I
Warren E. Buffett, celebrated chairman of Omaha, Nebraska-based Berkshire Hathaway, Inc., started
an investment partnership with $100 in 1956 and went on to accumulate a personal net worth in
excess of $50 billion.
Buffett is famous for his razor-sharp focus on the competitive advantages of Berkshire's wide
assortment of operating companies, including Benjamin Moore (paints), Borsheim's (jewelry),
Clayton Homes, Dairy Queen. Fruit of the Loom, GElCO (insurance), General Re Corporation
(reinsurance), MidAmerican Energy, the Nebraska Furniture Mart. See's Candies, and Shaw's
Industries (carpet and floor coverings). Berkshire subsidiaries commonly earn more than 30 percent
per year on invested capital, compared,with the l o percent to 12 percent rate of return earned by
other well-managed companies. Additional contributors to Berkshire's outstanding performance are
substantial common stock holdings in American Express, Coca-Cola, Procter & Gamble. and Wells
Fargo, among others. As both a skilled manager and an insightful investor, Buffett likes wonderful
businesses with high rates of return on investment, lofty profit margins, and consistent earnings
growth. Complicated businesses that face fierce competition and require large capital investment are
Buffett's success is powerful testimony to the practical usefulness of managerial economics.
Managerial economics answers fundamental questions. When Is the market for a product so
attractive that entry or expansion becomes appealing? When is exit pteferable t o continued
operation? Why do some professions pay well, while others offer only meager pay? Successful
HOW I S MANAGERIAL ECONOMICS USEFUL?
Economic theory and methodology lay d o w n d e s for improving business and public policy
decisions.
Evaluating Choice Alternatives
Managerial
Economics
Applips econamr
Managerial economics helps managers recognize h o w economic forces affect o r g w t i o n s
and describes the economic consequences of managerla1 behavior. It also Links econonuc
tools and techniques
to business and
admlusrratiue derislun
malung
1 lnformatian about Warren Buftett's investment philosophy and Brrbhire Hathab,ay, Inc,can be found
on the Internet,htp:/,'w.berkshirehathawapcam.
Part 1:O~eNlewofMdnagerlalEcanomic~
4
concepts and quantitative methods to develop vital tools for managerial decision making.
This process is illustrated in Figure 1.1.
Managerial economics identifies ways to achieve goals efficiently. For example,
suppose a small businas seeks rapid growth to reach a sue that permits efficient use
of national media advertising, managerial economics can be used to identify pricing
and production strategies to help meet this short-run objective quickly and effectively.
Similarlb managerial economics provides production and marketing rules that permit the
company to maximize net profits once it has achieved growth or market share objectives.
Mmagerial economics has applications in both profit and not-for-profit sectors. For
exampie, an administrator of a nonprofit hospital strives to provide the best medical care
possible given limited medical staff, equipment. and related resources. Using the tools
and concepts of managerial economics, the administrator can determine the optimal
allocation o i these l~mitedresources. In short, managerial economics helps managers
arrive at a set 01 operating rules that aid in the efficient use of scarce human and capital
resources. By following these rules, businesses, nonprofit organizations, and government
agencies are able to meet objectives efficiently
Making the Best Decision
TO establish appropriate decision rules, managers must understand the economic
enviromlent in which they operate. For example, a grocer?; retailer rnay offer consumers
a highly price-sensit~vcproduct, such as milk, a t an extremely low markup over
cost-say, 1 percent to 7 percent-while offerrng less price-sensitive products, such
as nonprescription drugs. at markups of as hlgh as 30 percent over cost. .Managerial
economics desrrrl~esthe logic of t h s pricing practice with respect to the goal of profit
maximization. Similarly, managerial economics reveals that auto import quotas reduce
the availability of substitutes for domestically produced cars, raise auto prices, and
create the possibility of monopn!? profits for domestic manufacturers. It d ~ not
~ explain
s
n
broader
whether imposing quotas is jiood publ~cpolicy; that is a d e c ~ s ~ o1nvi)lving
polttical considerations. Managerial econ,~mcsonly describes the predrctsble economic
mnsecpenccs of such actlons.
of economic throry and
Managerial economics offers a comprehensive nppl~cat~<,n
methodology to management decision making. It is as rele~,antto the management ot
government agencies, cooperatives, schools, hospitals, nulseums, and similar not-forprofit institutions as ~t is to the management of profrt-oriented businesses. Although this
text focuses primaril~on business applications, it also includes examples and problems
from the government and nonprofit sectors to illustrate the broad relevance of managerial
economics.
Managerial economics uses economic concepts and quantitative methods to solve managerla1 problems.
-
Product selection. output, and pricing
Internet strategy
Organization design
Pmduct development and promotion
Stick by your princ~plesPrinciples arenot for saleat any
.
Marginalanalysis
Theory of consumer demand
Theory of the f i n
Industrial organizaUon and firm
Numerical analpis
StaHsbal estimation
Forecastingpracedures
Game-theory mnaepts
However, unethical conduct is inconsistentwith value
maximiration andcantraryto theenlightened self.lnterest
of management and
If
pervade
America,the abil,ty tocanduct
wouldcollapse. Eventually, the truth always comer out, and
whenitdoerthe unrcrupulour loseaut,Forbetterorworse,
weare known by the standards we adopt.
To becomesuccessful in burlners,everyane
adopt
a set of principles.Ethicalrules to keep in mind when
conducting burlnerr include:
Use of m n o m i c concepts and
quantitative memodsto 6 0 h
management decision pmblems
.
Above all else. keep your word. Say what you mean,and
mean what you say.
Dothe right thingA handshake with an honorable
perron irwonh mare than a ton of legal documenrr from
a corrupt ~ndividual.
Accept responsibility or your mistaker,and fix them.Be
quick to share credit for success.
Leave somethingon [he fable prolt w!th
curtomer,
not offyour customer.
Doesthe"hgh road"leadro corporate succerr?Consider
the experience ofone of America's most famous winnersOmaha b~ll~onaire
Warren E. Buffen, chairmanof Berkshlre
Hathaway, in=.BUffett and
Munger, the number-'wo
man at Berkshire,arefamousfordoing mult~million-dollar
dealson the basis oia simple hand5hake.A~
Berkrhire.
management relies upon the character of the people that
they aredealingwith rather than expenrlve accounting
audits, detailedlegal opinions, or liability insurance coverage.
Buffen rays that after some early mistakes he learned to go
into business only with people whom he likes, trusts, and
admires. While a company won't necessarily prosper becaure
its managers display admirable qualities. BufFen rays he has
never made a goad deal with a bad person.
Doing the right thlng not only makes sense from an
ethical perrpecrive,it makes business Sense too!
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Pan
6
1
O v e n e w ofMinagerlal E ~ o n o m ~ o
THEORY OF THE FIRM
Firms are useful for producing and distributing goods and services.
Expected Value Maximization
I
Theory ofthe
Firm
Basic model of
bussness
Expected Value
Maximization
U p m i r a n o n oi
pmfirsin
uncenamtv
md
"me "=Iue or
mane)
At its simplest level, a business enterprise represents a series of contractual relationships
that specify the rights and responsibilities of varlous parties (Figure 1.21. People directly
involved mclude customers, stockholders, management, empioyees, and suppliers. Society
is also involved because businesses use scarce resources, pay taxes. provide empiovment
opportunities, and produce much of society's material and services output. The model
of busmess is called the theory of the firm. L7 its s i m p l ~version,
~t
the firm is thought to
have profit maximization as its primary goal. The firm's owner-manager is assumed to be
working to maximize the iirm's short-run profits. Toda)! the emphasis on profits has been
broadened to encompass uncertainty and the time vaIue of money In this more complete
model, the primary goal of the firm is long-term expected value maximization.
The value of the firm is the present value of the firm's expected future net cash flours. If
cash flows are equated to profits for simplicity. the value ot the firm today, or its present value,
is the value of expected profits, discounted back to the present at an appropnate interest rate.?
This model can be expressed as follows:
Value af the Firm
\'dluc
Prusenl value of
the f i n d s e r p p ~ k d
iuhm net cash
L?!
ihr. Firrn = Picsirrl
I'o!iii2
qf Erpciied Futtrrr Profits
-
+ 2 L + . . . +
( 1 + 1)'
(I > I 2
nows
Present Value
Worth in current
dni~a~
Here, n,, n2,..., nn represent expected profits in each year, 1, and i is the appropriate
interest, or discount, rate. The final form for Equation (1.1) is stmply a shorthand
expression in which sigma (Z) stands for "sum up" or "add together." The term
means, "Add together as t goes from 1 to n the values of the term on the right." For
Equation ( l l ) ,the process is as follows: Let t = 1 and find the value of the term n , / ( l + i)',
the prrsent value of year 1profit; then let t = 2 and calculate n,/(l + i)?, the present value of
year 2 profit; continue until t = n, the last year included in the analysis; then add up these
present-value equivalents of yearly profits to find the current or present value of the firm.
Because profits ( n ) are equal to total revenues (TR) minus total costs (TC), Equation
(1.1) can be rewritten as
2
Discounting is required beause prohe obtained in the hbxe are less valuabie than profits earned
presently One dollar today ir worthmore than $ 1 to be m e i v e d a year from now because 51 today can
be invested and.with mterest, grow to a larger mount by the end ofthe year. OnedoUar invested at
10 percent interest would grow to 51.10 Ln 1 year. Thus. $1 is defined as the preen1 valve of $1.10 due in
1 year when the appmpriate interest rate is 10 percent.
