Embed Size (px)
Citation preview
CHAPTER 1: HOW CAN ECONOMIC THEORY HELP
THE BUSINESS MANAGER?
Indian Mall struggling
By Grover Welch
JONESBORO -- The silence in Indian Mall is almost eerie, with empty halls that once
bustled with shopping traffic. Those shoppers, and their dollars, have shifted a few
blocks east, leaving the iconic fixture of Jonesboro's retail district in a lurch.
Since the March opening of The Mall at Turtle Creek, local shoppers have not been
coming to the 40-year-old Jonesboro shopping outlet as they once did, straining stores
trying to hang onto their retail spot in the mall. "It is almost like you look out into the
mall from your store and you see tumbleweeds roll by," said Crystal McClung, assistant
manager at Afterthoughts, a woman's boutique located in the Indian Mall.
Stores at the mall are suffering from separation anxiety, as they lose money to the other
mall, said Katrina Johnson, assistant manager of Gadzooks, a clothing store aimed at
teens and college-age women. "We are really missing our customers," Johnson said. "We
are not even seeing half the business we used to. Currently our numbers represent the
damage -- we are 69 percent below projections and 94 percent below this day last year.
The company's lease is until October, but I don't think we will be able to hold out that
long. That decision is way above me though, so officially we are going to be here until
October."
Store spaces throughout the mall are vacant as the mall's management company,
Warmack & Co. LLC, said Wednesday afternoon that it would not comment on the future
of the mall or on the nearly 140 acres of land where it had planned to build a 1-million-
square-foot mall last year.
The news came as no surprise to Alanna Hawkins, assistant manager of Lady Foot
Locker in the Indian Mall. "We are advertising and putting out coupons to lure in
customers," she said. "It's just really slow, and we don't really know anything beyond our
lease is up in October." Mall staff continue to keep the mall clean and stores continue to
open, but the cost is quickly outweighing the benefit, Johnson said. "We have many
items that we have placed on sale and still our sales are less in a week than we used to
make on one Saturday," she said. "I guess the stores here will just continue to hold on
until the final chapter is done."
Managers at Dillard's and Sears refused to comment on the future of their Indian Mall
stores. Representatives of many of the 17 stores left in the mall were unable to comment
because of corporate restrictions. But mall employees are frustrated, said one Foot
Locker employee who asked to remain anonymous. "It sucks," he said. "The sales are in
the dumper, and we are just hanging on. I am just a low-level peon, and when the
decisions are finally made, I'll just react. It doesn't look good for the Indian Mall,
though."
Re-printed Jonesboro Sun, June 2, 2006.
Managerial Economics: The Philosophy of this Text
What do economists have to offer business managers? Accounting professors teach
students how to prepare financial statements and measure unit cost. Marketing professors
teach the four P’s (product, price, place, promotion). Finance professors teach students
how to make the maximum use of financial resources. But what do economists do, and
how can they help business managers make better decisions?
We should probably begin with a brief apology: economists are social scientists,
not practitioners of applied business science. Many lack any formal education in
business. Many have never had formal coursework in accounting, marketing, or
operations.
As social scientists, however, we understand how competitive markets work: how
the free enterprise system harnesses self-interest and channels it into the production of
goods and services desired by consumers. We also understand how competitive markets
create incentives for efficiency at the workplace and lead to cut-throat pricing. And we
understand how imperfectly competitive markets work against consumer welfare.
Much of the thrust of economic thinking is geared toward public policy. When
consumers whine about rising gasoline prices and demand government-instituted price
freezes, economists understand the problems created by price ceilings. We understand
why international trade does not result in a net mass outmigration of jobs to third-world
countries. And on the macro front, we understand why balancing the federal budget
during a recession is a bad idea, or why the Fed may raise interest rates during periods of
strong economic growth.
This is the essence of economic thinking: to understand the world around us and
to make predictions or policy recommendations for the future. Indeed, business
managers often rely on economists to tell them the outlook on the economy; for insights
as to future short-term economic growth, inflation, and interest rates. But we do not, as a
rule, tell business managers how to build a better mousetrap, take care of their books, or
piece together a promotional campaign. But learning about the macroeconomy is not the
impetus for enrolling in a managerial economics class, which is typically rooted in
microeconomic theory. Managers want to know how economic theory can make them
better managers.
So, I retreat to my original question: what do economists have to offer to business
managers? This textbook departs from most of the other managerial economics texts. I
believe it is a disservice to business managers to simply present managerial economics as
“intermediate microeconomic theory with regression analysis.” A well-known textbook
on microeconomic theory by Henderson and Quandt makes an excellent point on the
application of theory to specific firms:
“the requirement of a strict conformity between theory and fact would defeat the very purpose of theory. Theories represent simplifications and generalizations of reality and therefore do not completely describe particular situations. The data-variable distinctions and behavior assumptions of the theories...are satisfied by few, if any, actual market situations. A stricter conformity to facts would require a separate, highly detailed theory for each individual market situation, since each possesses its own distinctive characteristics...The more general theories are fruitful because they contain statements which abstract from particulars and find elements which many situations have in common. (p. 2)”1
The world of the academic economist who seeks to make broad-based predictions
about the innerworkings of markets is laden with overly simplistic models, assumptions,
and shortcuts. We assume linear demand functions, well-behaved nonlinear cost
functions, and perfectly informed firms and consumers. As simplistic as our models can
1 Henderson, James M. and Richard E. Quandt. Microeconomic Theory: A Mathematical Approach, Third Edition, McGraw-Hill: New York, 1980.
be, they do a good job of predicting how markets behave, which, after all, is our primary
goal. A strict application of the theory of the firm to a specific business, however, is
fraught with problems. A firm’s demand function may not be linear (in fact, in a world
of discrete numbers, no demand curve is linear). A firm’s actual cost function may be
difficult to reconcile with the economic theory of costs. And of course, neither firms nor
consumers are perfectly informed.
Does this render economic theory useless to the business manager? Hardly.
Economics has quite a bit to offer to the business manager. However, rather than to
simply re-teach the overly simplistic models that inhabit our intermediate microeconomic
textbooks, the economics instructor must translate the critical components of theory into
the real world of the business manager.
A primary goal of this text is to link economic theory with the various functions
of a business. This is increasingly important as many MBA programs actively seek to
integrate the courses in the curriculum rather than to teach them as “stand-alone” courses
that require the student to connect the dots between, say, managerial accounting and
marketing. Teaching students to graph an isoquant and look for the tangency isn’t a
valuable tool for the business manager. Linking production theory to lean management,
MRP, MRPII, and JIT manufacturing practices, on the other hand, integrates the
importance of production and cost efficiency with actual operations practices that can be
put into practice by the manager. Similarly, it is a disservice to explain the importance of
marginal cost in business decisions without explaining how various cost accounting
practices report average variable cost or average total cost rather than marginal cost---and
how various cost accounting practices could distort the manager’s decision. Likewise,
from the manager’s perspective, the basic economic theory of monopolistic competition
is less important than learning proactive strategies for product differentiation. Business
students will, of course, study market segmentation and product differentiation in greater
detail in their marketing classes, but managerial economics can provide the necessary
framework to bridge the gap between competitive market pressures and the need to
differentiate one’s good or service. In this manner, managerial economics can serve as
both the unifying perspective and the “jumping off point” for the core business courses
will take in their program.
Another goal of this text is to make it proactive. A fair amount of microeconomic
theory is useful in terms of developing economics as a social science, but not particularly
useful to managers who seek to put theory into practical use. For this reason, I’ve tiptoed
around elements of economic theory that are likely to be too abstract and general for the
business manager, while concentrating on the theoretical implications that the manager
can “take back to the office.” For professors who feel a need to derive theory formally,
I’ve included appendixes that include the use of calculus and algebra. However, these
appendixes can be skipped in their entirety without losing the continuity of the material.
