, Felix has one potential customer who will pay him $35 to mow her lawn, another who will pay $30, a third who will pay $26, a fourth who will pay $23, and so on. Table 7-5 lists what he can receive from each of his seven potential customers per day, in descending order according to price. So if
Felix goes from 0 to 1 lawn mowed, he can earn $35; if he goes from 1 to 2 lawns mowed, he can earn an additional $30; and so on. The third column of Table 7-5 shows us the marginal benefit to Felix of each additional lawn mowed. In general, marginal benefit is the additional benefit derived from undertaking one more unit of an activity. Because it arises from doing one more lawn, each marginal benefit value appears between the lines associated with successive quantities of lawns.
TABLE
7-5
Felix’s Marginal Benefit of Mowing Lawns
Quantity of lawns mowed
Felix’s total benefit
0
$0
1
35.00
2
65.00
3
91.00
4
114.00
5
135.00
6
154.00
7
Felix’s marginal benefit of lawn mowed
$172.00
$35.00
30.00
26.00
23.00
21.00
19.00
18.00
There is decreasing marginal benefit from an activity when each additional unit of the activity produces less benefit than the previous unit.
The marginal benefit curve shows how the benefit from undertaking one more unit of an activity depends on the quantity of that activity that has already been done. It’s clear from Table 7-5 that the more lawns Felix has already mowed, the smaller his marginal benefit from mowing one more. So Felix’s lawn-mowing business has what economists call decreasing marginal benefit: each additional lawn mowed produces less benefit than the previous lawn. Or, to put it slightly differently, with decreasing marginal benefit, the marginal benefit of an activity falls as the quantity already done rises.
Just as marginal cost could be represented with a marginal cost curve, marginal benefit can be represented with a marginal benefit curve, shown in blue in Figure 7-2.
The height of each bar shows the marginal benefit of each additional lawn mowed; the curve through the middle of each bar’s top shows how the benefit of each additional unit of the activity depends on the number of units that have already been undertaken.
Felix’s marginal benefit curve is downward sloping, because he faces decreasing marginal benefit from lawn-mowing. Not all activities have decreasing marginal benefit; in fact, there are many activities for which marginal benefit is constant—that is, it is the same regardless of the number of units already undertaken. 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 it behaves within its industry. We’ll also see in Chapters 10 and 11 why economists assume that declining marginal benefit is the norm when considering choices made by consumers. Like increasing marginal cost, decreasing marginal benefit is so common that for now we can take it as the norm.
Now we are ready to see how the concepts of marginal benefit and marginal cost can be brought together to answer the question of “how much” of an activity an individual should undertake.
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7-2
The Marginal Benefit Curve
The height of each bar is equal to the marginal benefit of mowing the corresponding lawn. For example, the 1st lawn mowed has a marginal benefit of $35, equal to the height of the bar extending from 0 to 1 lawn. The bars descend in height, reflecting decreasing marginal benefit: each additional lawn produces a smaller benefit than the previous one. As a result, the marginal benefit curve (drawn by plotting points in the top center of each bar) is downward sloping. >web ...
Marginal benefit of lawn mowed
$35
30
25
Marginal benefit, MB
20
15
10
5
0
1
2
Marginal Analysis
Table 7-6 shows the marginal cost and marginal benefit numbers from Tables 7-4 and
7-5. It also adds an additional column: the net gain to Felix from one more lawn mowed, equal to the difference between the marginal benefit and the marginal cost.
We can use Table 7-6 to determine how many lawns Felix should mow. To see this, imagine for a moment that Felix planned to mow only 3 lawns today. We can immediately see that this is too small a quantity. If Felix mows an additional lawn, increasing the quantity of lawns mowed from 3 to 4, he realizes a marginal benefit of $23.00 and incurs a marginal cost of only $15.50—so his net gain would be $23 − $15.50 =
$7.50. But even 4 lawns is still too few: if Felix increases the quantity from 4 to 5, his marginal benefit is $21.00 and his marginal cost is only $18.00, for a net gain of
$21.00 − $18.00 = $3.00 (as indicated by the highlighting in the table).