This expanded equation can be used to examine how the expected value maximization
model relates to a firm's >arious functional departments. The marketing department often
has primary responsibility for promotion and sales (TR); the production department has
primary responsibility for development costs (TC);and the h a n c e department has primaq
responsibility for acquiring capital and, hence, for the discount factor ( i ) in the denominator.
Important overlaps exist among these functional areas. The marketing department can help
reduce costs tor a given level of output by influencing customer order size and timing.
The production department can stimulate sales by improving quality. Other departments.
for example, accounting, human resources, transportation, and engineering, provide
informahon and services vital to sales growth and cost control. The determination of TR
and TC is a diificult and complex task. All managerial decisions should be analyzed in
tern= of their effects on value, as expressed in Equations (1.1) and (1.2).
Constraints and the Theory of the Firm
Organizations frequently face limited availability of essential inputs, such as skilled labor,
raw materials, energy, specialized machinery, and warehouse space. Managers often face
limitations on the amount of inveshnent funds ax ailable for a particular project or activity.
Decisions can also be constrained by contractual requirements. For example, labor
contracts limit flexibility in worker scheduling and job assignments. Conhacts sometimes
require that a minimum level of output be produced to meet delivery requirements. In
most instances, output must also meet quality requirements. Some common examples
of output quality constraints are nutritional requirements for feed mixtures, audience
exposum requirements for marketmg promotions, reliahllity requirements for elechonic
products, and customer service requiremenb for minimum satisfaction levels.
Part 1Overveulaf Manaqeral Ecanomlir
8
respOn~ib~lity
is important and urill be discussed late: ~n the chapter. For now, it will
prove useful to examine the concept of profits, which is central to the theory of the krm.
Legal restrictions, which affect both production and marketing activities, can also
play an important role in lnanagerial decisions. Laws that define minimum wages, health
and safety standards, pollution emission standards, fuel efficiency requirements, and far
pricing and marketing practices all limt managerial flexibility.
The role that constraints play UI managerial decisions makes the topic of constrained
optimization a basic element of managerial economics. Later chapters consider important
economlr implications of self-imposed and social constraints. This analvsis is important
because value maximization and allocativ~~ffiriencyin society depend on the efficient
use of scarce economic resources.
Free enterprise dcpends upon profits and the profit motive. Both play a role in the
efficient allocation of economic resources worldn.tde.
Business Versus Economic Profit
Limitations of the Theory of the Firm
Optimize
SOI~LLL""
Satisfile
Seek ratisfactory
irptimn~resu~tr
In practice, d o managers try to optimize iseek the best result) or merely satisfice
(seek satlsfact~ryrather than optimal results!? Do managers seek the sharpest needle
in a haystack (optimize), or do they stop after finding one sharp enough for sewing
(satisfice)? How can one tell w-hether company support of the United Wa): for example,
leads to long-run value maximization? Are generous salaries and stock options necessary
to attract and retain managers who can keep the firm ahead of the competition? When
a risky- venb~reis turned down, is this inefficient risk avoidance? Or does it reflect an
appropriate decision from the standpoint of value maximization?
It is impossible to give definitive answers to questions like these, and this dilemma
has led to the development of alternative theories of firm behavior. Some of the more
prominent alternatives are models in which size or growth maximization is the assumed
primary objective of management, models that argue that managers are most concerned
with their own personal utility or welfare maximization, and models that treat the firm as
a collection of individuals with widely divergent goals rather than as a single, identifiable
unit. These alternative theories, or models, of managerial behavior have added to our
understanding of the firm. Still, none can supplant the basic value maximization concept
as a foundation for analyzing managerial decisions. Examining why prov~desadditional
insight into the value of studying managercal economics.
Research shows that vigorous competition !ypically forces managers to seek value
maximization in their operating decisions. Competition in the capital markets forces
managers to seek value maximization in then financing decisions as well. Stockholders
are, of course, interested m value maximization because it affects their rates of return
on common stock investments. Managers who pursue their own interests instead of
stockholders' interests run the risk of losing their job. Unfriendly takeovers are especially
hostile to inefficient management that is replaced. Moreover, recent studies show a strong
correlation between firm profits and managerial compensation. Management has strong
economic incentives to pursue value maximization through their decisions.
It is sometimes overtooked that managers must consider all relevant costs and benefits
before they can make reasoned decisions. It is unwise to seek the best technical solution
result, what often appears to be satisficing on the part of management can be interpreted
as value-maximizing behavior once the costs of information gathering and analysis are
considered. Similarly, short-run growth maximization strategies are often consistent
with long-run value maximization when the production, distribution, and promotional
advantages of large firm size are better understood.
Finally, the value maximization model also offers insight into a firm's voluntary
"socially responsible" behavior. The criticism that the traditional theory of the
firm emphasizes profits and value maximization while ignoring the issue of social
Profit is u s u a l l ~defined as the rcsidual of sales revenue minus the explicit costs of doing
business. It is the amount available to fund equlty capital after payment for all other
guslnerr~rofit resources used b!; the fun1 This definition of profit is accuunting profit, or business
~ e ~ d olsales
uli
reYrn"F
mmus
ofdorngbusu'elr
NarmalRate
Averagepmii,
,,,,,
The economist also def~nesprofit as the excess of rel,enues over costs. However,
that must be compensated. The economist includes a n o r ~ ~ i rate
a l of return on equity
capita! plus an opportunity cost for the effort of the owner-entrepreneur as costs of
doing business, just as the interest paid on debt and the wages are costs in calculating
business profit. The risk-adjusted normal rate of return on cap~talis the minimum
return necessary to attract and retain investment Similarly. the opportunity cost
attract and rela>"
Capitalism and democracy are mutually reinforcing. Same
philasophers havegoneso far ar to saythat capitaltsm and
democracy are intertwined. Wlthaut capitalism, democracy
may be imposrible.Withaut democracy, capitalism may fail.
Ata minimum,frereely competitive markets give cansumerr
broad cho~cer,and reinforce the individual freedoms
protected in a democratic sooety. In democracy, government
doe5 not grant individual freedam. Instead, the political
power ofgovernment emanaterfrom thepeople.Similariy,
the flaw ofeconomic reraurcer orig~nateswith rhe individual
customer in a capitalistic system It ir not centrally dirwfed
by government.
Capltalirm is sociallydestrabie because of rrrdecentral~red
and customer-oriented nature.The menu ofproducts to be
produced is derived hom market priceand output signals
originating In competitive markelr. not from theoutput
scheduler of a centralized planning agency. Resources and
product5 arealroailocated through marketforcesThey a r e
Competttion is a fundamentally artracttvefeature of
the capitalistic system because i t keeps costs and prices
low. By operating efficiently, firmr are able to produce
the maximum quantjty and quality of goods and services.
Mars production is, by definition, production for the
masses. Competition airo limits concentrarian of economic
and pailtical power Simiiarly, the democratic farm of
government is inconsirtentwith consolidated economic
influence and decision making.
Totalitarian forms afgavernment are in retreat. China has
experienced vloient upheaval as the country embarks on
much-needed economic and polltical reforms. In the former
Soviet Union, Eastern Europe, India. and Latin America,
years of economic failure forced government5 to dismantle
entrenched bureaucracy and install ecanamlc incentives.
Rising living standards and pol~ticalfreedom have made life
in the West the envy af the world. Against this backdrop, the
future is bright for capitalirmonddrmocracy!
not earmarked onthe baris of favoritism orsociai status
Through their purchase decisions, customers dictate the
quantity andquality of products brought tomarket.
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Pan 1 OvervewalManageral Ecanomrr
11
WHY DO PROFITS VARY AMONG FtRMS?
Many firms earn significant economic profits or experience meaningful losses.
Disequilibrium Profit Theories
FrictionalProfit
Theory
Abnormal prclhts
obsewed foiiow,nq
unanhcip31c-d
'hang""demand
or cost condinons
Monopoly Profit
Theory
Aba,.emmai
by barriers to
en"'h"hit
mnlpetition
One explanation of economic proftts or losses is frictional profit theory. It states that
markets are sometimes in disequilibrium because of unanticipated changes in demand or
cost conditions. Unanticipated shocks produce positive or negative economic profits for
some firms.
For example, automated teller machines (ATMs) make it possible for customers of
ftnancial institutions to easily obtain cash, enter deposits, and make loan payments.
Though ATMs render obsolete many of the functions that used to be carried out at
branch offices, they foster ongoing consolidation in the industry Similarly, new userfriendly software increases demand for htgh-powered personal computers (PCs] and
boosts retums for efficient PC manufacturers and software vendors. A rise in the use of
plastics and aluminum in automob~lesdrives down the profits of steel manufacturers.
Over tune, barring impassable barriers to entry and exit, resources flow into or out of
financial institutions, computer manufacturers, and steel manufacturers, thus driving
rates of return back to normal levels. During interim periods, profits might be above or
below normal because of kictional factors that prevent instantaneous adjustment to new
market conditions.
A further explanation of above-normal prohts is the monopoly profit theory, an
extension of frictional proftt theory. Some flrms earn above-normal profits because
they are sheltered from competition by htgh barriers to entry. Economies of scale, high
capital requirements, patents, or import protection enabie some firms to budd monopoly
positions that allow above-normal profits for extended periods. Monopoly profits can also
arise because of luck (being in the right industry at the right time) or from anticompetitive
behavior. Unlike other potential sources of above-normal prof~ts,monopoly profits are
often seen as unwarranted and subject to hem)- taxes or otherwise regulated.
general, compensatory profit theory describes above-normal rates of return that
iirnls for extraordinarv success in meeting customer needs and maintaining
efficient operation:: It iirrns that oper,ite at the industry's averaRe level oi efficiency
receive normal rates of return, it is reasonable to expect f~rmsoperahnc at above-a\-erage
levels of efficiency to earti aboxe-normal rates of return 1nefficierrt;irms earn belor%normal rates of return
Con~pensatoryprofit theor). a$o recob+rs econt~micprofit as a11important re~vardto the
entrepreneurid function of owners and managers. tvem product starts as an idea for sen-ing
better some establislied or percetved need of uxi>tu~gor potentla1 customers. ' h i s need
Role of Profit5 in the Economy
Each of the preceding therrrie- describes econonuc profits obtained for different rensons.