A central element of the proactive approach is the use of case studies gathered
from secondary sources such as the Harvard Business School and Ivey Publishing. Case
studies should not be confused with “real-world examples.” A quality case study requires
the student to make a decision or critically examine a decision made by an actual firm.
One proactive real-world case study from one of these secondary sources has been
chosen to accompany each chapter. Although the case studies read as applied business
problems rather than “economics problems”, each one requires the use of the economic
theory covered in the corresponding chapter. The chapter begins with an overview of the
Harvard/Ivey case study and integrates the case into the body of the chapter.
In addition to the case studies from secondary sources, a shorter case study
involving a hypothetical firm appears at the end of the chapter. The intent is to create a
short, albeit self-contained application of material covered within the chapter; to allow
the student to begin each chapter with an actual business problem and then see how
economic theory can be used to resolve the issue. Finally, the end-of-chapter problems
have been written as applied business problems that utilize economic theory rather than
as microeconomic problem sets.
One characteristic that distinguishes this book from other managerial economics
textbooks is the Hands-on Exercises section that accompanies each chapter. I have been
a disciple of active learning for over ten years and it permeates throughout my teaching.
The literature on economic education has also embraced active learning as a teaching
strategy. Active learning is, in short, “learning by doing”. At the opposite end of the
spectrum is “passive learning” which describes the standard classroom setting in which
the instructor lectures and the students passively take notes.
A subset of active learning is cooperative learning, in which students work in
small groups on active learning exercises. Unlike homework problems, in-class
cooperative learning exercises promote the thinking process that is conducive to learning
rather than the “getting the right answer” mindset that is pervasive in out-of-class
homework assignments. Because students learn more when they are actively involved in
the classroom, the exercises allow students to learn on their own what might otherwise be
presented in a straight lecture format.
The hands-on exercises found in this textbook reflect the manner in which I teach
all of my courses. As a practitioner of active and cooperative learning for ten years, I can
provide testimony to its success; my students have a much better feel for the intuition
underlying economic theory than during my days of “chalk-and-talk.” Although I
strongly encourage instructors to use the Hands-on Exercises in class, they are free to rely
on the traditional lecture and allow the students to use the exercises to teach themselves
the relevant economic concepts outside of class.
There is one element of the exercises that I would call to the instructors’ attention.
Over the past several years, I have moved away from teaching theory through the
traditional graph-based emphasis to a table-based method. The heavy use of graphs in
economic education evolved from the “one picture is worth a thousand words”
philosophy. Indeed, the use of graphs makes it easier for students to understand the
comparative statics of basic supply-and-demand analysis. However, I have learned that
graphical analysis does a poor job of teaching the “marginal thinking” that is so critical to
the discipline. Students readily know that firms produce “where marginal revenue is
equal to marginal cost” and have no problem finding it on a graph, but cannot explain
how and why they got there. In fact, the basic principles we teach (MR=MC, P=ATC,
MPL/w = MPK/r, etc.) are implications of the differential calculus of the theory of the
firm. Not only are the implications based on the unrealistic notion of continuous
numbers, the “marginal thinking” storyline behind the implications is frequently lost.
For the business manager, for example, the notion that one should produce all units for
which the marginal revenue exceeds the marginal cost is far more important than the
calculus-based MR=MC implication (in much the same way as a football coach is more
concerned with moving the ball down the field than he is about the location of the end
zone). The manager’s task is learning to identify and anticipate marginal changes in
costs and revenues.
My experience is that once students began working with tables (allowing them to
visualize and understand changes in revenues and costs as production increased), their
understanding of marginal thinking increased tenfold. I still use graphs to teach
economics (and many may be found in each chapter), but I tend to reference them after
the “marginal thinking” story has been told.
This general movement away from the heavy use of graphs echoes the
recommendations made by well-known economic education researchers Lee Hansen,
Michael Salemi, and John Siegfried.2 In fact, much of the philosophy underlying the
structure of this text reflects Hansen et al.’s recommendations. Specifically, they
recommend that instructors focus on problems, issues, policies, and puzzles. They also
believe instructors should create more opportunities to practice economics. Rather than
lecture on three different topics in three days, instructors should introduce a topic on one
day, work through an application on the next day, and analyze a case, complete a
cooperative learning exercise, or discuss a newspaper article on the third day.
Although these recommendations are largely intended for principles classes, they
contain important implications for managerial economics students. The vast majority of
students who enroll in managerial economics classes are not economics majors, but
business majors and predominantly MBA students. Because they aspire to be successful
2 W. Lee Hansen, Michael K. Salemi, and John J. Siegfried. (2002) “Use it or Lose it: Teaching Literacy in an Economics Principles Course,” American Economic Review Papers and Proceedings, 92 (No. 2): 463-72. In this paper, the authors cite the Cohn et al. 2001 study that revealed students did not learn more from lectures with graphs than they did from lectures without graphs. In fact, the authors conclude “We recommend that instructors develop graph-free strategies for teaching most concepts.”
business managers, they need a course that emphasizes problem-solving and applications.
Theory is important, but only if it can be readily applied at the office.
This is not to say this text is not well-suited to economics majors. However,
economics instructors need to determine what distinguishes “managerial economics”
from “intermediate microeconomics”. I would argue that although the latter ought to be
taught as a social science, economics majors who do not aspire to business careers can,
nevertheless, benefit from linking theory with real-world business case studies and
applications. Managerial economics should complement intermediate micro theory and
not be viewed as a substitute. Moreover, this text is written with the philosophy that
marginal thinking in business decisions is far more important than the calculus-based
implications that comprise the first-order conditions of profit-maximization. If nothing
else, then, the style of the book reinforces the focus on marginal thinking that may have
been lost since the students first enrolled in their principles courses.
What Are the Critical Elements of Managerial Economics?
A. The Importance of Opportunity Cost
How can economic theory help the business manager make better decisions? One of the
most important elements of economic thought is opportunity cost. Opportunity cost
refers to the highest-valued alternative foregone by an individual or firm. When
consumers make purchase decisions, they cannot spend the same money twice. Because
purchasing one item implies foregoing other goods they value, this reality economists call
scarcity forces consumers to pick and choose. Consequently, it is essential for any
successful business to understand that the incentive of consumers is to minimize
opportunity costs. As the price of a good rises, consumers can be counted on to seek
cheaper alternatives. When gasoline prices rose in the mid-2000s, SUV sales plummeted
as consumers sought less expensive means of transportation.3 When the Omnibus Budget
Reconciliation Act of 1990 imposed heavy taxes on luxury yachts, tax revenues were
only half of their original projections, as wealthy consumers substituted into non-taxed
goods.
The propensity of consumers to find a cheaper alternative, or to do without
entirely, depends on the product. The first instinct of the consumer, of course, is to find
an identical substitute at a lower price. For some goods, such as gasoline or milk, one
firm’s goods may be perceived as identical to another’s. This forces firms to be aware of
the prices charged by their key competitors. For other goods, the gaps among substitutes
may be greater. Cars differ in style, color, gas mileage, and options. The bells and
whistles that distinguish one cell phone from another can be vast. Consumers may be
less likely to switch into competitor’s brands when the price rises, but sustained price
increases will eventually result in substitution. And some goods, such as electricity, are
necessities that may seem to have no available substitute. But even when no close
substitutes are available, consumers may opt to purchase fewer units or do without. For
example, as the price of electricity rises, consumers may become more vigilant about
making sure the lights are turned off in unused rooms or they may make more
conservative use of air conditioning. In sum, the basic concept always holds: because
consumers experience opportunity cost every time they make a purchase, they evaluate
alternatives to lower their opportunity cost each time the price of a good or service rises.
3 Freeman, Sholnn. “SUV Sales Down Sharply, GM, Ford Shift Production to Cars,” Washington Post, December 2, 2005, p. D01.
