CHAPTER 9: Production Costs and Business Decisions

Rational Behavior and Marginal Cost Marginal cost is the additional cost incurred by producing one additional unit of a good, activity, or service.. __________________________________

Production Costs and

Business Decisions

The economist’s stock in trade—his tools—lies in his ability to and proclivity to think about all questions in terms of alternatives The truth judgment of the moralist, which says that something is either wholly right or wholly wrong, is foreign to him The win- list, yes-no discussion of politics is not within his purview He does not recognize the either-or, the all-or-nothing situation as his own His is not the world of the mutually exclusive Instead, his is the world of adjustment, of coordinated conflict, of mutual gain

James M Buchanan

ost is pervasive in human action Managers (as well as everyone else) are

constantly forced to make choices, to do one thing and not another Cost or

more precisely, opportunity cost is the most highly valued opportunity not

chosen Although money is a frequently used measure of cost, it is not cost itself

Although we may not recognize it, cost also pervades our everyday thought and

conversation When we say “that course is difficult” or “the sermon seemed endless,” we are indicating the cost of activities If the preacher’s extended commentary delayed the

church picnic, the sermon was costly Although complaints about excessive costs

sometimes indicate an absolute limitation, more often they merely mean that the benefits

of the activity are too small to justify the cost Many people who “can’t afford” a

vacation actually have the money but do not wish to spend it on travel, and most students who find writing research papers “impossible” are simply not willing to put forth the

necessary effort

This chapter explores the meaning of cost in human behavior We will begin by

showing how seemingly irrational behavior can often be explained by the hidden costs of

a choice We will then develop the concept of marginal cost, which together with

demand and the related concept of supply defines the limits of rational behavior, from

personal activities like painting and fishing to business decisions like how much to

produce

Inevitably, points made earlier will be reviewed and extended in this chapter

There is a cost in this repetition, but there is also some benefit in a few varied

reiterations We will use the cost analysis to make points that seem to defy common

sense in business For example, we will show that a firm should not necessarily seek to

produce at the level at which the average cost of production is minimized

C

Explicit and Implicit Costs

Not all costs are obvious It is not difficult to recognize an out-of-pocket expenditure—

the monthly price you pay for a product or service This is called an explicit cost

Explicit cost is the money expenditure required to obtain a resource, product, or service

For example, the price of your book is an explicit cost of taking a course in economics

Other costs are less immediately apparent Hidden costs of the course might include the time spent going to class and studying, the risk of receiving a failing grade, and the

discomfort of being confronted with material that may challenge some of your beliefs

These are implicit costs; together they add up to the value of what you could have done

instead Implicit cost is the forgone opportunity to do or squire something else or to put

one’s resources to another use Although implicit costs may not be recognized, they are often much larger than the more obvious explicit costs of an action (Then, there are

some “costs” that are recognized on accounting statements that should not be considered

in making business decisions These costs are called “sunk costs.” See the box on the

next page.)

The Cost of an Education

A good illustration of the magnitude of implicit costs is the cost of an education

Suppose an MBA student—Eileen Payne—takes a course and pays $2,000 for tuition and

$200 for books The money cost of the course is $2,200, but that figure does not include the implicit costs to the student To take a course, Eileen must attend class for about 45 hours and may have to spend twice that much time traveling to and from class,

completing class assignments, and studying for examinations The total number of hours

spent on any one course, then, might be 135 (30 hours in class plus 105 hours of

traveling, studying, and so forth)

The student could have spent that time doing other things, including working for a money wage If Eileen’s time is valued at $25 per hour (the wage she might have

received if working), the time cost of the course is $3,375 (135 hours x $6) Moreover, if she experiences some anxiety because of taking the course, that psychic or risk cost must

be added to the total as well If Eileen would be willing to pay $500 to avoid the anxiety, the total implicit cost of taking the course climbs to $820

Total implicit cost $3,875

Total costs of course $6,075

The opportunity cost of the student’s time represents the largest component of the total cost of the course The value of one’s time varies from person to person For

students who are unable to find work, the time costs of taking a course may be quite

small That is why many young people go to college Their time cost is generally lower

than that of experienced workers who must give up the opportunity to earn a good wage

in order to attend classes full time

The Cost of Bargains

Every Wednesday, supermarkets run large newspaper ads listing their weekly specials