In some cases, several theor~esmay apply An efficient manutacturer like Bocing may
earn an above-normal rate of return in accordance with cornpensator). theorr; but, during
a strike by competitor i r b u s employees, these above-average profits 111ay be augmented
by fr~ctionalprofits. Microsoft's profit positivn can be partly explained by all four
theories: The company has earned high fricttonal profits ~vhileGoogle, IBhl, and Oracle,
among 3 host of others, xramble to offer new cixnputer software, games. '2nd services;
hlicrosoft has earned monopoly proflts because it has some copyright and patent
protection; it has certainly benefited !?om successhl innovation; and it is well managed
artd thus has earned compensatnry profits
Form 5-1 regiltration rtatementsare filedwlth the Securties
Compensatory Profit Theories
Innovation Profit
Theory
Abovenamai
pmahtha,fallow
rumerful invention
O'modemization
Innovation profit t h e o v describes above-normal profits that arise following successful
invention or modernization. For example, innovation profit theory suggests that
Microsoft C o r p o r a t l ~ nhas earned superior rates of return because it successfully
introduced and marketed the graphical user interface, a superior image-based rather than
command-based approach to computer software instructions. Microsoft has continued
to earn above-normal returns as other firms scramble to offer a wide variety of "user
friendly" software for personal and business applications. Only after competitors
have introduced and successfully saturated the market for user-friendty software will
Microsoft profits be driven down to normal levels. Similarly, Apple Corporation has
earned above-normal rates of return as an early innovator with its iPod line of portable
digital music and video players. With increased competition from Microsoft's line of
Z ~ n edevices, among others, it remains to be seen if Apple can maintain tts position in
the portable digital device market, or will instead see its market dominance and abovenormal returns decline. As in the case of frictional or disequilibrium profits, profits that
are due to innovation are susceptible to the onslaught of competition from new and
established competitors.
and Exchange Commission by companies that want to sell
sharer to the mverting publ~c.U~uallywritten by lawyers
and fified with legaiese, Googie cofounder Larry Page
shattered Wall Street tradition when he used the company's
5-1 ~tatementtolay out Google's phlorophy on thesocial
rerponsibility of buslners.
'Don't beevii,"Page wrote"We believe smnglytharin the
long twm,wewill be better served-as shareholdersand~nall
otherwayr-by a companythatdwr g w d thtngr hrtheworld
even ifwe forgo some rhort-term gainr.Thir is an rmportant
aspect ofour cultoreand is broadly shared within the company."
'We aspire to make Google an inrtitut~onthat maker the
world a better place. With our productr. Google connects
people and information all around the world for free. w e
areadding other powerful rervicer ruchar Gmdil that
provider an efficient 1-gigabyreGrnaii accaunt for free. By
for free, we hope to help brrdgethe digital
divide. AdWardr connects urerr and adveniserrefficientiy,
helping both. AdSenre helps fund a hugevar~etyofanline
web s~tesandenablesauthors who couldnot atherwire
publi5h"ln 2003, the company created Googe Grants to fund
prograrnr m which hundreds ofnanprafits address irsues.
inrlud~ngthe environment, poverty, and human r~ghts,and
recefve heeadvertir~ngto further their mission. In 2004. the
company committed part of the proceeds from its initial
public offering and I percent ofongoing profits to fund the
Googie Foundation, an organizat~onintended to ambitiously
apply ionovatlon and resourcestoward the solution ofworld
problems.
Google is cornrn~nedto optimize for rhe long term, and
will support high-risk. high-reward projects and manage
them as a portfoiio.The company will be run collaboratively
in an effort to attract creative, committed new employees. It
will be nteresting to trackthelr progress.
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Pan 1 O V D N ~ ~Managera1
UU~
Ermornio
Economic profits play an important role in any market-based economy Above-normal
profits serve as a valuable signal that firm or industry output should be increased.
Expansion by established firms or e n t v by new competitors occurs quickly during highprofit periods. lust as abuve-normal profits signal the need for expansion and entry,
below-normal profits signal the need for contraction and exit. Economic profits are
one of the most important factors affecting the allocation of scarce economic resources.
Above-normal profits also reward innovation and efficiency, just as below-normal profits
penalize stagnation and inefficiency Profits play a vital role in prov~dinfi~r~centives
for
innovation and productive efficiency and in allocatmg scarce resources.
ROLE OF BUSINESS IN SOCIETY
Business makes a b ~ gcontribution to economic betterment in the United States and
around the globe.
Social Responsibility of Business
What does all this mean with respect to the social responsibility of bus~ness?Ts the value
maximization theor)- of the firm adequate for examining issues of social responsibility
and for derelop~ngrules that reflect the role uf business in society?
As seen in Figure 1.3, firms are primarily economic entlties and can be expected
social responsih~iityfrom within the contest of the economic model of the
to
firm. X s 12: an important consideration when examining inducements used to channel
Why Firms Exist
Firms exist because they are useful. They survive by public consent to serx3csocial
needs. If social welfare could be precisely measured, business firms might be expected
to operate in a manner that maximizes some index of social well-being. Maximization of
social welfare requires answering the following important questions: What combination
of goods and services (including negative bv-products, such as pollution) should be
produced? How should goods and services be provided? How should goods and services
be distributrd? These are the most vital questions faced in a free-enterpr~sesystem, and
they are key social issues.
Although the process of market-determined product~onand allocation of goods
and services is highly efficient, problems sometimes arise in an unconstraind market
economy Society has developed methods for alleviating these problems through the
political system. To illustrate, the economics of producing and distribuhg electric power
are such that only one firm can efficiently serve a given c o m m e v . Furthermore, there
is no good substitute for electric lighting. As a result, electric companies are in a position
to exploit consumers; they could charge high prices and earn excessive profits. To avoid
potential exploitation. prices charged by electric companies and other utilities are held to
levels thought to be just sufficient to provide a fair rate of returm on inveshnent. In theoIy
the regulatory process is simple. In practice, it is costly, and difficult to implement. It can
be arbitrary and a poor, but sometimes necessary, substitute for competition.
Problems can also occur when, because of economies of scale or other barriers to
entry, a limited number of firms serve a given market. If firms compete fairly with each
other, no difficulty arises. However, if they conspire with one another in setting prices,
they may be able to restrict output, obtain excessive profits, and reduce social welfare.
Antitrust laws are designed to prevent such collusion. Like direct regulation, .antitrust
laws contain arbitrary elements and are costly to adrmnister, but they too are necessary if
social justice is to be served
The market economy sometimes faces difficulty when firms impose costs on others
by dumping wastes into the air or water. If a factory pollutes the air, causing nearby
residents to suffer lung ailments, a m e a h g f u l cost is imposed on those people and
society in general. Failure to shift these costs back onto the firm and, ulhmately, to the
consumers of its products, means that the firm and its customers benefit unfairly by not
having to pay the full costs of production. Pollution and other externalities may result in
an inefficient and inequitable allocahon of resources. In both gove-ent
and business,
managerial motives
Decision management and
Divisional pay forperfomence
Pan I Orervlew otManagenal Ecanomjo
~ h ~ ~ the~ text,
~ the
h emphasis
~ u t is on the pract~salappl~cahonof economic analysis to
managerial decision problems.
Devetopment of Topics
The prlnting press sends information from the printer ta the
general public. It is aone-way method of cammunication
In the new millennium, we have the Internet Not only
is transmitting inforrnatlon via the Internet cheaperand
farterthan I" the piintedform, but it ~ r a l s o a
two-way
method o f communication.The internet is a revolutionary
c~mrnunicationrt o d because it has the patentiaifor
feedback from one consumer to another, or from one
company to another
internet makes the production ofeconom~cnewsand
information democratic by reducing the informationgathering advantages of very large corporations and the
traditional print and broadcast media.
Wtth thelntemet, theab~iityta communicateeconomic
newrand~nfarmationaroundtheglobe irjurt a mouieciick
away.With the internet, com~anlesare abie to k e p in touch
with suppliers on acontlnuous basis. inremet technology makes
gun In timemproductimporrible,if notmandatory If also
For thefivst time, the Internet giver flrmr and the,:
customers m New York City, in Jackson Hole, Wyoming.
and In the wilds of Africa the same timely access to widely
publicized economic news and information. With the
internet, up-to-the-minute globat news and analysis are just
mouseclicks away.The internet aim gives global con5umers
and businessesthe opportunity to communicatewith one
anather and thereby ueoter fresh news and information,
puts companies in touch with theircustomerr 24 hours a day.
7 d a p a week 24i7 is more thana wayoidoing burlness;it has
Over the Internet, curtomerr can ommunicate about pricing
become the banie c~ofthecustomer-focusedorganizatian.
internet technology ir a blessing for efficient companies
with products customen crave. i t is acurrefor the inefficient
and siow to adapt.