Beyond its effect on buyer behavior, opportunity cost is equally important to the
firm. It is not sufficient for a firm to make a profit or even to maximize profits within a
given industry. An entrepreneur, for example, may be forced to quit his/her job to start a
business. Thus, the business must generate a profit that is at least as great as the
entrepreneur’s foregone salary. Similarly, if the firm had sunk its operating expenses into
an investment portfolio, it could have earned interest and dividend income. Thus, the
funds poured into the business need to generate at least a great a profit as the alternative
investments. Further, although a firm may be maximizing its profits at its existing
location, perhaps it could earn even greater profits if it relocated. Sometimes the firm
would benefit from changing industries altogether. In summary, a firm that truly seeks to
maximize profits must consider not only the bottom line in its income statement, but also
foregone income opportunities.
B. Managerial Economics: The Importance of Thinking on the Margin
Another significant contribution of the “economic way of thinking” into the world of the
business manager is our emphasis on marginalism. If you’ve taken courses in principles
of micro- and macroeconomics, you were undoubtedly bombarded with terms containing
the word “marginal”: marginal revenue, marginal cost, marginal propensity to consume,
marginal revenue product, marginal product, etc. “Marginal” means “additional”. In this
context of economic thought, we assume that all decisions are made on the margin.
Patrons at a bar during happy hour, for example, don’t decide how many drinks they’ll
order in advance. Rather, they make their decisions one drink at a time. Does the first
drink justify the necessary expenditure (i.e. opportunity cost)? Does the second? Does
the third?
Economists often refer to stocks and flows. A stock refers to something one has
at a single point in time. A firm’s balance sheet, for example, reports the sum total of its
assets and liabilities at a given point in time. Nothing in the report shows when or how
the assets or liabilities were accumulated. A flow, on the other hand, refers to changes
that occur over time. An income statement reports the sum of the revenues accrued and
expenses incurred between two discrete points in time. Again, nothing in the income
statement ties revenues or expenditures to specific decisions made by the firm.
Unfortunately, because most business statements are time-based rather than decision-
based, firms want to make decisions on the margin, but are confronted with data that
reports only totals and averages. Hence, the firm’s decision-making ability is often
clouded by data that doesn’t allow it to focus on what’s relevant: the marginal impact of
the decision on revenues and expenses. Economic theory, however, allows the business
manager to anticipate the marginal impact of a strategic initiative that may not be
properly captured in an income statement or balance sheet.
To Close or Not to Close: A Simple Application of Marginal Thinking
To illustrate, let’s apply this concept of marginal thinking in a world of totals and
averages to a real-world business dilemma. This chapter begins with an article re-printed
from the Jonesboro Sun newspaper in 2006. In March of that year, a new shopping mall
called the Mall at Turtle Creek was constructed in the town of Jonesboro, Arkansas. The
new mall rendered the outdated existing Indian Mall obsolete. Once the new mall
opened, patronage at the old mall plummeted. One store at the old mall reported its sales
were 94 percent below the figure posted on the same day in the previous year. Although
most businesses in the old mall closed their doors immediately, a few remained open.
What rationale might one have for shutting down? Quite conceivably, some firms may
have decided to close their doors because their income statements revealed they were
losing money due to the mass exodus of customers. Why might some businesses remain
open? Perhaps they were locked into a lease and figured that as long as they were forced
to lease a space in the old mall, they might as well use it.
So who’s right? Should a retailer shut down its operations because it’s losing
money, or should a firm remain open in the face of sustained losses because it has to pay
for the lease anyway? Ironically, both rationales are flawed. The key to making the right
decision is to “think on the margin.” The firm that closed its doors because it was losing
money is guilty of looking at its bottom line which only reveals the difference between
revenues and expenditures during the accounting period. As noted, however, the firm has
a lease with the older mall---it is still obligated to pay most, if not all, of its lease
payments whether it remains open or not. As long as the firm must pay fixed expenses, it
is destined to lose money regardless of whether it remains open or shuts down. Clearly,
then, the firm needs to determine which option will cause it to lose the least amount of
money.
And what about the firm that chose to remain open because it was going to have
to pay for the space it was leasing anyway? What’s wrong with that rationale? To
understand, let’s alter the scenario. Suppose you take a job in Dallas that pays $75,000
and sign a year’s lease at an apartment complex that obliges you to pay $1,000/month in
rent. Three months into the lease, you get a job offer in Atlanta that promises an annual
salary of $750,000. Would you refuse the job because you’re stuck with the lease in
Dallas? Hardly. Instead, you’d take the job in Atlanta and use some of the additional
salary to pay off the Dallas lease. The same is true for the mall that’s saddled with the
lease. If shutting down the business causes the firm to lose less money, why remain
open? Keeping one’s doors open to your own detriment just because you have to honor a
lease doesn’t make sense.
How should the business determine whether to stay open or shut down? The key
is to think on the margin. “Thinking on the margin” requires the firm to focus on a
decision and to determine the revenues and expenses that will change if the decision is
implemented. In other words, the firm must determine the marginal impact of a decision
on revenues and expenses. The revenues that will change if the decision is implemented
are called incremental, or relevant revenues. The expenses that will change if the
decision is undertaken are called incremental, or relevant costs. Only those revenues
and costs that change if the decision is executed are relevant. Expenses that must be paid
anyway are called sunk costs and should not play a role in the decision. Likewise, any
revenues that will accrue regardless of the decision made by the manager are not relevant
and should be ignored.
Let’s create a hypothetical income statement for a shoe store at the older mall in
Jonesboro, Arkansas. Table 1 shows the store’s income statement for the month of June
before and after the new mall opened for business. If we jump to the bottom line, we can
see the store earned an after-tax profit of $39,184 prior to the opening of the new mall,
but lost $11,398 one year later after the new mall opened for business.
At first glance, it seems obvious the store should close its doors. It’s already
losing more than $11,000/month, and with the new mall responsible for the drop-off in
business, it is not a situation that is likely to reverse itself.
But this is why the economic approach to decision-making is so important.
Income statements reflect accounting periods, not decisions. As such, they merely
surmise the sum total of all revenues and expenses incurred between two discrete points
in time. Economists, on the other hand, look to marginal changes that are tied to specific
decisions.
In this instance, the shoe store, which was thriving in the previous year, is losing
money and will likely continue to do so in its present location. Should it shut down its
operations or remain open? The key to making the right decision is to isolate on the
relevant costs and revenues associated with the decision to shut down. Only those
revenues and expenses that will change if the shoe store shuts down should be
considered. Any other revenue/expense that will not be affected by the decision is
irrelevant and should be ignored. Ultimately, therefore, if closing the store causes
revenues to fall by more than its costs, the proper decision is to remain open. Even if the
store continues to lose money, it would lose even more money if it shut down altogether.
Similarly, the store should only close if doing so causes its revenues fall by less than its
costs.
As we review the income statements in Table 1, it is tempting to simply subtract
the corresponding revenue/cost items to determine the changes in revenues and costs that
occurred before and after the new mall opened. However, economic theory contains
some unique insights to suggest this might be an oversimplification of the actual impact
of closing on revenues and expenditures.
Instead, let’s examine the income statement item-by-item to determine what is
relevant to the shoe store’s decision. The first objective is to determine the amount by
which revenues will decrease if the shoe store closes down. This is rather straightforward
to determine; if it shuts down, its revenues at the existing location will drop to zero. In
this case, the lost revenue stream totals $55,540.
However, is it correct to assume that closing down will result in lost revenues of
$55,540? Economic theory suggests that the new mall caused the demand for shoes at
the old mall to decline. The firm may determine that in the face of declining demand, it
may need to lower its price. Dropping its price may not revive unit sales to its pre-mall
level, but it may result in greater revenues and a higher gross margin than it would by
charging the same prices as before. Indeed, the Jonesboro Sun article shows that some
retailers at the old mall lowered prices in response to declining demand.
Next, we need to determine the costs relevant to this decision. The first cost item
in the income statement is the cost of sales. This reflects the cost of purchasing inventory
and making it available for sale. Clearly, if the store closes its doors, the firm will no
longer have to stock inventory. Consequently, the cost of sales is a relevant cost.