Generally only a few items are offered at especially low prices, for store managers know that most bargain seekers can be attracted to the store with just a few carefully selected

specials Once the customer has gone to the store offering a special on steak, he would

have to incur a travel cost in order to buy other items in a different store Even though

peanut butter may be on sale elsewhere, the sum of the sale price and the travel cost

exceed the regular price in the first store Through attractive displays and packaging,

customers can be persuaded to buy many other goods not on sale, particularly toiletries, which tend to bear high markups

Supermarket chains do not necessarily make huge profits The grocery industry is reasonably competitive, and supermarket chains as a group are not highly profitable

compared to other corporations The stores manage to recoup some of the revenues lost

on sale items by charging higher prices on other goods In other words, the cost of a

bargain on sirloin steak may be a high price for toothpaste

PERSPECTIVE: Why “Sunk Costs” Don’t Matter

A sunk cost is a past cost Economists define past costs as historical costs that cannot be altered by

current decisions Such costs are beyond the realm of choice Will a rational, profit-maximizing business firm base its current decisions on its historical costs?

An example can help to answer this question Suppose an oil exploration firm purchases the mineral rights to a particular piece of property for $1 million After several month of drilling, the firm

concludes that the land contains no oil (or other valuable mineral resources) Will the firm reason that, having spent $1 million for the mineral rights, it should continue to look for oil on the land? If the chances of finding oil are nonexistent, the rational firm will cease drilling on the land and try

somewhere else The $1 million is a sunk cost that will not influence the decision to continue or cease exploration Indeed, the firm may begin drilling on land for which it paid far less for mineral rights, if management believes that the chances of finding oil are higher there than on the $1 million property The underlying reason that sunk costs do not matter to current production decisions is that in the economist’s use of the term, sunk costs are not really costs The opportunity cost of an activity is the value of the best alternative not chosen In the case of an historical cost, however, there are no longer any alternatives Although the oil exploration firm at one time could have chosen an alternative way to spend the $1 million, once the choice was made the alternative ceased to be available Nor can the firm resell the mineral rights for $1 million; those rights are now worth far less because of accumulated evidence that the land contains little or no valuable minerals Sunk costs, however painful the memory

of them might be, are gone and best forgotten by the firm Profits are made by looking forward, not backward.

Some shoppers make the rounds of the grocery stores when sales are announced For such people, time and transportation are cheap A person who values his or her time

at $10 an hour is not going to spend an hour trying to save a dollar or two The cost of

gas alone can make it prohibitively expensive to visit several stores Because of the costs

of acquiring information, many shoppers do not even bother to look for sales The

expected benefits are simply not great enough to justify the information cost These

shoppers enter the market “rationally ignorant.”

Marginal Cost

So far we have been considering cost as the determining factor in the decision to

undertake a particular course of action The rational person weight the cost of an action

against it benefits and comes to a decision: whether to invest in an education, to shop

around for a bargain, or to operate an airplane The question is, how much of a given

good or service will an individual choose to produce or consume? How does cost limit a behavior once a person has decided to engage in it? The answer lies in the concept of

marginal cost

Rational Behavior and Marginal Cost

Marginal cost is the additional cost incurred by producing one additional unit of a good,

activity, or service Marginal cost is the cost incurred by reading one additional page,

making one additional friend, giving one additional gift, or going one additional mile

Depending on the good, activity, or service in question, marginal cost may stay the same

or vary as additional units are produced For example, imagine that Jan smith wants to

give Halloween candy to ten of her friends In a sense, Jan is producing gifts by

procuring bags of candy If she can buy as many bags as she wants at a unit price of fifty cents, the marginal cost of each additional unit she buys is the same, fifty cents The

marginal cost is constant over the range of production

Marginal cost can vary with the level of output, however, for two reasons The

first has to do with the opportunity cost of time Suppose Jan wants to give each friend a miniature watercolor, which she will paint herself over the course of the day To make

time for painting, Jan can forgo any of the various activities that usually make up her day She may choose to give up recreational activities, housekeeping chores, or time spent on work or study