*c:'Dictatanmd~h~nternel:rne w u ~ ~ s , r m i n v i n o r o ~ , ~ ~ ~ . o n o b e ~ ~ , ~ o a i .
h"P"mlinewsirOm.
the efforts of business in directions that society deslres. Similar considerations should
also be taken into account before applying political pressure or regulations to constrain
f u m operations. For example, from the consumer's standpoint it is desirable to pay low
rates for gas, electricity, and telecom services. If public pressures drive rates down too
low, however, utility profits could fall below the Level necessary to provide an adequate
return to investors. In that event, capital would flow out of regulated mdustries.
innovation would cease, and service would deteriorate. When such issues are considered,
the economic model of the firm provides useful insight. This model emphasizes the
close relation between the firm and society, and indicates the importance of business
parhcipation in the development and achevement of social objechves.
STRUCTURE OF THIS TEXT
This text should help you accomplish the following objectives:
Develop a clear understanding of the economic method in managerial decision
I
Acquire a framework for understanding the nature of the firm as an integrated whole
as opposed to a loosely connected set of functional departments.
Recogruze the relation between the firm and society and the role of business as a tool
for social betterment.
R e value maximizahon framework a useful for characterizhg actual managerial decisions
and for de~elopingrules that can be used to improve those decisions. The basic test of the
\,due r n d 1 t i o n model, or any model. i
s its ability to expldln real-world behawor This tevt
w l t & t s the complementan- lat ti on between theon- and practice. Theory is I L W ~to improve
m a n a g e d decision making and practical experience icads to the development of better theor).
Chapter 2, "Basic Economic Relations," begins by examining the !mportant role that
marginal analysis plays in the opturuization process. The balancing of marginal revenues
and r n a r p l cosh to determine the profit-maximizing output level is explored, as are other
fundamental economic relations t h ~help
t
organizations employ scarce resources efficiently
AU of these economic relations are constdered based on the simpliimg assumption that
cost and revenue relations are know-n n,ith certainty Later in the hnok, this assumption
is relaxed, and the more realistic circumstance of decision milking with uncertainty is
examined. This matertal shows how optimization concepts can be effectively employed in
situabons when managers have extensive information about the chance or probability of
certaln outcomes, but the end result of managerial dec~sionscannot be forecast precisely.
Tools used by managers in the analysls of economic data are the sobject of Chapter
3, "Statistical Analysis of Economic Relatiom." Given the challenges posed by a rapidly
changing global environment, a careful statist~calanalysis of demand, cost and market
structure relations is often conducted to provide the information necessary for effective
decision making The concepts of demand and supply are also basic to understanding
the effective use of economlc resources. The general ovenriew of "Demand and Supply"
m Chapter 4 provides a framework for the more detailed inquiry that follows. Chapter
5 , "Demand Analysis and Estimation." emphasiz~sthat the successful management of
any organmation requires a complete understanding of the demand for its products. The
demand function relates the sales of a ~ r o d u c tto such important factors as the price of
the product itself, prices of other goods, income. advertising, and even weather. The role
of demand elasticities, whch measure the strength of relations expressed in the demand
function, is also emphasized. Issues addressed in Chapter 6, "Forecasting," provide a
useful framework for the estimati~nof demand and cost relations.
this material. These chapters present economic analysis as a context for understanding
the logic of managerial decisions and as a means for developing improved practices.
Chapter 7, "Production Analysis and Compensation Policy," develops rules for
optimal employment and demonstrates how labor and other resources can he used
in a profit-maximizing manner. Chapter 5, "Cost Analysis and Estimation," focuses
on the identificat~onof cost/output relations so that appropriate decisions regarding
product pricing, plant size and location, and so on can be made. Chapter 9, "Linear
Programming," inboduccs a tool from the decision sciences that can be used to solve a
variety of optimization problems This techmque offers managers input for short-run
operatmg decisions and information helpful in the long-run planning process.
The remainder of the hook builds on the foundation provided m Chapters 1 through
9 to examine a variety of topics in the theory and practice of managerial economics.
Chapter 10, "Competitive Markets," offers perspective on the nature of competition in
v~gorouslycompetitive markets; Chapter 11, "l'erformance and Strategy in Competitive
~
1
Pan I Ovwv8ew of Managerla Economicr
I
Markets," shows how firms succeed m competihve markets by being
faster, or
better than the competition Chapter 12, "Monopoly a n d Monopsony," illustrates how
product differentiation, barriers to enhy, and the availability of idomation interact to
determine the vigor of compehtion in markets d o m n a t e d by a s ~ n g l eseller (monopoly)
or a single buyer (monopsony). Chapter 13, "Monopolishc Competition a n d ohgopoly,"
consider.; industries in which interactions among competitors are
h, chapter
14, "Game Theory and Competitive Strategy," competition among the few is described
w[th Jn eye toward understanding and improvmg business strateg?. Chapter 15, "pricing
Practices." shows h o w the forces of supply and demand interact in settings \,.here market
Power is prevalent. Importantly, t h ~ schapter analyzes pricing practices
observed in business a n d shows h o w they reflect the predictions of economic theon:
Chapter 16, " k s k .hdysis," illustrates how the predictions of economic
can be
applied m the real-world s e m g of uncertamty Chapter 17, "Capital Budgeting," e k a n ~ e s
key elemen% of an effechve long-term planning framework. Chapter 18, fr~rganization~~~i~
and Corporate Governance," offers insight concerning the value-maumlzing design
the
fum and documents the unportance of buslness ethics. Finally Chapter 19, "
~
~ in ~
the Market Economy," shldies the role of government and how the tools and t e c h q u e s of
managerial economics can be used to analyze and improve public sector decisions.
Managerial economics applies economic theory
and methods to business and administrative
Profit margin, or net
TIe hasic model of the business enterprise is
the theory of the firm. The pnrnary goal is seen as
long-term expected value maximization.
The value of the firm 1s the present value of the
firm's expected future net cash flows, where
present value 1s the value af expected cash flows
discounted back to the present at an appmpnate
interest rate.
' Valid questions are sometunes raised about whether
managers really optimize (seek the best solution) or
merely satisfice (seek satisfactory rather than optimal
Most OftenespecLau~
when informahon
costs are considered, managers can be seen as
Business profit, or accounting profit, is the resJdual
of sales revenue minus the explicit accounting
cash of domg business. Business pmht often
incarPorates a normal rate of return on cap~tal,or
the n l ~ ~ u n ureturn
m
necessary to attractand reta~n
investment for a particular use.
d,,,,ded by sales, and
the return on stockholden'equity, or accounhng
net income d h ~ d e dby the book value of total assets
m u s total l~abihtles,are practical indicators of
firm performance.
.
~
~
~
~
~
t
the short run is unc~tteited.
hut In the longer run,
unlt sales are expected to declme.
E. The Federal Rescrvc Syitem takes actlons that
lower ~ntrrrstrates dramahcally.
F. An esPrctrd incrraie ~n intlatlon causes generally
hlgher mterest mies, and, hence, the d~scountrate
increases.
Q1.4 In the wake of corporate scandals at Enron.
Tyco, and Worldcorn, some argue that mapagers of
Large, puhlLclyowned tirms sometimes makc dtnsmns
41.8 Why IS the ~mnceptat enl~ghtmedself-interest
~mpvrtautm econornica'
41.9 "In the long run, a profit-maximlzmg flrm wob!d
never knowingly market unsafe products However, In
the short run. unsafe products can do a lot of damage."
D~scus,this 3tatement.
41.10 Is ~t reasonable to expect funis to take actlons
that are In the ~ u b l i cinterest but are detr~mentalto
stockholders? Is regulation alw'ays necessary and
apprupri~teto induce f~rmsto act in the public mterest'
Frictional profit theory describes abnormai profrts
observed following unantlc~patedchanges ~n
product demand or cost condibons.
' Monopoly profit theory asserts that abo1.e-normal
.
.
profits are sometimes caused by barners to entrv
that limit competition,
~nnovationprofit theory describes above-normal
profits that arise as a result of successful invention
or moclernlzation.
Compensatory profit theory holds that above.
normal rates of return can sometimes be seen as a
reward to firms that are extraordinarily successful
In meehng customer needs, mantaming efficient
operations, and so forth.
Theuseof economic methodology toanalyze and impmve
the managerla1 decisxon-making pmcess
the
study of theory and practice The primary
of
managerial econormcs lies m its usefulness. ]t works\
Your beverage would be nonaicoholic to
ensure widespread appeal among both young
and old alike. It would be cold rather than hot
after-taste, consumers will be able to drink a s
m u c h of your product as they Ilke. By adding
sugar to make your belrerage sweet, it gains food
~
D ~ ~ c sDecember
l,
29,
3 See Charles T Munger "Hon- Do 'lou Get Wor!dly PV~sdom'"O u t s t o ~ l d r nIwt'ifor
1997 2 6 3 1
Part I .
four times as much. Typical profit rates, let alone
operating losses, are unheard of at Coca-Cola. I t
e n i o ~ slarge a n d g r o w i n g profits, a n d requires
practically n o tangible capital investment. Almost
i t s entire v a l u e i s d e r i v e d f r o m b r a n d e q u i t y
d e r i v e d f r o m generations o f a d v e r t i s i n s a n d
carefully nurtured positi1.e IoUapaLooza effects.
an overall basis, i t i s easy to see w h y Buffen and
Mungerregard Coca-Cola as a ,'perfect,, business,
al
A. O n e o f the most important skilis to learn
in managerial economics is the a b ~ l i t yto
Adams, Renee B. and Darnel Ferr~ira."A Theory of Friendly
Boards "Jnurwl ?.CF!nance62,no. 1(February. 2M17). 217-'50.