Although the cost of sales will drop to zero if the firm shuts down, will the cost of sales
decline by $32,000? Some of the inventory costs may be sunk costs; that is, they reflect
inventory that has already been purchased and cannot be returned.
To see why this is important, consider the distinction between a retailer that
purchased a pair of shoes at the wholesale price of $50 with one that is considering
purchasing a pair of shoes for $50. In the latter case, it would make no sense to order the
shoes unless the retailer knew it could re-sell the shoes for at least $50. In the former
case, however, the retailer has already purchased the shoes and cannot return them.
Because the cost of purchasing the shoes is sunk, the retailer is better off selling them at
any price than it is by charging $60 and allowing them to go unsold.
Note how this discussion of selling the single pair of shoes is another marginal
decision. If the shoes have not yet been purchased as new inventory, the relevant cost of
buying the shoes is $50. Hence, the firm should only purchase them if it can charge at
least $50. If, on the other hand, the shoes have already been purchased, the decision to
sell them does not result in any additional cost; the inventory cost has already been
incurred and will not rise or fall if the shoes are sold. Because the relevant cost of selling
the pre-purchased pair of shoes is $0, the store will benefit by selling them at any price.
If the shoes are sold at $1, therefore, the store is $1 richer for having sold them.
Does that mean the store should sell any or its entire prepaid inventory at any
price? Not necessarily. Recall the importance of opportunity cost. The pair of shoes can
only be sold once. Clearly, the firm is better off selling them for $1, than not selling
them at all, but once the bill is rung up and the patron leaves the store with the shoes,
they cannot be sold to any subsequent customer who might have been willing to pay
more.
Note how complicated the process of determining the level of relevant revenues
and costs can become? It’s much more than simply subtracting the corresponding line
items from the “before-and-after-the-new-mall” income statements. This leads us into
the next important subtopic: forward-thinking. Any decision is, by definition, to be
implemented in the future. Hence, relevant revenues and costs must reflect future
revenues and future costs. If declining demand forces the firm to lower its prices, it must
incorporate the new prices and unit sales into its projection of relevant revenues.
Similarly, any costs relevant to a decision must reflect future, not historical costs. We
should note, therefore, that accounting data always reports historical costs, not future
costs. Although historical costs may reflect future costs, this may not always be the case.
In the case of the shoe store, we may even wish to subdivide the decision into two
components: the first decision is to determine whether to remain open until the existing
inventory is sold. If this proves to be wise, the second decision is whether to remain open
for some or the entirety of the remaining lease and continue to order and sell new
inventory. We could even add a third decision: whether the retailer should renew its
lease upon expiration.
We can proceed to the next line item, which is composed of sales and marketing
expenses. Clearly, if the firm shuts down, it will no longer purchase ads or mail
promotional materials to potential customers. However, the Jonesboro Sun article
suggests that the decrease in relevant costs may exceed the $8,000 totals that appear in
Table 1. With the decline in business due to the opening of the new mall, retailers were
concerned that customers may not be aware that they were still in business or that they
were offering their inventory on sale. As the article suggests, absent the usual flow of
customers through the mall, remaining open could necessitate increasing promotional
expenditures to attract patrons.
The next items are the general and administrative expenses. The income
statement reveals a monthly payroll of $7,525. Clearly, this expenditure will be
eliminated if the store closes; hence, it is relevant to this decision. Will the payroll
decline by $7,525? Not necessarily. The payroll reflects the number of persons
employed to handle the flow of customers. With demand down by 80%, the firm may not
have to staff as many employees, particularly during the leanest hours.
What about depreciation? As we will discuss in the chapter on capital budgeting,
depreciation is not a cash flow; although the income statements list a monthly
depreciation expenditure of $2,000, the store is not actually spending this money. Rather,
depreciation is an accounting procedure to allow the cost of assets to be spread out over
their useful life. Because the assets have already been purchased, they are sunk costs and
depreciation is not a relevant cost.
The shoe store’s rent consists of two components: fixed rent and percentage rent.
Fixed rent refers to a monthly payment that must be made to lease the space regardless of
the volume of sales. Percentage rent, on the other hand, frequently appears in lease
agreements for retailers in shopping malls. Typically, a breakpoint level of sales is
negotiated between the mall and the retailer. If sales exceed the breakpoint, additional
rent (usually a small percentage of the additional sales revenues) must be paid to the mall.
If sales fail to reach the breakpoint level, no additional rent is paid beyond the fixed
amount.
The income statements in Table 1 reveal a monthly fixed payment of $15,000.
Because the retailer must honor the lease regardless of whether it remains open or shuts
down, the fixed rent is not a relevant cost. However, lease agreements often contain
clauses that call for fixed payments that are much less than the remaining monthly fixed
payment for the duration of the lease. As an example, suppose the retailer has three years
remaining on the lease (or a total of $540,000 in fixed lease payments), but can get out of
the lease if it pays $150,000. If the lease contains these provisions, is the fixed payment a
relevant cost?
The answer once again lies in the decision. Paying off the lease mandates an
expenditure of $150,000, or the equivalent of ten months of fixed payments. For the next
ten months, therefore, the monthly $15,000 payment is not a relevant cost. If the retailer
decides to remain in the mall beyond ten months, however, it will bear higher fixed
payments than if it shuts down before then. The additional fixed payments are relevant
costs to the decision to remain in business more than ten months.
The percentage rent is potentially a relevant cost because it is tied to sales. No
percentage rent is paid if the retailer ceases to do business. However, because the rent is
paid only for sales beyond the pre-negotiated breakpoint level, the income statement
suggests the firm’s sales are below the breakpoint. Assuming this is a permanent state of
affairs, shutting down will not result in any decrease in percentage rent. In other words,
the percentage rent is a relevant cost, but will be $0 as long as sales are below the
breakpoint.
Insurance may be a relevant cost, but perhaps not for the immediate short-term.
The firm may have a contractual arrangement that may be terminated relatively quickly.
Until the retailer is in a position to terminate its policy, insurance is not a relevant cost.
Interest payments are expenses for debt already accumulated. From this
perspective, they constitute a sunk cost and are not relevant to the decision. Taxes are
clearly a relevant cost because the shoe store’s profits will no longer be taxed if it shuts
down. However, if the shoe store is part of a larger conglomerate, any losses sustained
by this particular store may reduce the overall tax burden of the conglomerate
(alternatively, in the case of a sole proprietorship, its losses may be applied against the
owner’s income from other endeavors). In either case, the tax impact of sustained losses
on other income sources ought to be considered in the analysis.
For purposes of simplification, let’s suppose that all of the considerations we’ve
discussed are already embodied in the two income statements. Table 2 shows the
summary of relevant costs and revenues owing to the decision to close the shoe store.
According to the table, closing the store will cause revenues to decline by $55,540 and
costs to fall by $47,738. Because revenues fall by a greater amount than costs, the shoe
store is $7,802/month better off if it remains open.
So is that the final verdict? Hardly. There are other considerations that are
relevant to the analysis. The first is opportunity cost. If the store closes, the funds that
might have been used for its operating expenditures could be dedicated to an investment
portfolio. By remaining open, the shoe store is missing out on investment income that
compounds with each passing month.
Alternative uses of the funds are relevant to the analysis. In addition, suppose the
shoe store had another branch in town. Any aggressive strategy to increase sales at the
old location might cannibalize sales elsewhere. Any change in sales at other locations
that occur if the store closes down its operations at the old mall need to be incorporated
into the analysis.
So what does economics have to offer to the business manager? Quite a lot,
obviously. Whereas balance sheets summarizes a stock of assets and liabilities, and the
income statements report the flow of revenues and expenses between two points in time,
economics focuses on the marginal impact of a decision on revenues and expenses.