If she behaves rationally, she will give up the activities she values least To do

the first painting, she may forgo straightening up her room—an activity that is low on

most people’s lists of preferences The marginal cost of her first watercolor is therefore a messy room To paint the second watercolor, Jan will give up the more next-to-last item

on her list of favorite activities As she produces more and more paintings, Jan will forgo more and more valuable alternatives In other words, the marginal cost of her paintings

will rise with her output

If the marginal cost of each new painting is plotted against the quantity of

paintings produced, a curve like the one in Figure 9.1 will result Because the marginal

cost of each additional painting is higher than the marginal cost of the last one, the curve

slopes upward to the right

Although the marginal cost curve is generally assumed to slope upward, as the

one in Figure 9.1 does, that need not be the case If Jan placed equal value on all the

forgone activities, her marginal cost would be constant and the marginal cost curve would

be horizontal

FIGURE 9.1 Rising Marginal Cost

To produce each new watercolor, Jan must

give up an opportunity more valuable than

the last Thus the marginal cost of her

paintings rises with each new work

The Law of Diminishing Returns

The second reason marginal cost may vary with output involves a technological

relationship known as the law of diminishing marginal returns According to the law

of diminishing marginal returns, as more and more units of one resource labor,

fertilizer, or any other resource are applied to a fixed quantity of another resource

land, for instance the increase in total added output gained from each additional unit of

the variable resource will eventually begin to diminish In other words, beyond some

point less output is received for each added unit of a resource That is, more of the

resource will be required to produce the same amount of output as before Beyond some

point, the marginal cost of additional units of output rises

Although the law of diminishing returns applies to any production process, its

meaning is most easily grasped in the context of agricultural production Assume you are

producing tomatoes You have a fixed amount of land (an acre) but can vary the quantity

of labor you apply to it If you try to do planting all by yourself dig the holes, pour the

water, insert the plants, and core them up you will waste time changing tools If a

friend helps you, you can divide the tasks and specialize Less time will be wasted in

changing tools

The time you would have spent changing tools can be spent planting more

tomatoes, thus increasing the harvest At first, output may expand faster than the labor

force That is, one laborer may be able to plant 100 tomatoes an hour; two working

together may be able to plant 250 an hour Thus the marginal cost of planting the

additional 150 plants is lower than the cost of the first 100 Up to a point, the more

workers, the greater their efficiency, and the lower the marginal cost—all because of the

economies of specialization At some point, however, the addition of still more laborers

will not contribute as much to production as in the past, if only because a large number of workers on a single acre of ground will start bumping into one another Then the

marginal cost of putting plants into the ground will begin to rise

Diminishing returns are an inescapable fact of life If returns did not diminish at

some point, output would expand indefinitely and the world’s food supply could be

grown on just one acre of land (For that matter, it could be grown in a flower box.) The

point at which output begins to diminish varies from one production process to the next,

but eventually all marginal cost curves will slope upward to the right, as in Figure 9.1

Table 9.1 shows the marginal cost of producing tomatoes with various numbers of workers, assuming that each worker is paid $5 and that production is limited to one acre Working alone, one worker can produce a quarter of a bushel; two can produce a full

bushel (columns 1 and 2) The third column shows the amount each additional worker

adds to total production, called the marginal product Marginal product is the increase

in total output that results when one additional unit of a resource—for example, labor,

fertilizer, and land is added to the production process, everything else held constant

The first worker contributed 0.25 (one quarter) of a bushel; the second worker, an

additional 0.75 of a bushel, and so on These are the marginal products of successive

units of labor

The important information is shown in the last two columns of the table

Although two workers are needed to produce the first bushel (column 4), because of the

efficiencies of specialization, only one additional worker is needed to produce the second Beyond that point, however, returns diminish Each additional worker contributes less,

so that two more workers are needed to produce the third bushel and give more to

produce the fourth If the table were extended, each bushel beyond the fourth would

require a progressively larger number of workers

Column 5 shows that if all workers are paid the same wage, $5, the marginal cost

of a bushel of tomatoes will decline from $10 for the first bushel to $5 for the second

before rising to $10 again for the third bushel That is, increasing marginal costs (or

diminishing returns) emerge after the addition of the third worker

If the marginal cost of each bushel (column 5) is plotted against the number of

bushels harvested, a curve like the one in Figure 9.2 will result Although the curve

slopes downward at first, for most purposes the relevant segment of the curve is the

upward-sloping portion above point a, will be explained in detail later)