Bemheim B. Douglas and Antonio Range! "Toward ChoireTheoretic Fuundatons for Behavioral Welfare Ecunomics"
Ammicon Economic Rtuiea 9 7 no 2 ((Ma): 2007). 46G470.
Blach. Francis, Carance Genirot, and Debrai Ray "Reriproctty
In Groups a n d the Limits to Social Capital." Amrricln
Emnarnir Reuim 97, no 2 (May, 2007): 6Ch9.
Bloom. Niik. "Uncertainty a n d the Dynamtcs o f RbrD."
Amcncon Economic Reuiew 97, no 2 (Ma): 2W7): 25C-255.
Boone, Audra L., Laura Casares Field, Jonathan M. Karpoff,
and Charu C. Raheia. "The Determinants of Corporate
Board Sire and Composition: A n Empir~calAnalysis:'
lourno1 ofFinonciai Economics 85, no 1 (July2W7) 6 6 1 0 1 .
B o u r g u i g n o n , Francois a n d Mark S u n d b e r g . "Aid
E f f e c t i v e n e s ~ m i n gthe Blark Box." American Econcrnic
R W I97,~ no. 2 (May, 2W7): 316321.
Cremer, Iacques. Luis Garicano, and Andxa Rat. "L-anguage
and the l l m r y of the F m " Quoileily journal a/Econamics
122, no. 1 (February. 2007): 373-407.
Cukrowski, Jacek and Manfred M. Fischer. "Efficient
Organization of Information Processing " Monagerlnl and
Decision Economics 28, no. 1 Uanuari. 2007): 1% 26
Glimcher, Paul William, loseph Kable, and Kenway Louie.
"Neuraeconomlc Sludies of Impulsivity. Now Or just as
h s . Maarten and Alan M m i n g . "Lousy and Lovely Jobs:
The Rising Polarization of Work in Britain.'' Reuieul of
E m o m i n and StatisticsR9, no 1 (February. 2W7): l l g 1 3 3
OverviewalManagera Economjcr
identify a good business. Discuss at least f o u r
characteristics o f a good business.
B. Identi& 2nd talk about at least four
cornpallies
that you regard as havingthe
characteristicshste,j here,
~ ~ ~ ~ ~ ~ ~ ~ ~ , " ~ , " ~ ~ , " Manazers
~ ~ ~maked tough
n ,choices
~ ~that ~involve
~ $benefits
~ ~and ~costs.~ Until recently, however,
i t was
simply impractical to compare the relative pluses and minuses of a large number of managerial
decisions under a wide variety of operating conditions. For many large and small organizations,
economicoptimization remained an elusive goal It is easy to understand why early users of personal
computers were delighted when they learned how easy i t was to enter and manipulate operating
information in spreadsheets. Spreadsheets were a pivotal innovation because they put the tools for
insightful demand, cost, and profit analysis at the fingertips of dec~sionmakers. Today's iow-cost
but powerful PC5 and user-friendly soflware make it possible to efficiently analyze company-specific
data and broader information from the Internet. It has never been easier or more vital to consider the
implications of managerial decisions under an assortment of operating scenarios.
years
now' how would
you
k n o w i f your analysis was correct? What
w o u l d convince y o u that your analysis was
wrong?
mee
Harford, Jarrad and Kal LI ' D e c o u p l i n ~CEO Wealth and
Firm Performance. The Care a t Acquiring CEOs " fniiinei
Frnoncr 62. no. 2 ( ~ p r i l2007):
,
917-949
Hart, Oliver and john Moore. "Incomplete Contiarts and
Ownership: Some Zrw Thoughts." Arn~riconEcanomir
R n a m 97, no 2 (May, 2007): 182-186.
Heron, Randall A. and Erik Lie "Does Backdating Explain
the Stock Price Pattern Around Executive Stock Optlan
Granb?" lourno1 ojF~noncialE~onomics83, no. 2 (Februarj.
20371 271-295.
Hochberg, Yael V , Alexander Ljungqvist, and Yang Lu.
l
"Whom You Know Matters. Venture C a p ~ t a Networks
and Investment Performance." lournoi of Finan~.t62, no. I
(February, 2007): 251-301
Levy. Ciiat "Decision Makmg in Committees Transparency,
Reputation, and Voting Rules." American Ecanomtc Revim
97, no. 1 (March. 2007): 15&168
MacLeod, W. Bentley. ''Can Contract Theory Explain Social
Preferences?" American Economic R e v i m 97, no. 2 (May,
2037): 187-192.
Nonaka, Ikujiro. "The Knowledge-Creating C o m p a n y n
Homrd Rurlnrss Rrnieu~05. no. 7 . 8 (July 1,2007): 162-171
R a p . LUISand Gary 5. Becker. "Evolutionary Efficiency
a n d Happiness." Journal of Politico1 Economy 115.
no 2 (April, 2007): 302-337. Robson, Arthur J and
Preferences."Arneitcan Economtc R m i m 97, no 2 (May. 2W7):
496500.
Weinberger, David. "If You Love Your Information, Set ~t
Free."Honvlrd Busrnesr Review 85, no. 6 1Jttne 7, 20071- 2C-21.
EHective managers most collect, organize, and process relevant operating information. However,
efficient information processing requires more than electronic computing capability; it requires a
fundamental understanding of basic economic relations. Within such a framework, powerful PCs
and a wealth of operating and market information become an awesome aid to effectlve managerial
decision making.
This chapter introduces fundamental principles of economic analysis. These ideas form the basis
for describing all demand, cost, and profit relations. Once basic economic relations are understood,
optimization techniques can be applied to find the best course o f action.'
ECONOMIC OPTfMlZATlON PROCESS
Effective managerial deciwon m a k i n g is the process of a r r i v ~ n gat the best solution to a
problem.
'
Optimal Decisions
Should the quality of inputs be enhanced to better meet low-cost i m p o r t competition?
I s a necessary reduction in labor costs efficiently
achieved through a n across-the-board
decrease in staffing, o r is it better to make targeted cutbacks? F o l l o w i n g a n increase in
product demand, i s i t preferable t o Increase managerial staff, l i n e personnel, o r both?
lourno1 Unllne, Aprd 1Y2007, http '/online.wsl.rom
1 k j a c k Hough, "Eihcieny Experts,'. T v Wall Sfref
Part I OYSVI(.*
21
u i ~ a n a g r n a l~ ~ a n o r n i ~ ~
These are the types of questions facing managers on a regular basis ihat require a careful
consideration of basic economic relations. Answers to these questions depend on the
objectives and preferences of management. Just as there is no single "best" purchase
decision ior all cusloniers at all times, there i i no single "best" investment decision ior
all managers a t all times. When alterrative courses of action are available, the decision
OptimalDecirion that produces a result most consistent with managerial objectives is llic optimal
iho~i~altrrnal~vederision.
ti>., pmducer
A challenge that must be met Ln the 3ecision-making process is characterizing the
a result most
con>atvntw ~ t h
desirahtliiy of decision alternatives in terms of the obiectives of the organization. Decision
managenil
makers must recognize all available choices and portray them in terms of aqpropriate
i
REVENUE RELATIONS
Fffectlve production and prictng decisions depeuc. upon a ctrrtul understar!uing of
revenue relations.
Price and Total Revenue
Tables are the simplcst and most direct form for presentins ecor1o:nXc data. CVhpn these
data are displayed eleitn~nicallyIn thc tormat of an accounting income statement or
balance shect the tables n r r referred to as spreadsheets. bi'hen tfie underlying rrlal~on
hetween economic data 1s 5imple. tahles and spreadslwcts may Se hufficie~tiilr ,r~wlyt~caI
purposes. In such instatrces, a s~rnplegraph or \ixual representation of t b p data can
provide valuable ~nhight.Complex economic relations require more soplusticated
methods of expresslnn A2 equation is an cxpresslon <>ftlre iunctionnl relationship or
connection amrlng economlr variables.
The easiest way to exsrnine iras~cecc~nunlitconcepts 1s to cana~derthr' functional
reiat~onsiilcorpurated in the b.lslc valuation mildel. C c n s d e r the relation betireen
output, Q,and total revenue, TR Using functlondl rotatton, tot.11 revcnui,is
provides tools for analyzing a~:d evaluattng decision alternatives. Economic concepts and
methodr3logy are used to select the optimal course oi action in light of available options
and objectives.
Principles of economic analvsls form the basis for describing demand, cost,
and profit relations. Once basic econcmic relations are understood, the tools a n d
7'K =,f(Ql
because they offer a realistic means for dealing with the complexihes of goal-oriented
managerial achvitles.
Equatlon ( ? 2 ) is read, 'Total revenue 1s a iunitlon of output." The i-alue ot the
dependent var~able(total rexenue) 15 determined by the jndependent vanable {output)
-~
Maximizing the Value of the Firm
I n managerial economics, the primary objective of management is assumed to he
maximization of the value of the tirm This value maxinlizntion objective was introduced in
Chapter 1 and is again expressed in Equation (2.1):
value=;w
_2
,.,
Pndi~~
-
(1
+ i)'
Maximizing Equation (2.1) is a complex task that involves consideration of future
revenues, costs, and discounl rates. Total revenues are directly determined by the
quantity sold and the prices obtained. Factors that affect prices and the quantity sold
include the choice of products made available for sale, marketing strategies, pricins and
distribution policies, competition, and the general state of the economy. Cost analysis
includes a detailed examitlation of the prices and availability of various input factors,
alternative production schedules, production methods, and so on. Finally, the relation
between an appropriate discount rate and the company's mix of products and both
operating and financial leverage must be determined. All these factors aifect the value ~f
the h r m as described in Equation (2.1).