Much of this textbook is centered on the theme of identifying relevant revenues and
costs. We will begin with a discussion of basic demand theory. This lends insights into
the consumer whose purchase decisions always take place on the margin. Understanding
the law of demand and price elasticity helps a firm to determine the extent to which
revenues will change if a given strategy is implemented. From there, we will segue into a
discussion of relevant revenues and market structures. The ability of consumers to
substitute into alternative goods has a significant impact on relevant revenues. Moreover,
the relative ease at which firms can enter an industry has the potential to squeeze
revenues and gross margins for profitable firms. We will complete the discussion of
relevant revenues with a discussion of product differentiation and pricing strategies. The
goal of product differentiation is to create temporary market barriers to stave off the
influx of competition. Various types of price discrimination allow the firm to increase
revenues by charging different prices to various segments of the market.
In the next section, we will focus on determining the relevant costs. We begin
with a discussion of production theory from which the economic theory of costs will be
derived. Then, we will reconcile the economic theory of costs with actual cost
accounting practices. As we will learn, whereas economists stress the importance of
marginal cost (the additional cost incurred when producing an additional unit of output),
most cost accounting techniques only report average variable costs or average total costs.
Each cost accounting technique has important implications for determining relevant cost.
From there, we will begin a chapter on capital budgeting. This adds to the
discussion of relevant revenues and costs by building opportunity costs directly into the
analysis. Although usually covered in finance, this text emphasizes the economics
underlying capital budgeting. We will also discuss economic theory and its insights into
the two critical components of capital budgeting: estimating cash flows and determining
the cost of capital.
The second section of the textbook deals with risk and decision-making. Quite
often, the relevant revenues and costs associated with a decision are not known with
certainty. Hence, we shift into a discussion of the expected changes in revenues and costs
associated with a decision. Although the concept of game theory is usually covered
exclusively in discussions of oligopolistic markets, this text devotes most of its
discussion of game theory as a supplement to basic decision theory. By examining the
world from the perspective of one’s primary competitor(s), the level of risk associated
with a given pricing strategy (or other strategic initiative) may be reduced or even
eliminated.
As we enter into a world of globalization, firm’s need to understand the
economics underlying foreign exchange markets. As exchange rates change, firms
engaging in international transactions incur risks. Sometimes a change in exchange rates
results in an unanticipated windfall for one of the firms. On other occasions, the changes
reduce the revenues or increase the costs of a business. In this chapter, we discuss both
the determinants of exchange rates and the tools for managing exchange rate risk.
Strategic decisions and discussions of expected costs and revenues are not
confined to the product market. Businesses also need to understand input markets. A
driving force behind a worker’s decision to choose an employer is opportunity cost. If
the worker is employed by one firm, he/she foregoes the wages, benefits, and working
conditions of other employers. Profit maximization, therefore, hinges on the ability of
firms to understand the marketplace and to attract and maintain a productive workforce.
Although labor unions have been on the decline since the early 1950s, roughly 12% of
American workers are presently unionized. In our discussion of labor markets, we also
introduce the economics of labor relations and collective bargaining.
This section of the text concludes with a discussion of organizational design.
Although the goal of a firm is to maximize profits, its employees seek to maximize
utility. For this reason, the behavior of the employees may interfere with the ability of
the firm to achieve its goals. By understanding the motives of workers and how they
respond to incentives, an organization must be designed such that the behavior of the
workers is aligned with those of the firm.
In the final section of the textbook, we examine quantitative methods and their
ability to improve the firm’s decisions. Regression analysis is a tool that serves as the
foundation of empirical research by academic economists. Although some econometric
tools are far too sophisticated for business managers (i.e. forecasting macroeconomic
activity), a basic understanding of regression can be used to forecast sales, allocate
overhead expenditures, and identify specific strengths and weaknesses within an
organization.
The section also includes a chapter on forecasting. Forecasting sales is an
important element of any business, but too many still rely on qualitative “best-guessing”
or using accounting-based goals to estimate sales. Again, although forecasting
techniques can become quite sophisticated, this chapter focuses on quantitative
techniques that are relatively easy to learn and implement.
The quantitative section of the text also includes a chapter on quantitative tools to
promote operational efficiency. This includes discussions of inventory management and
a basic examination of queuing theory.
In summary, the goal of this text is to bring economic theory into the world of the
business manager rather than the other way around. Microeconomic theory contains
many useful insights that can help a business manager make more effective decisions.
Table 1
June Income Statement June Income Statement
(Before New Mall Opened) (After New Mall Opened)
Revenues: $252,456 Revenues: $55,540
Cost of Sales: $146,424 Cost of Sales: $32,213
Gross Margin: $106,032 Gross Margin: $23,327
Sales & Marketing Expenses: Sales and Marketing Expenses:Ads: $5,000 Ads: $5,000Mailing: $3,000 $8,000 Mailing: $3,000 $8,000
General and Administrative Expenses: General and Administrative Expenses:Payroll: $7,525 Payroll: $7,525Depreciation: $2,000 Depreciation: $2,000Rent: Rent: Fixed: $15,000 Fixed: $15,000 Percentage: $6,000 Percentage: $0Insurance $1,000 $31,525 Insurance $1,000 $25,525
Profit Before Interest and Taxes: $66,507 Profit Before Interest and Taxes: ($10,198)Interest $1,200 Interest $1,200Profit Before Tax $65,307 Profit Before Tax ($11,398)Tax $26,123 Tax $0Profit After Tax: $39,184 Profit After Tax: ($11,398)
Table 2
Decision: Close the Shoe Store
Decrease in Relevant Revenues: $55,540
Decrease in Relevant Costs:
Cost of Sales: $32,213
Ads: $5,000
Mailings: $3,000
Payroll: $7,525 $47,738
Net Change in Profit/Loss: ($7,802)
APPENDIX I
REVIEW OF SUPPLY AND DEMAND
When I ask students what economics is all about, most of the time, I get shriveled up
faces conveying the infamous “How should I know?” look. Those who are bold enough
to respond invariably say “Supply and Demand”. However, when I push them to
elaborate, they quickly join the ranks of the shriveled-face “How should I know?” group.
Oh, well, at least they remembered a buzz phrase after 17 weeks in the classroom.
Supply and demand could otherwise be phrased “A simple, brief, yet useful model
for describing how competitive markets operate”. Market demand refers to the
quantities of a good or service that buyers are willing to buy at various prices. Because
no one can spend the same money twice, the price of a good implies the value of other
goods foregone. For example, if you wanted to buy a shirt for $60, that $60 could not be
used to purchase other goods and services you may value. Consequently, in deciding
whether to buy the shirt, you must compare with the value you place on the other goods
and services that could be purchased for $60. Suppose 10,000 consumers decide the shirt
means more to them than the other goods and services they could buy for $60. What
would happen if the price of the shirt rose to $75? Although some consumers might still
prefer the shirt, others might decide the opportunity cost is too high and choose not to
buy it. As a result, the quantity of shirts demanded decreased when the price of the shirt
increased. Because the value one places on a good must be compared with alternative
goods and services that can be purchased at that price, it should make intuitive sense that
as the price of a good rises, fewer units of the good will be demanded. The notion that as
the price rises, the quantity demanded decreases is called the law of demand.
Market supply refers to the quantities of a good or service that producers are
willing to supply at various prices. We assume the goal of most firms is to maximize
profits. With this in mind, we assume that at any given price, firms will produce every
unit that can be sold at a profit. Suppose, for example, the going price is $10. We would
expect producers to supply every unit that can be manufactured at a unit cost of less than
$10. It would make no sense to expend $12 to produce a good if you knew you couldn’t
sell it for more than $10. If the price were to rise to $13, the firms would continue to
produce all of the units that cost less than $10 to produce, but would also produce those
units that cost more than $10, but less than $13. In other words, as the price rises, the
quantity supplied increases. This is known as the law of supply.
When we combine supply and demand, we see the market forces at work.