But if Felix goes ahead and mows 7 lawns, that is too many. We can see this by looking at the net gain from mowing that 7th lawn: Felix’s marginal benefit is $18.00, but his marginal cost is $23.75. So mowing that 7th lawn would produce a net gain
TABLE
7-6
Felix’s Net Gain from Mowing Lawns
Quantity of Felix’s marginal benefit of lawn mowed lawns mowed
Felix’s marginal cost of lawn mowed
Felix’s net gain of lawn mowed
0
$35.00
$10.50
$24.50
30.00
11.25
18.75
26.00
13.25
12.75
23.00
15.50
7.50
21.00
18.00
3.00
19.00
20.75
−1.75
18.00
23.75
−5.75
1
2
3
4
5
6
7
3
4
5
6
7
Quantity of lawns mowed
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of $18.00 − $23.75 = −$5.75; that is, a net loss for his business. And even 6 lawns is too many: by increasing the quantity of lawns mowed from 5 to 6, Felix incurs a marginal cost of $20.75 compared with a marginal benefit of only $19.00. He is best off at mowing 5 lawns, the largest quantity of lawns at which marginal benefit is at least as great as marginal cost.
The upshot is that Felix should mow 5 lawns—no more and no less. If he mows fewer than 5 lawns, his marginal benefit from one more is greater than his marginal cost; he would be passing up a net gain by not mowing more lawns. If he mows more than 5 lawns, his marginal benefit from the last lawn mowed is less than his marginal cost, resulting in a loss for that lawn. So 5 lawns is the quantity that generates Felix’s maximum possible total net gain; it is what economists call the optimal quantity of lawns mowed.
Figure 7-3 shows graphically how the optimal quantity can be determined. Felix’s marginal benefit and marginal cost curves are both shown. If Felix mows fewer than
5 lawns, the marginal benefit curve is above the marginal cost curve, so he can make himself better off by mowing more lawns; if he mows more than 5 lawns, the marginal benefit curve is below the marginal cost curve, so he would be better off mowing fewer lawns.
The table in Figure 7-3 confirms our result. The second column repeats information from Table 7-6, showing marginal benefit minus marginal cost—or the net gain— for each lawn. The third column shows total net gain according to the quantity of lawns mowed. The total net gain after doing a given lawn is simply the sum of numbers in the second column up to and including that lawn. For example, the net gain
The optimal quantity of an activity is the quantity that generates the maximum possible total net gain.
Figure
7-3
The Optimal Quantity
Marginal benefit, marginal cost of lawn mowed
Quantity of lawns mowed Felix's net gain of lawn mowed
0
Optimal point
$35
1
30
2
MC
25
3
20
4
MB
15
5
10
6
5
7
0
1
2
3
4
5
6
Felix's total net gain $0
$24.50
18.75
12.75
7.50
3.00
–1.75
–5.75
24.50
43.25
56.00
63.50
66.50
64.75
59.00
7
Optimal quantity
Quantity of lawns mowed
The optimal quantity of an activity is the quantity that generates the highest possible total net gain. It is the quantity at which marginal benefit is equal to marginal cost. Equivalently, it is the quantity at which the marginal benefit curve and the marginal cost curve intersect.
Here they intersect at approximately 5 lawns. The table beside the graph confirms that 5 is indeed the optimal quantity: the total net gain is maximized at 5 lawns, generating $66.50 in total net gain for Felix.
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is $24.50 for the first lawn and $18.75 for the second. So the total net gain after doing the first lawn is $24.50, and the total net gain after doing the second lawn is
$24.50 + $18.75 = $43.25. Our conclusion that 5 is the optimal quantity is confirmed by the fact that the greatest total net gain, $66.50, occurs when the 5th lawn is mowed.