To determine the optimal course of action, marketing, production, and financial
decisions must be integrated within a decision analysis framework. Similarly, decisions
related to personnel retention and development, orgonization stnlcture, and long-term
business itrategy must be combined into a single integrated system that shows how
managerial initiatives affect all parts of the f i .The value maximization model provides
an attractiv~basis for such integration. Using the principles of economic analysis, it is
also possible to analyze and compare the higher costs or lower benefits o l alti.rnative
s u b o ~ t i m acourses
l
of action.
:
i
:
Capitalism Ir basedon vaiuntary exchange between relf~
interested parties. Market-basedexchange tr miuntary,
both parties must perceive benefits,or proiit,formarker
transanions to take place.lf only one parry were to benefit
fmm agiven transaction, there would be no incentivefor the
other partyto cwperate and novoluntary exchangewould
must also have in mind
take p1ace.A self-interestedcao~tal~st
the interefirof otherr.In contrart.a truly selfsh individual ls
only concerned with himselfor herself,without regard far the
well-be~ngof arhers.Selfinterestedbehavlor leads to profits
and ruiierr under capita1ism;relfishbehavior does not.
Management gu:u Peter Orucker has wrlnen that the
purposeofbusinessis tacreate a customer-someone that
will want ra do burcners with ,au and your company on a
regular bans.1" a business deal,both parties must benefit. f
notthere will be noongoing business relatisnship.
The only way this can be done is tomake sure that you
cuitomerr to complain or ieekalternatesuppiierr seek
out ways ofhelpng before they become obvious When
curtamerrbeneRt, so do*" and your company.Takem e
customer's perrpective,aiwaysSimilarly,it'sbest ro see every
business transactionfrom the standpoint of the person on
the other side of the table.
In dealing wnh employees.~t's
best to be honest and
forthr~ght,lf
you make a mistake,admit ~tand go on.When
management accepts respanrbiliry (or its faiurer, they gain
the trust of employees and thelr help ~nfindingsalutions far
the inevitable problem5 rhatalways arise.ln apbinrerview,
far exampie.strivetoseehow you can create value for a
potential employer it's natural to see rhingsfromones own
viewpoint;it is lypically much more beneficial toseetRlngr
from the perspective of the person slnlng on the other side
afthe table.
rootinuallVta~ethecusamertsperspectivecancustomerS ~ e : P e s r B e r l 0 ~ 1 ~ ~ ~ E l h ~ 1 i O I ; l h ~ W o ~ ~ i B e ~ l l ~ ~ r l l o l O l l l n e O c r o b e r 8 . 1 0 0 7
demand be met bener,heaper,orfaster? Don't wairfor
hnp:iianline.*l.com
marema1 revenue is pos~ti\-ewhen total revenue
IS
Increasing, but marg~nairevenue
relation also exists between marginal revenue and units sold. In such instances, hoth
prlce and margrnal revenue relations begin at the same point, but marginal revenue falls
twice as fast as prlce ~vithrespect to output. In the present example,
information about the effect ol a
.Precise
.
. . .
.
m output
l5
3
P=$215150
TR - $240 - $1 50'
= 524 - s.?~?
,iIr: = ITR
change in output on total revenue is given
arginal revenue is $7.50 over the range irom
to b units. Notice that margrnal revenue 1s positive so long as total revenue is increasing.
I
Revenue Maximization Example
;;T;,';;;;";;
1
.\I r< =
$24 - 43C) = 11
3Q=?4
Mn~o
8'0
From this marginal revenue rclat~on,A4R= fl when Q = 8 because I\IR :F24When Q = 8 , total re7,enue is maxirn~zedat 59h because
TR = 524Q - 5 l .5Q2
-;524(8) - $1.5(8')
= $96
I
1
1
-20.00
I
I
$96 and could be increased wlth a reduchon in volume. Only at Q=8 is total revenue
.
Output per tlme period (000 units)
$318) = O
.
advantages of short-term revenue maximization. To be consistent with long-run profit
maximizat~on,such advantages of short-run revenue maximization must be at least
sull~cie~>l
to iompmsa:e for the zorrespofiding loss In short-run profitabll~ty
30
Part 1 Orewew ot Managerla1E~~~~
,,
Haveyouever been ata sponing eventwhena pariicular
athlete's play became the center of anenrian,and wonde.ed:
"Where d d that woman itudy phyrirr?'or"Wow, who
taught that guy physiology?'~obody arks those questions
D i x u s r i o l usua ly centers an the playerr'rkill,finerse,or
tenacity Natural talent must bedeveloped through long
hours of dedicated training and intense competition before
one can become an accom~lishedathlete.@ut$you think
about it,successful athletes must also know a great deal
about angles,sped,ard acceleration.
may be ioreign to ruch.ndividuair,the m e t h o d o t ~ g ~
of opt~mizationis famiiiar ro each of lhem interms (,,
thelr everyday b~.sinesspractice Adjusting prtces ro
avoid rtockout ri:uations,increaring
quality to
"meet the competition,"and raising salariesta retafn
valued employees all znvoiue a practical underrranding of
optimization concepts.
Ihe behavior af both the successful athleteand the
successful executve can be described as consistent w ~ r h
a Process of 0ptimization.The fact that some practitoners
Whileruccerr in sports requires that one understand
the basic principles ofphysics and phyriology,most
learn manageriaieconomirithraugh hands-on experience
ratherthan In theclassroom doesn't d m ~ n s thevalueof
h
athletes develon ther.feel"for their sports on the tennis
court, golf course, baseball diamond,or gridiron.Sirn~larly,
s o w very successful businesses arc run by people
the'ormaleducationalerperience.ureiul theory describes
and predicts actual business decisronr.The old raw'Tharmay
be okay in t h e o w but ~tdoern't u o h i n practice'isplainiy
with lhttle or no formal training in accounting, f~nance,
managenent,or marke1ing.There execuriver'ruccerser
testify t o their ability t o develop a feel for businesr i n
much the same way *at the succer$ful athlete develops
a feel for his or her sport.Although the term oprimizahon
incarrect.Econorric theory
15 useful
for one simple reason-[t
WO*S.
Ie'FhndDunraL.'Fur*a
In-nrar
Rndsnonom
inesral>thc
o.
.mcwd!
out of rented office space might have a short-run period ~3.- brief as d lelq
on the office lease A firm ill the hazardilus waste disposal
weeks,
time
business has signlflcant long-laved assets and mav f a c r a 2!1- to 30-year ~ e r l o dof
operafin%iunjtrajrlts.Variable costs ftuct~iateir.ith output Expensei tor r,>rr.tnntennls,
depreciation associatrd w i t h the use of equipment. thr vanahif portion o f tltilit\.
charges, some labor costs, dnd sales comrntssions are all e ~ a n < p l ruf
s variable cxpcnses.
the short rurl, both variable and tised -osts are often I I I C ~ ~ ~ 111
L ' the
~ ~ . long run, all
costs are variable.
A sharp dlstInctionbeti\-.re" flxed and var~ablrc~htz15 neither ;~li\.~l?h
possihlr nor
realistic. F~~ pxamyle, CEO a n d staff salaries ma!- be lar#ely fi*rd. b u t dur'rlg %ewrc
h,lsiness doivnturn, cbrn C E C J tahe
~ a Fav cut. Slmilarlv. salaries for line mallager~and
within certain output ranges. Below a lower lin:ll. supervisors
supervlPorsare fixed
oft. Ahuve nn uppcr limit, add~tionalsuperr;isilrs and malraRerS
and managers get
hired. 'rhe ~ , , the
~ duration
g ~ ~ oi ~bnormaldemand. the greater the I l k r l i l l ~ oth'it
~
mmr fixed costc tvilt actuall~vary
jneqllation fl,rm, total cnst can he cxtxebseri as tile sum ~ l it l r r d and ~ ~ r l c l cb~Il~b t i .
TC- T C - l'i'
shown in ~
~ 2.2,b totall C l l~b t 1s tile sirnple sum ai the ~ - a r ~ a bcost
l e and fixed cost
categories with rrsppct to tllr c ~ fiqures
~ t shown In Table 2 2, the fixed and variable cost
categories can be expressed ill eq~ratiollform a5
s'r~"Ymaimii~e~Auv~~~~.~~7.hrm~~online.v~i.~om.
FC'=5'1
I'C - 5417 T FO.5Q2
COST RELATIONS
Meeting customer demand efficiently depends upon a careful understanding of cost
relations.
C o d Functions
Relation3 between
cost and o u ~ u i
Notice that fixed custs *re constant a t $8 and do not depend i~pntitllr level of oufput,
whereas variable costs rise with the amount of production. In this example, variable
costs rise faster than uutpul because thc vnridble cost function 15 qoadratic in nature; it
Table 2.2 Cort Output Relations
Totat Cost
S~O~.,,,~
Functions
cortniahonr
whenli*edmsb
~ o ~ ~ a
,p,,b,dec,rion.
Long-run Cort
~
Proper use of relevant cost concepts requires an understanding of various relations
hetween costs and output, or cost functions. Two basic cost functions are used in
managerial
~ a ~ e d decision making: short-run cost functions, used for day-to-day operating
decisions, and long-run cost functions, used for long-term planning. In economic
analysis. the short runis the operating period during w h c h the availability of at least one
input is fixed. In the long run, the firm has complete flexibility with respect to input use.