Suppose we have the data shown in Table A1:1. Note that if the price was equal to $15,
16,000 units would be available for sale (i.e. 16,000 units cost less than $15 to produce).
However, at that price, only 4,000 units are demanded. Because the quantity supplied
exceeds the quantity demanded, a surplus of the good exists at $15. Although 16,000
units were produced by firms in anticipation of profits, you can’t make money unless you
can sell the good. Consequently, in their zeal to attract buyers, the producers can be
expected to compete prices downward. Notice that as the price decreases, the quantity
demanded increases. The lower price is attracting more consumers into the market.
Similarly, as the price falls, the quantity supplied decreases. Units that would cost $14.50
to produce, for example, would be available for sale at a price of $15, but not at a price of
$14. In other words, as the sellers compete the prices downward, the size of the surplus
diminishes.
Table AI:1
Price Quantity QuantityDemanded Supplied
$15 4,000 16,000
$14 6,000 14,000
$13 8,000 12,000
$12 10,000 10,000
$11 12,000 8,000
$10 14,000 6,000
At the opposite extreme, suppose the current price is $10. At this price, 14,000
units are demanded, but only 6,000 are supplied. Because the quantity demanded
exceeds the quantity supplied, a shortage of the good exists. Producers are not willing to
increase production to 14,000 units because only those units that cost less than $10 to
produce will be available for sale. Therefore, because there aren’t enough units available
relative to the quantity demanded by consumers, we would expect consumers to bid the
price upward to assure the producers will sell to them and not somebody else.
Note what happens as the price is competed upward. Because sellers are only
willing to supply the units that could be sold at a profit, as the price rises, the quantity
supplied increases. Moreover, because consumers weigh the value of the good against
the alternative goods and services that could be purchased at that price, as the price
increases, the quantity demanded decreases. Hence, as the price is competed upward, the
size of the shortage decreases.
So far, we noted that when the price is “too high”, a surplus exists and
competition among sellers pushes the price downward. When the price is “too low”, a
shortage exists and competition among buyers forces the price upward. When will the
price stop rising or falling? If you examine Table AI:1, you can see that at $12, the
quantity of the good supplied is equal to the quantity demanded. At this price, sellers are
able to sell every unit they place on the shelf and all buyers who think $12 is an
acceptable price can buy all they want. Hence, we say the market clears at $12. This
price is called the equilibrium price or the market price because once the price reaches
$12, the market will no longer force the price upward or downward. The adjustment to
equilibrium in depicted in Figure AI:1.
[Figure A1:1 here]
Economic theory suggests that once the price reaches equilibrium, it will never
change. However, we see prices changing all the time. How does one reconcile ever-
changing prices with the market forces that drive the equilibrium price?
In fact, prices change when other factors shift the position of the supply or
demand curves. For example, suppose the cost of producing the good were to rise. This
would imply that fewer units could be sold at a profit at any given price. As shown in
Table AI:2, the decrease in supply would drive the equilibrium price upward to $13.
Table AI:2
Price Quantity QuantityDemanded Supplied
$15 4,000 12,000
$14 6,000 10,000
$13 8,000 8,000
$12 10,000 6,000
$11 12,000 4,000
$10 14,000 62,000
This is also shown from a graphical perspective in Figure AI:2. The rising cost of
production causes the supply curve to shift to the left (fewer units are available at each
price). A shortage now exists at $12 and the price rises until it reaches the new
equilibrium at $13.
[Figure AI:2 here]
Another factor that can shift the supply curve is technological improvement.
Improvements in technology allow the firm to produce more units of a good at any given
price. This will cause the supply curve to shift to the right. As shown in Figure AI:3, a
rightward shift in the supply curve will cause a surplus to exist at the current price.
Correspondingly, competition among sellers will drive the price downward until it
reaches the new equilibrium.
[Figure AI:3 here]
As any farmer can tell you, the weather can affect market supply. Frosts in
Florida decrease the supply of oranges and cause the price to rise, and droughts in Kansas
drive up the price of wheat.
Supply is also affected by the prices of other goods. We can also use the farmer
as an example. Farmers need to allocate their land according to the products they
produce. If the price of soybeans increases, more land will be dedicated to the production
of soybeans and less to the production of wheat. Consequently, when the price of
soybeans increases, the supply of wheat decreases.
In the long run, firms are expected to enter industries that are profitable and exit
those that cannot generate an acceptable profit. Consequently, the entry and exit of firms
causes market supply to change, which ultimately affects prices.
Finally, supply can be affected by price expectations. Suppose a firm in the oil
industry learned the government was going to impose a cap on oil prices at the beginning
of the new year. In all likelihood, the firm will supply more oil between now and the new
year in attempt to beat the price cap.
Changes in demand can also affect the market price. Going back to the demand
schedule in Table AI:1, assume the product becomes trendy and popular. As a result, we
would expect more consumers to want to buy the product. This implies that at any given
price, the quantity demanded will be greater than before. This is shown in Table AI:3.
Table AI:3
Price Quantity QuantityDemanded Supplied
$15 8,000 16,000
$14 10,000 14,000
$13 12,000 12,000
$12 14,000 10,000
$11 16,000 8,000
$10 18,000 6,000
Previously, the market cleared at $12. Now, the quantity demanded at every price
increased by 4,000 units. Consequently, a shortage exists at $12, causing the price to rise
until the market clears again at $13. This is shown graphically in Figure AI:4.
[Figure AI:4 here]
Beyond changes in consumer tastes, shifts in demand can also be caused by
changes in consumer incomes. Although we tend to think that consumers respond to an
increase in income by purchasing more goods, this is not necessarily true for all goods.
Rent-to-own furniture stores typically sell to a lower-income clientele. If one rents until
he/she owns the good, the cost is significantly greater than if the customer had purchased
the product outright. Therefore, most rent-to-own customers do so out of economic
necessity. If the incomes of the customers were to increase, they would likely substitute
purchases for rent-to-own. Consequently, the demand for rent-to-own furniture would
decrease in response to higher incomes. If the demand for a good increases when
consumer incomes rise (or if demand decreases when income falls), we say the product is
a normal good. If demand decreases in response to rising incomes (or increases when
incomes decrease), we say the product is an inferior good. The impact of a decrease in
demand on the equilibrium price is shown in Figure AI:5.
[Figure AI:5 here]
Changes in demand can also be prompted by a change in the price of related
goods. Suppose you are the manager of a supermarket. Currently, both Coke and Pepsi
are priced at $1 for a two-liter bottle. If you were to decrease the price of Pepsi to $.80,
your Pepsi customers would continue to buy Pepsi, and you might also attract some of the
Coke drinkers who do not have a strong preference for Coke. Therefore, although the
price of Coke did not change, the demand for Coke decreased because the price of a
substitute good decreased.
On the other hand, suppose the goods are complements rather than substitutes.
Imagine yourself as the manager of a sporting goods store. You decide to have a three-
day 50%-off sale on tennis racquets. What impact would this have on the sale of tennis
balls? Because of the complementary relationship between tennis racquets and tennis
balls, we would expect the demand for tennis balls to increase in response to the decrease
in the price of racquets.
Market demand can also be affected by the number of buyers. As a town grows
in size, demand for housing, utilities, water, etc., increase as well.
Finally, demand can be affected by changes in price expectations. When inflation
becomes problematic, consumers feel a need to stock up on goods to beat the rising
prices. (The fact that the increased demand caused by inflation fears fuels higher prices
is one of the reasons policymakers such as the Federal Reserve Board of Governors is
concerned about price instability).
From a managerial perspective, it’s extremely important to understand how the
interaction of supply and demand determines the market price. When examining the
product life cycle (PLC), for example, the growth stage is accompanied by rising
demand, which drives prices upward. Similarly, the decline stage implies a decrease in
demand, which pushes prices downward. Managers can also use their knowledge of
supply and demand to anticipate changes in supply. If a product is inordinately
profitable, competitors will inevitably flood the market, forcing prices downward.