PITFALLS
The example of Felix’s lawn-mowing business shows how you go about finding the optimal quantity: increase the quantity as long as muddled at the margin the marginal benefit from one more unit is greater than the marginThe idea of setting marginal benefit equal to marginal cost sometimes confuses people. Aren’t al cost, but stop before the marginal benefit becomes less than the we trying to maximize the difference between marginal cost. benefits and costs? And don’t we wipe out our
In many cases, however, it is possible to state this rule more simply. gains by setting benefits and costs equal to each
When a “how much” decision involves relatively large quantities, the other? But what we are doing is setting marginal, rule simplifies to this: the optimal quantity is the quantity at which marnot total, benefit and cost equal to each other. ginal benefit is equal to marginal cost.
Once again, the point is to maximize the
To see why this is so, consider the example of a farmer who finds that total net gain from an activity. If the marginal her optimal quantity of wheat produced is 5,000 bushels. Typically, she benefit from the activity is greater than the will find that in going from 4,999 to 5,000 bushels, her marginal benefit marginal cost, doing a bit more will increase is only very slightly greater than her marginal cost—that is, the difference that gain. If the marginal benefit is less than between marginal benefit and marginal cost is close to zero. Similarly, in the marginal cost, doing a bit less will increase the total net gain. So only when the marginal going from 5,000 to 5,001 bushels, her marginal cost is only very slightbenefit and cost are equal is the difference ly greater than her marginal benefit—again, the difference between marbetween total benefit and cost at a maximum. ginal 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.
The principle of marginal analysis says
Economists call this rule the principle of marginal analysis. It says that the that the optimal quantity of an activity is optimal quantity of an activity is the quantity at which marginal benefit equals marthe quantity at which marginal benefit is ginal cost. Graphically, the optimal quantity is the quantity of an activity at which equal to marginal cost. the marginal benefit curve intersects the marginal cost curve. In fact, this graphical method works quite well even when the numbers involved aren’t that large. For example, in Figure 7-3 the marginal benefit and marginal cost curves cross each other at about 5 lawns mowed—that is, marginal benefit equals marginal cost at about 5 lawns mowed, which we have already seen is Felix’s optimal quantity.
A Principle with Many Uses
The principle of marginal analysis can be applied to just about any “how much” decision—including those decisions where the benefits and costs are not necessarily expressed in dollars and cents. Here are a few examples:
■
The number of traffic deaths can be reduced by spending more on highways, requiring better protection in cars, and so on. But these measures are expensive.
So we can talk about the marginal cost to society of eliminating one more traffic fatality. And we can then ask whether the marginal benefit of that life saved is large enough to warrant doing this. (If you think no price is too high to save a life, see the following Economics in Action.)
■
Many useful drugs have side effects that depend on the dosage. So we can talk about the marginal cost, in terms of these side effects, of increasing the dosage of a drug. The drug also has a marginal benefit in helping fight the disease. So the optimal quantity of the drug is the quantity that makes the best of this trade-off.
■
Studying for an exam has costs because you could have done something else with the time, such as studying for another exam or sleeping. So we can talk about the marginal cost of devoting another hour to studying for your chemistry final. The optimal quantity of studying is the level at which the marginal benefit in terms of a higher grade is just equal to the marginal cost.
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economics in action
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 major highways to 60 kilometres per hour, but the cost of such a lower speed limit—in time and money—is more than anyone is 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 in 1999, after a horrifying 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 way too little on traffic safety. 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 an activity is represented graphically by the marginal cost curve. An upward-sloping marginal cost curve reflects increasing marginal cost.
The marginal benefit of an activity is represented by the marginal benefit curve. A downward-sloping marginal benefit curve reflects decreasing marginal benefit.
The optimal quantity of an activity is found by applying the principle of marginal analysis. It says that the optimal quantity of an activity is the quantity at which marginal benefit is equal to marginal cost.
Equivalently, it is the quantity at which the marginal cost curve intersects the marginal benefit curve.