Total costs comprise fixed and variable expenses. Fixed costs do not vary with
output. These costs include interest expenses, rent on leased plant and equipment,
depreciation charges associated with the passage of t i e , property taxes, and salaries
for employees not laid off during periods of reduced activity Because all costs are
Shoe Run
~p~~~~~~~~ variable in the long run,long-run fixed costs always equal zero. In economic analysis,
dw,,*hich
the short run is the operating period during which the availability of at least one input is
avarlab*itrofar
fixed. In the long run, the firm has complete flexibility with respect to input use. In the
least one input is
short run. operating decisions are typically constrained by prior capital expenditures.
hxed
In the long run, no such restrictions exist. For example, a management consulting firm
F~~~~~~~
8.00
tort R L , ~ ~ o ~
whenaUcorrJare
valiable, used for
m
i E-tmp~,p
8.00
10.00
16.50
24.00
R.OO
32.50
40.50
ROO
42.00
52.50
b4.W
76.50
9o.on
50.00
60.50
72.00
84.50
9s.00
8.00
Y.UO
10
8
8.00
18.00
24.50
32.00
Pam 1-Overviewof Managera Ecanrm(
involves output squared, or Q2,
because total cost equals fixed cost plus variable cost, the
total cost function can be expressed in equation f o m as
~
Because total rost is the sum of fixed and variahle costs, and vdrlahle costs rise with
output, total costs rise with the amount produced.
-
Average Cost Minimization Example
Marginal and Average Cost
Marsinat cost
Change ~n total
m s iacsana~
~ ~ [ ~h- ua n i ~
change in output
"
MC=AC, and average iost falls hith an exp~nsio!~
in output. then L C is at a maximum If
MC=AC, Jnd average cost rises with an expansion In output, then AC E at a 11Ur~11um.
Marginal cost is the change in total cost a~ocintedw ~ t ha I-unit change in output.
h?C = dTC/dQ
2.7
where the uppercase Greek letter delta is again used to express the word "change." Thus,
the expressior~MC=ATC/dQ is read as follows: "Marginal cost is the chance in total cost
caused by a I-unit changein the number of unitsprodiced (Q)."
As shown in Table 2.2 and Figure 2.3, total cost rises from 524.59 to $32.00 when the
number of u n ~ t produced
s
rises from 3 to 3 units. This means that mareinal
cost is 57.50
.
0
when output rises over the range from 3 to 4 tlnits. Similarly, marginal cost is $8.50 over
the range from 4 to 5 units. Notlce that marginal cost is positive and increasing over
the range from I to 10 w i t s produced. Marginal cost is almost always positive because
almost ail goods and services entail at least some labor and/or materials. It is also
common for marginal costs to riseas output expands, but this is not universdlly hue.
Average cost is simply total cost divided by the number of units produced:
At every output level, tine relat~onsl~ip
between marginal cost and output indicates the
change in total rost that will occur with a I-unit change in the number ai units produced.
Similarly thc rclationsh~pbetiv;.rn marginal c<,it and average cost can be studied to
determine the change in average cosi that will occur with a I-unit change in the number
of units produced. For example, the totai cost and niarrinal cost relations described by
the data in Tablc 2.2
....
C U L L uL
....,.-..
1
~
Average Cost
Because average cost is total cost divided by the number of units produced, the average
cost relatlon is
Total mst dwhdpd
L
to clarify rrlatioians among rnarglnals, averages, and totals a n d the ~mpartanceof these relations i
n the
optimirahon process.
I
38
Part I Overview ar Maoagenal fianomlo
At the profit-maximizing activity IeveI, M R = M C and the added amount of revenue
brought in by the last unit produced (marginal revenue) is just suffiaent to offset added
cost (marginal cost), and profit wouId fall with an expansion in production. Because
almost alI goods and services entail the use of at least some labor and rarv materials,
MC>O in all hut the most unusual circumstances. 'This fact has important ~ n r n p l i c ~ t i o ~ ~
fur profit versus revenue maximization. With a downward-sloping demarid curve, both
price and marginal revenue decline following an increase in the number of units sold,
and settlng output >%.hereM R = M C will occur at a lower level of act~\:itvthan ivhPre
M R = @ The amountproduced and sold at the profit-max~mizingactivity level will he
the same as the amount produced and sold at the revenue-maximizing activitv lelrel oniy
in the unlikely event that MR=MC=O. The profit-maximizing adivity level will also
tend to drfter from the average cost-minimizing activity level where M C = A C . Recall
that finding the point of lol\.est average costs involves a consideration of marginal cost
and average cost relations only, no revenue implications are considered. The polnt of
proiit maximization can be less than, equal to, or greater than the po~ntof average cost
minimization.
Behavioral Economics
Economic theory is built on the Premise that men and women
are capable of conductingthe sometimescomplex calculations
necersaryto productivelyseekwealfhandavoidonnecersw
labor As a resuit,materiai and financial tranractfonramong
individualsand arganizationrreflect ratianal,relf-interested
human behaviorDuringthe late nineteenthCenNV,
respected
highly influential economirfr
builtsaphisticrted
exirtr.and that all economic activity involver uncertainty
and<irk.
Behavioral economics differs from more tradit.(onal
approaches byargulng:
mathtmat~al
modelsto de5uibe"economic man,"= pwson
who acted ratior~ally
out of self-interest with complete
.
knowledgeand the desire for wealfh.Whilk the economic man
concept war o"ginally intendedara necesraryabaract,on
hum economic and human realitler.thestudyof economics
evolved during the twentieth centuv tarard the vlw
thatactual human behavior closely parailelr that of homo
economlcus{economic man).
Recent1y.anew and exciting branch olecanomlcs
ca1ied"behavioraleconomics-has emerged to question the
descriptive and predaive capabilityof the economic man
COnCept.Criti~s
argue that utility maximization requires a
complex understandingof human emotions and economic
phenomena that i s far beyond the cognitive ability ofmart
economic a~ents.Economlcdecisions are thought to reflect
widespread uncertainry,rather than the precire calculations
of h l l y informed and dispassionatedecision makers.
Behavioral economists argue that perfect knowledge never
.
'
Peopletend to make decisions based on approximate
rulesofthumb lusing'b~unded rationality"),notfully
inhrmed rationalanalyres.
The way problems are presented[Iframed") affects
wonorn~cRelations
p W C R ~ ~ ~ ~ ~ ~ ~
CONCEPT IN ECONOMIC ANALYSIS
when economic decisions have a lumpy rather than continuous impact on output, use of
the incremental concept is appropriate
Marginal Versus Incremental Concept
~t is important to recognize that marginal relations measure the effect associated with
changes in output Many managerial decisions involve a consideration of chznges
that are broader in scope. For example, a manager might be ~nterestedin analyzing the
potential effects on revenues, costs, and profits of a 25 percent increase In the firm's
production level. Alternatively, a manager might want to analvze the profit impact
of introduang an entirely new product line, or assess thc cost impact of changlng an
entire production system. In all managerial decisions, the study of difi~rencesor cJzungrn
is the key element I n the selection of an optimal course of action. The marginal concept.
although correct f~lr,inalyring unitary changes in output, is too narrui\- to provide d
general methodology for evaluating all alternative murses of action.
The incremental concept is the economist's generalization of the marginal concept.
Incremental anaiYsis in\'ol\,e examining the impact of nlternat~vemanagerial decisions
or courses of action on revenues, costs, and profit. It focuses on changes or differences
among available alternatives. The incremental change is the change resulting from a
lncremental
given managerial decision. For example, the incremental revenue of a new item in a
Change resdlinl:
fim's product line is measured as the difference between the firm's total re\-enue before
maserialdecision
and after the new product is introdnced.
Incremental Profits
Intrernental Profit
asucrated wth a
given
Observed marketoutcomes often vary from rational
expectationsand market efficiency.
Same traditional economists are rkeprical of the
experimental and survey-baredmethodsused by behavioral
economists.and stress the importance of preferences
revealed through market transactions (revealed preferences)
rather than simply declaredin ruweysor experimental
reitingr (stated mferencesl. Raponenll of behavioral
economics note that neoclarsicalmodels rometimes fail to
predid real-worldoutcomes and that behavioralinsight can
be used to improve upon traditionalapproaber.
Sce:*nnOairand~eiln w ; B e a n ~ r n ~ ~ ~ ~ ~ u b b k a ~ ~ r i c ~ ~ c ~ ~ ~ ~ i h ~ ~ ~ ~ ~
Smcrhvrnolonl~ne.ocmbpr 19.lm7,
h~;i/onllne.~)ron.
lncremental profit is the profit gain or loss associated with a given managelial decision. Total
profit increases so long as incremental pmht is positive. When innemental pmfit 1s negative,
total pmfit deches. S d a r l p imxmnrntal pmfit is positive (and total profit increases) if the
incremental revmue associated with a decision exceeds the innemental cost. The inmemental
concept is so mtuitively obwous that it is easy to overlook both its siRnificancein managerial
decision making and the potennal for ddficulty in correctly applying it.
For this reason, the incremental concept is sometimes violated in practice. For
example, a firm may refuse to sublet excess warehouse space for $5,000 per month
because it figures its cost as $7,500 per month-a price paid for a long-term lease on
the facil~tyHowever, if the warehouse space represents excess capacity with no current
value to the companv, its hstorical cost of $7,500 per month is irrelevant and should be
disregarded. The firm would foreso $5,000 in profits by turning down the offer to sublet
the excess warehouse space. Similarly, any firm that adds a standard allocated charge
for fixed costs and overhead to the hue incremental cost of production runs the risk of
turning down profitable business.