Figure AI:1
Price Supply
$15
$12
$10
Demand
4,000 6,000 10,000 16,000 Quantity
14,000
Quantity QuantityDemanded Supplied
Quantity QuantitySupplied Demanded
Figure AI:2
Price S2
S1
$13
$12
Shortage
Demand
6,000 8,000 10,000 Quantity
Figure AI:3
Price S1
S2
Surplus
P1
P2
Demand
Q1 Q2 Quantity
Figure AI:4
Price S
$13
Shortage $12
D2
D1
10,000 12,000 Quantity
Figure AI:5
Price S
Surplus
P1
P2
D1
D2
Q2 Q1 Quantity
APPENDIX
REVIEW OF CALCULUS
Pursue a graduate degree in economics and you’ll enter a mindnumbing world of
mathematics: a world of scalars, Hessians, Jacobians, determinants, and n x m matrices.
The theories you were taught in your micro- and macroeconomics courses are, in fact,
derived from mathematical models intended to capture the environment and motives of
the firm.
Those of you who haven’t had a calculus course since the signing of the Magna
Carta need not fear. Most business functions do not require the use of calculus. In fact,
one of the distinguishing features of this text is to position microeconomic theory closer
to accounting, finance, marketing, management, and operations, where calculus is
seldom, if ever, used. Nonetheless, many academic economists believe theory needs to
be taught with calculus. To accommodate this approach, several of the chapters include
technical appendices that incorporate calculus. The purpose of this appendix is to give
you a quick refresher course in calculus and how it can be applied to economics.
We will begin with a discussion of dependent and independent variables. As its
name implies, a dependent variable is one whose value depends on another variable.
The independent variable is the variable whose value is “given”. Advertisers, for
example, use day-after-recall (DAR) to test for the effectiveness of an advertisement. We
can generally assume the more people who are exposed to an ad, the greater the number
who will recall it. If the DAR is 20%, then if one million persons are exposed to the ad,
200,000 will recall its content. If two million persons see the ad, 400,000 are likely to
remember it. Hence, the number of persons who recall an ad is the dependent variable
and the number exposed to the ad is the independent variable. In mathematical terms, we
say:
# of persons who recall the ad = f(# of persons exposed to the ad)
The mathematical convention is to label the dependent variable as y and the
independent variable as x. Hence, y = f(x). Suppose we have the following table:
Table AII:1
X Y
0 100
1 200
3 300
4 400
5 500
The table indicates a positive correlation between X and Y: as the value of X increases,
so does the value of Y.
At this point, you may recall learning about the coordinate system in which the
dependent variable, y, appears on the vertical axis and the independent variable, x,
appears on the horizontal axis. If we were to plot the values in Table A1 on a coordinate
system, we would see a series of points. If the points were connected, we would see an
upward-sloping line as shown in Figure AII:1.
[Figure AII:1 here]
You may also recall that all lines have equations. The generic equation of a line
is y = a + bx, where a is the y-intercept and b is the slope. Intuitively, the y-intercept
refers to the value of the dependent variable (y) when the independent variable (x) is
equal to zero. Graphically, it can be seen as the value of y when the line crosses the
vertical intercept. The slope of the line refers to the change in the value of the dependent
variable caused by a given change in the value of the independent variable, or ∆y/∆x. We
can visualize the slope by examining the graph in Figure AII:1. To get from point A to
point B, y increases by 200 units (from 300 to 500) and x increases by one unit (from 2 to
4). Hence, the slope is ∆y/∆x = 200/2 = 100. To get from point A to point C, y
increases by 100 units (from 300 to 400) whereas x increases by one unit (from 2 to 3),
for a slope of ∆y/∆x = 100/1 = 100. Note that the slope from A to B is the same as the
slope from A to C. This is a unique characteristic of a straight line: the slope between
any two points is identical. Hence, the slope from A to B is the same as the slope from A
to C, which is the same as the slope from A to D or A to E.
Now consider the slope from point A to point A'. The distance between point A
and A' is so infinitesimally small that it cannot be seen in Figure AII:1 without a high-
powered microscope. Even though we can’t see the distance between the two points, we
know the slope must be equal to 100. Thus, we can determine the slope between two
points even as the distance between them approaches zero. In calculus, this leads to the
concept of the derivative. As the changes in x approach zero, the marginal relationship
between X and Y is expressed as the derivative dy/dx. The derivative is analogous to
∆y/∆x. In proper mathematical notation,
In short, we can think of the derivative as the slope of a point. The distinguishing
characteristic of a line is that every point on a line has the same slope.
The notion that points have slopes is convenient as we move from straight lines to
curves. Suppose we have a curve such as the one shown in Figure AII:2. With a
nonlinear function, each point has its own slope. To determine the slope of a point
graphically, draw a line tangent to the point, as shown in the figure. The slope of the
tangent line is the slope of the point. In Figure A2, note that points A and B both have
positive slopes, implying that as X increases, Y increases. However, notice that the slope
at B is smaller than the slope at A. This suggests that successive increases in X lead to
smaller and smaller increases in Y.
[Figure AII:2 here]
Examine the slope at point C. As the graph indicates, C sits on the highest point
on the curve. The slope of the tangent line is horizontal, which means the slope is equal
to zero. Keep this in mind, as it will become very important later on: the highest point
in a curve has a slope equal to zero.
Beyond drawing tangent lines to a point and measuring the slope graphically, we
can determine the slope of a point by taking the derivative. Given a function:
y = kxa,
the slope of any point in the function is calculated as:
For example, suppose we have the equation y = 3x2, which is shown graphically in Figure
AII:3. We can determine the slope at any given point by taking the derivative. In this
case, the derivative is:
As shown in Figure AII:3, when x = 1, the point on the function has a slope equal to 6(1),
or 6. When x = 2, the corresponding point on the function has a slope of 6(2), or 12.
[Figure AII:3 here]
Unconstrained Optimization
Now that we’ve reviewed some basic concepts of calculus, let’s apply them to the theory
of the firm. Suppose a firm competes in an industry for which the market price is $10.
Assume the firm’s total costs are described by the equation:
TC = 20 +5Q + 0.1Q2
We can describe the firm’s profits as:
Π = Total Revenue – Total Cost, or:
Π = [P x Q] – TC, or:
Π = [10Q] – [20 + 5Q + 0.1Q2], which simplifies to:
Π = 5Q – 0.1Q2 - 20
Note that the profit equation establishes the firm’s profits as the dependent variable and
output as the independent variable (i.e. π = f(Q)). A graph of the profit function appears
in Figure A4. You can see the nonlinear form of the profit function. At zero units of
Examples of Basic Derivatives
Function Derivative
1. y = 3x2 dy/dx = 2•3x2-1 = 6x
2. y = 10x dy/dx = 1•10x1-1 = 10x0 = 10
3. y = 5 dy/dx = 0•5x0-1 = 0
4. y = 4x3 dy/dx = 3•4x3-1 = 12x2
5. y = 2/x, or y = 2x-1 dy/dx = -1•2x-1-1 = -2x-2 = -2/x2
6. y = 4x2 + 5x + 8 dy/dx = 2•4x2-1 + 1•5x1-1+0•80-1 = 8x + 5
output, the firm incurs a $20 loss. Then, as the output level increases, the losses become
smaller and the firm becomes profitable. As output continues to increase, the firm’s
profit rise, reach a maximum, and then begin to fall.
The objective of the firm is to find the profit-maximizing output. We can
accomplish this by using the tools of differential calculus. As we noted earlier, the slope
of the highest point on the profit function is equal to zero. Hence, by taking the
derivative of the profit equation and setting it equal to zero, we can solve for the profit-
maximizing output.
dπ/dQ = 5 – 0.2Q = 0,
5 = 0.2Q, or
Q* = 25 units
Having determined the profit-maximizing output, we can plug Q back into the profit
equation to calculate the profits that will be earned:
Π = 5(25) – 0.1(25)2 – 20, or:
Π = $42.50
Identifying Maximums and Minimums
But wait! Can we really guarantee the firm will maximize profits by producing 25 units?