TABLE 9.1 Marginal Costs of Producing Tomatoes

Contribution Number of

As production expands with the addition of new

workers, efficiencies of specialization initially cause

marginal cost to fall At some point, however—here,

just beyond two bushels —marginal cost will begin to

rise again At that point, marginal returns will begin

to diminish and marginal costs will begin to rise

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The Cost-Benefit Tradeoff

Just as a producer’s marginal cost schedule shows the increasing cost of supplying more

goods, the demand curve, as explained earlier, shows the decreasing value or marginal

benefit of those goods to the people consuming them Together, marginal costs and

benefits determine how many units will be produced and consumed up to the intersection

of the marginal cost and demand (marginal benefit) curves, the marginal benefit of each

additional unit exceeds it marginal cost In other words, people can gain through

production and consumption of those units The intersection of the two curves represents the limit of production, or the point at which welfare is maximized To see this point,

consider the costs and benefits of an activity like fishing

The Costs and Benefits of Fishing

Gary Schmidt likes to fish What he does with the fish he catches is of no consequence to us; he can make them into trophies, give them away, or store them in the freezer Even if

Gary places no money value on the fish, we can use dollars to illustrate the marginal

costs and benefits of fishing to Gary (Money figures are not values, but a means of

indicating relative value.)

What is important is that Gary wants to fish How many fish will he catch? From

our earlier analysis of Jan’s desire to paint (page 181), we know that the cost of catching

each additional fish will be higher than the cost of the one before Gary will confront an

upward-sloping marginal cost curve like the one in Figure 9.3 Gary’s demand curve for

fishing will slope downward, for as the cost of catching each additional fish rises, Gary

will be less and less inclined to spend more time on the activity (see Figure 9.3)

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FIGURE 9.3 Costs and Benefits of Fishing

For each fish up to the fifth, Gary receives more

in benefits than he pays in costs The first fish

gives him $4.67 in benefits (point a) and costs

him only $1 (point b) The fifth yields equal

costs and benefits (point c), but the sixth costs

more than it is worth Therefore Gary will catch

no more than five fish

From the positions of the two curves, we can see that Gary will catch up to five

fish before he packs up his rod and heads for home He places a relatively high value of

$4.67 on the first fish (point a in the figure) and places the relatively low marginal cost of

$1 on forgone opportunities for it (point b) In other words, he gets $3.67 more value

from using his time, energy, and other resources to fish than he wold receive from his

nexr best alternative The marginal benefit of the second fish also exceeds its marginal

cost, although by a small amount ($2.75-$4.25 $1.50) Gary continues to gain with the third and fourth fishes, but the fifth fish is a matter of indifference to him Its marginal

value equals its marginal cost (point c) Although we cannot say that Gary will actually

bother to catch a fifth fish, we do know that five is the limit toward which he will aim

He will not catch a sixth—at least during the period of time offered by the graph—

because it would cost him more than he would receive in benefits

The Costs and Benefits of Preventing Accidents

All of us would prefer to avoid accidents In that sense we have a demand for accident

prevention, whose curve should slope downward like all other demand curves

Preventing accidents also entails costs, however, whether in time, forgone opportunities,

or money Should we attempt to prevent all accidents? Not if the cost of ensuring that

you will never stumble down the stairs is $100 (again, we are using dollars to indicate

relative value) If the only injury you expect to suffer were a bruised knee, would you

spend $100 to prevent the accident?

As with the question of how long to fish, marginal cost and benefit curves can

help illustrate the point at which preventing accidents ceases to be cost effective

Suppose Al Rosa’s experience indicates that he can expect to have ten accidents over the course of the year If he tries to prevent all of them, the value of preventing he last one,

as indicated by the demand curve in Figure 9.4, will be only $1 (point a) The marginal

cost of preventing it will be much greater: approximately $6 (point b) If Al is rational,

he will not try to prevent the last accident As a matter of fact, he will try to prevent only

five accidents (point c) As with the tenth accident, it will cost more than it is worth to Al

to prevent the sixth through ninth accidents He would try to prevent all ten accidents

only if his demand for accident prevention were so great that his demand curve

intersected the marginal cost curve at point b

Some accidents may be unavoidable In that case, the marginal cost curve will

eventually become vertical Other accidents may be avoidable in the sense that it is

physically possible to take measures to prevent them—although the rational course may

be to allow them to happen

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FIGURE 9.4 Accident Prevention

Given the increasing marginal cost of preventing

accidents and the decreasing marginal value of

preventing the accidents, c accidents will be

prevented

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The Production Function in Pictures

Business firms combine various factors of production in order to produce various goods

and services Although there are thousands of different factors of production, or inputs,

for simplicity we often use a model with only two factors, labor and capital We can then study how the two inputs can be combined to produce an output The relationship

between inputs and output is called the production function The general equation for

the production function is:

Q = f (L, K)

where Q is output, L is labor, K is capital, and f is the functional relationship between

inputs and output In the short run, we assume that capital cannot be varied; labor is

therefore, the only variable factor To increase output, then, a firm must increase the

amount of labor

The relationship between the amount of the variable input (labor) and output can

be illustrated with a total product curve such as that in the upper half of Figure 9.5

Suppose that the curve is that of a commercial fishing firm The firm’s capital—the boat

and equipment—is fixed in the short run Only the number of workers can vary As the

amount of labor increases from zero, the fish catch (output) increases Between zero and

5 workers, output increases at an increasing rate As more workers are hired total output continues to increase, although at a decreasing rate, until 15 workers are hired Beyond

that point, hiring more workers reduces output

The reason the total product curve has that particular shape can be seen more

clearly in the lower half of Figure 9.5, which shows the average and marginal product

curves The average product of labor is total output divided by the amount of labor, or

Q/L The marginal product of labor is the change in total output brought about by

changing the amount of labor by one unit Because at least some workers are needed to

operate the boat and the equipment, the first few workers hired greatly increase total

output; marginal product is rising Between 5 and 15 workers, the marginal product of

labor falls, although the average product continues to rise (because it is less than marginal product) Total product continues to rise, but no longer at an increasing rate The law of diminishing marginal returns has taken effect At seven workers, marginal product

equals average product and average product is maximized As more workers are hired

average product falls Note that as long as marginal product is positive, more labor

means more output and the total product curve will have a positive slope Beyond 15

workers, marginal product becomes negative and total product falls The boat may be so crowded that workers bump into each other and reduce the amount of work that each

does To catch more fish once this stage has been reached, the firm must buy a larger

boat

Some economists divide the production function of Figure 9.5 into three stages

In stage one, from zero to seven workers, total product and average product of labor both rise In stage two, between seven and 15 workers, total product rises while average

product falls In stage three, beyond 15 workers, total product and average product both fall (and marginal product is negative)

Price and Marginal Cost: Producing to Maximize Profits

“Production” is not generally an end in itself in business Most firms seek to make a

profit How can we think about how they go about the task of trying to maximize profits? The total and marginal product curves need to be converted to cost curves Only then can

we engage in familiar cost-benefit analyses

Granted, many business people derive intrinsic reward from their work They may value the satisfaction of producing a product that meets a human need just as much as the profits they earn Some business people may even accept lower profits so their products can sell at lower prices and serve more people For most business people, however, the

profit generated by sales is the major motivation for doing business

FIGURE 9.5 Total, Average, and Marginal

Product Curves

The total product curve shows how output

changes when the amount of the variable

input, labor, changes Total product rises first

at an increasing rate (0 to 5 workers), then at

a decreasing rate (5 to 15 workers), before

declining (beyond 15 workers) The marginal

and average product curves reflect what is

happening to total product Marginal product

rises when total product is rising at an

increasing rate and falls when total product is

rising at a decreasing rate Marginal product

is positive when total product is rising and

negative when total product is falling

How much will a profit-maximizing firm produce? Assume its marginal cost

curve is like the one in Figure 9.6(a) Assume further that the owners can sell as many

units as they want at a price of P 1 Because this firm is in business to make a profit, the

price of its product can be thought of as the marginal benefit of each additional unit P 1 is

also the firm’s marginal revenue Marginal revenue is the additional revenue a firm

acquires by selling an additional unit of output Each time the firm sells one additional

unit, its revenues rise by P 1

Clearly, a profit-maximizing firm will produce and sell any unit for which the

marginal revenue acquired (MR) exceeds the marginal cost (MC) (Profits are the

difference between total costs and total revenues Therefore a firm’s profits rise whenever

an increase in revenues exceeds the increase in its costs.) At a price of P 1, then, this firm

will produce up to, and no more than, Q 1 , products For every unit up to Q 1, price is

greater than marginal cost

FIGURE 9.6 Marginal Costs and

Maximization of Profit

At price P 1 (part (a)), this firm’s marginal

revenue, shown by the shaded area under P1,

exceeds its marginal cost up to an output level

of Q 1 At that point total profit, shown in part

(b), peaks (point a) At price P 2, marginal

revenue exceeds marginal cost up to an output

level of Q 2 The increase in price shifts the

profit curve in part b upward, from TP 1 to TP 2,

and profits peak at b