Take a gander at Figure A5. Just as the slope of a line tangent to the highest point on a
curve is equal to zero, the same can be said for a line tangent to the lowest point on a
curve. Theoretically, then, the gem of a recommendation you passed on to your
supervisor (to produce 25 units of output) may not lead to maximum profits, but could, in
fact, minimize profits. (This is not a route that will lead to promotion).
So how can we tell if a zero slope corresponds to a maximum point or a minimum
point? Very simply, we can identify maximums or minimums by taking the second
derivative, which is simply the “derivative of the derivative”. Suppose, for example,
that 25 units of output take you to the highest point on a curve, as shown in Figure AII:4.
[Figure AII:4 here]
Because you’re standing at the “top of the hill”, you are looking downward toward
negative slopes. Hence, if the second derivative is negative, you are “at the top of the hill
looking downward”. If the second derivative is positive, on the other hand, you are at the
lowest point on the curve. Consider the illustration in Figure AII:5. Should 25 units of
output place you at the bottom of the curve, you are at the “bottom of the hill” looking
upward.
[Figure AII:5 here]
Let’s return to our example to verify that 25 units of output maximize profits.
The first derivative is:
dπ/dQ = 5 – 0.2Q
By taking the second derivative (i.e. the derivative of the first derivative), we get:
d2π/dQ2 = -0.2
Because the second derivative is negative, we know that 25 units is the maximum point in
the profit curve (i.e. we are at the top of the hill, looking down).
Partial Derivatives
Another important concept in calculus is the partial derivative. The standard demand
curve asserts that the quantity demanded is a function of the price, or Q = f(P). In fact,
however, the demand curve does not assume other factors don’t influence the quantities
consumers wish to buy. Rather, the demand curve assumes the other factors are held
constant. Should one of the other demand determinants change, the demand curve will
shift. The partial derivative refers to marginal changes in the dependent variable that
come about due to a change in an independent variable, assuming the values of all other
independent variables are held constant. As an example, suppose we have the following
demand equation:
Q = 500 – 20 x P + 12 x PS,
where Q is the quantity demanded, P is the price of the good, and PS is the price of a
substitute. If we take the derivative with respect to P (i.e. the partial derivative), we get:
∂Q/∂P = -20
The term ∂Q/∂P is analogous to dQ/dP, except that it acknowledges the existence of other
independent variables in the equation. In this instance, the partial derivative states that a
one-unit increase in the price will cause a 20-unit decrease in the quantity demanded,
assuming the price of the substitute is held constant. Likewise, if we take the partial
derivative with respect to PS, we get:
∂Q/∂PS = 12.
This states that a one-unit increase in the price of a substitute will result in a 12-unit
increase in the quantity demanded, assuming the price of the good is held constant.
Constrained Optimization
In the previous example, we determined the firm would maximize profits by producing
25 units of output. But suppose the manufacturing facility had a capacity of 20 units.
This is an example of constrained optimization. We must determine the output level that
maximizes profits given that production is constrained to 25 units.
We can solve a constrained optimization problem either through the substitution
method or the LaGrangian method. Suppose we have a firm that produces two goods (X
and Y) out of the same manufacturing plant. Total production is constrained to 100 units.
The goal of the production supervisor is to determine the combination of X and Y that
will minimize total costs subject to the constraint that the facility produce at capacity.
Production costs are captured by the equation:
TC = 3X2 + 4Y2 – 3XY
The firm’s objective is to minimize the above cost function while producing 100 units of
output, we know that the total production of X and Y must sum to 100, or X + Y = 100.
The substitution method incorporates the constraint into the cost function. If we
were to re-write the production constraint as X = 100 – Y, and substitute it into the cost
function, we would obtain:
TC = 3[100-Y]2 + 4Y2 – 3[100-Y]Y
Expanding the cost equation yields:
TC = 30,000 – 600Y + 3Y2 + 4Y2 – 300Y + 3Y2, or, collecting the terms:
TC = 10Y2 – 900Y + 30,000
If we take the first derivative and set it equal to zero (also called the first-order
condition), we get:
dTC/dY = 20Y – 900 = 0, or:
Y = 45 units. Total production of X, therefore, is simply 100 – 45, or 55 units. Total
production costs will, therefore, be equal to:
TC = 3(55)2 + 4(45)2 – 3(55)(45) = $9,750.
To assure the solution minimizes total costs, we take the second derivative, or:
d2TC/dY2 = 20.
Because the second derivative is greater than zero, the solution occurs at the minimum
point.
Another means to determine the cost-minimizing production of X and Y is
through the LaGrangian method. This is an attractive alternative to the substitution
method when there are a relatively large number of constraints. Here, we construct a
LaGrangian equation composed of two parts: the objective function and the constraint.
The objective function in our example is the firm’s total cost equation. The constraint is
the production constraint. However, we will incorporate the production constraint by re-
writing it as 100 – X – Y = 0 (for reasons to be divulged momentarily). Because the
objective of the firm is to minimize total costs subject to the production constraint, we
can create the LaGrangian equation:
min ℓ = 3X2 + 4Y2 – 3XY + λ(100 – X – Y)
objective function constraint
Notice how the production constraint is built into the equation. In the absence of the
constraint, the firm would determine the unconstrained optimum via the objective
function. However, by re-writing the constraint such that it is equal to zero, the
LaGrangian reduces to the objective function. The (λ) term is called the LaGrangian
multiplier. Its purpose is to identify the marginal effect of increasing the constraint by
one unit. In this case, the LaGrangian multiplier will tell us the impact of increasing the
production constraint by one unit on the firm’s total cost.
The LaGrangian is solved by taking the partial derivative with respect to each of
the three variables:
∂ℓ/∂X = 6X – 3Y – λ = 0;
∂ℓ/∂Y = 8Y – 3X – λ = 0;
∂ℓ/∂λ = 100 – X – Y = 0.
Based on the first two equations,
6X – 3Y = 8Y – 3X.
Simplifying this equation yields:
9X = 11Y.
By re-writing this equation as:
X = (11/9)Y and plugging it into the last of the three derivatives, we get:
Y = 45 units and X = 55 units.
To get a feel for the impact of the production constraint, consider the solution to
the unconstrained equation. We really don’t need calculus to do this, but let’s work
through the mechanics anyway. If the firm was free to determine the cost-minimizing
production of X and Y without a production constraint, it would seek to minimize:
min TC = 3X2 + 4Y2 – 3XY.
If we take the first-order conditions of the cost equation, we get:
∂TC/∂X = 6X – 3Y = 0; and
∂TC/∂Y = 8Y – 3X = 0.
If we solve these two equations simultaneously, we get:
6X – 3Y = 8Y - 3X, which yields:
X = (11/9)Y.
Clearly, when X = 0, Y = 0, and TC = $0. For any positive value of X, both Y and TC
take on positive values. This implies that in the absence of a production constraint, total
costs are minimized when nothing is produced (I told you we didn’t need calculus).
Nonetheless, the unconstrained solution presents some insights as to the meaning of the
LaGrangian multiplier. Absent the production constraint, the optimal cost is $0; with the
constraint, the optimal cost is $9,750. Hence, the production constraint adds $9,750 to
the firm’s expenses.
Figure AII:1
Y
∆x = 2 500 B
400 ∆y =200 C
D300 E
A
200
100
0 1 2 3 4 5 X
Figure AII:2
Y
B C dy/dx=0
• ∆y ∆x
A • ∆y ∆x
X
Figure AII:3
Y
y = 3x2
dy/dx = 12
dy/dx = 6
1 2 X
Figure AII:4
Profits
dπ/dQ = 0
Π = 5Q – 0.1Q2 - 20
25 Q -$20
Figure AII:5
Profit
dπ/dQ = 0
25 Q