Care must also be exercised to ensure against incorrectly assigning overly low7
incremental costs to a decision, incremental decisions involve a time dimension
that cannot be ignored. Not only must all current revenues and costs be considered,
but any likely tuture revenues and costs must also be incorporated in the analysis.
assume that the excess warehouse space described earlier came
For
about following a downturn in the overall economy. Also, assume that the excess
Par1 1 Drenlew ofManageria1 Econ~m,rr
i
I
warehouse space w a s sublet for 1 year at a price of $5,000 per month, or a total of
$60,000. A n incremental loss might be experienced if the firm later had to lease
additional, more costly space to accommodate a n unexpected increase in production.
If $75,000 had to be spent to replace the sublet warehouse facility, the decision to
sublet would ~ n v o l v ea n incremental loss of $15,000. To be sure, making accurate
projections concerning t h e f u t u r e p a t t e r n of r e v e n u e s a n d costs is risky a n d
subject t o error. Neijertheless, expectations about the future cannot h e ignored in
incremental analysis.
Another example of the incremental concept involves measurement of the incremental
revenue resulting from a new product line. Incremental revenue lncludes not only
the revenue received from sale of a new product but aIso any change in the revenues
generated over the remainder of the firm's product line. Incremental revenues rise
when revenues jump for related products. Similarly, if a new item takes sales away ifom
another of the firm's products, thls loss in revenue must be accounted for in measuring
the incremental revenue of the new product.
I
To further illustrate the incremental concept. consider the financing decision typically
associated with business plant and equipment financing. Suppose a buyer has a $100,000
purchase offer accepted b y the seller of a small retail facility The buyer must obtain
financing to complete the transaction. The best rates are a t a local financial institution
that otters a renewable 5-year mortgage at 9 percent interest with a down payment of
20 percent, or 9.5 percent interest on a loan with only 10 percent down. In the first case,
the buyer is able to finance 80 percent of the purchase price; ~n the second case, the
buyer is able to finance 90 percent. For simplicity, assunle that both loans require interest
payments only during the hlrst 5 years. After 5 years, either note would be renewable a t
then-current interest rates a n d would he restructured with monthly payments designed
to amortize the loan over 20 years. A n important question facing the buyer is: What is the
incremental cost of additional funds borrowed when 90 percent versus 80 percent of the
purchase price is financed?
Because n o principal payments are required, the annual financing cost under each
loan alternative can be calcuIated easily. The 80 percent loan requires a 20 percent down
payment and has annual financing costs in dollar terms of
80% Loan Financing Cost = Interest Rate X Loan Percentage
[ncremelltsl F l n a ~ i i ~ Cost
ng
Loan Enanclng Cost - 80% Loan Financing Cost
550 - $7.2011
= 51.350
= 90:;
= Sh
These incremental f i n a n c ~ n gcosts must be c ~ m p a r e dto the incremental a m o u n t
borrowed, where
Incremental Amount Rorro~ied= 90C; Loan Amount - SlI': Loan m o u n t
= $9l1,(100- - $80 00P
= 510.0110
In percentage trrlni, the incremental cost r ~ +lit,
t
additional funds borrowed under the
90 percent fii~ancingdltcrllat~rei>
Incremental Concept Example
I
costs incurred %.ith the incremental amount of funds borrowed. In dollar terms. the
, c x m e n t a l financing cost per year is
X
Purchase Price
~
~~
. J~ ~F F1llancing
~~~ ~Cost
~
~~ ~
~
~
' ~~
i~
~
~
t
j cllst
~ rercentage
~ ~ =~
1ncri.meiitaI Anloullt Borrowed
51,350
51(1,LIL10
= 0.135 or 13.5%
=
The incremental cost of funds for the last $10,000 borrowed under the 90 percent
financing alternative is 13.5percent, not the 9.5 percent interest rate ¶uoted for the e n t ~ r e
loan. Although the high incremental cost of funds for loans that reflect relatively little
down payments may be surpri3ing to some borrowers, it is not unusual. Lenders demand
high rates of interest for loans that involve snbstantial risk, and the chance of default 1s
much higher when 90 percent, as opposed to 80 percent, of the purchase p r ~ c eis financed.
When it comes to iorv d o w n payment mortgages, both borrowers and lenders need to
lheincremental concept is important for managerial decisions because it focusw attention
on relevant differences anlong available alternatives. Revenues and costs unaffected by a
given choice are irrelevant to that decision and should be ignored in the analysis
= 0.09 X 0.8 X$lOO,OOO
= $7,200
The corresponding annual financing cost f o r the 90 percent loan involving a 10
percent down payment is
90% Loan Financing Cost = Interest Rate X Loan Percentage X Purchase Price
= 0.095 X 0.9 X $100,000
= $8,5.50
To calculate the incremental cost of added funds borrowed under the 90 percent
financing alternative, the borrower must compare the amount of incremental financing
Effective managerial deris~onmaking is the process ot
finding the best solution to a given prublrm. Both the
methodology and tools of managerial economics play
an important role in t h ~ Ps ~ C C S S .
The decision alternative that produces a result most
ronslstent w ~ t hn~anagerialobjectiues is the optimal
Tables are the simplest and most direct form
for presenting rconomlc data. When thcsc data
are displayed electronically in the format uf an
accounting ~ncornestatement or balanre sheet, the
tables are referred to as spreadsheets.
h equation rs an expres~onoi the funchonal
relahnnshipor connection among esonomicvariables
For example, totd revenue (sales)is a function of
output. The value of the dependent vaiable (total
revenue)is de!ermined by the independent variable
(output) The iariable to the left of the equal sign
i
Part
A. Set up a table or spreadsheet lor NPI's order
quant~ty( Q ) ,inventory-related total cost
(TC),purchase price (PI, use requirement
( X i , order cust (Q), and carrying cost (Ci.
Establish a range for Q from O to 2,000 m
~ncrementsof 100 he., 0,100,200, . . . ,2,000).
B. Based on the NP1 table or spreadsheet, determine the order quantity that will minimize
1:Overureu ofMaeageria1 Etanomb
the company's inventory-related total costs
during the planning period.
C. Placing inventory-related total costs, TC, on
the vertical or Y-axis and the order quantity,
Q,on the horizontal or X-axis, plot the
relation between inventoy-related total costs
and the order quantity.
-ibis appendix providi.s a brief and selective discussion of mathematical terms and
B a n d l e r a , Or~ana, l w a n Barankay, a n d Lmran Rasul.
'lnientii'es for Manager5 and Inequality among Workers:
Evidence from a Firm-Level Experiment." Qiinrfrrly hurnal
of Economics 122, no. 2 (May. 2UD;) 729-i73
Brunncrmeier. Markus K., Christian Collier, and Jonathan
A Parker ''Optimal Belle$. r s e t Prrces. and the Preference
Ior Skewtd Returns" Amerlciin Economic Rrortw 97, no. ?
(May, 2007) 159-165.
Butler, D a v d J. and Graham C iaarnes. "Imprecision As a n
An.nunt of the Preference Reversal
,4mPncon
Economlr R m i i i , 9:. no. 1 (March. 2DOiJ: 277-297
Caplm,Andrew and M
~ .
~ .
~ T D ~
ol Learmng:' AmencaTi Econ,,m;r R ~ , ; , ~9;..~Ira 2
2007): 14R-152.
Desai, hllhir A., Alexander Dyck, and L U ~ zingales
~ I
.,~h?it
and Taxes." jovrnal of F~nonciol~ ~ , r n ~ m84,
, i sno. 3 (june,
2007): 591423.
Dgnan. Karen E. and Enrlchetta Ravina. "lncreaang Income
Inequality, External Habits, and Self-Reported Happrnss."
An?rrlcan Eronomtc Revim 9 i no. 2 (May, 2 W i ) 226231.
Easterly. Willlam "Was Development Assistance a M b t a k e '
American Economic Reuim 97. no. 2 (May, 2007): 328-332.
Fehr. Ernst and Lorenz Goette. "Do Workers Work More
l f Wages Are Hlgh7 Evidence firom a Randomized Field
c~~~
Erper~ment.'Amerlrin Economic RLWIW 97, no. i iMarch,
2007). 2Q8-317
~
~ E~~~~
h a~n d ~l~~~
,
schrnidl . . A ~ a ~ , ~to ~the
Carrot? The Interaction 01 Bonuses and Rnes." dmericon
~
~
~no 2 [May.2007)
~
177-16,,
~
~
j
Fcneira,
A, and
..Corporate Governance,
~
~
~
~
methods colllmonly used in managerial economics. The first section covers basic
properties of real nurllbers that Ile!p us understand how to solre equations. It 1s iollo\%eri
bv an explanation oi the use nf exponents and rad~cals.The next section descr1t.e~
equations, their dlfterent forms, and the operations used to
the fundamentals
manipulate them, ~h~ fo]li\rving sectiorl pxp!ains the use of losarithrns. The filial SeCtlOn
~
~ ol ~'alculus.
g
,
covers~ some basic
rules
Idlosmcratlc Ksk, and lniormatlon Flow? l a u i r ~ a o(Frnoflce
l
62, no 2 (April, 2007): 951-989.
Geweke. John. "Bayesian Model Comparison and Validahon''
Amrrirnn Eronomir R m e w 97, no. 2 (May, 200il. m 4 .
V .N ~ and~Aleh T s~~ v i n s k i~."Optimal~ Taratlon
~G O ~~ O ~S ~Mhkhail
~
"tth Endogenous Insurance Markets." Qiiar~rily
journal of
Econom8rj 122. no. 2 (May, Z O i ! 437-534
Games. Orlando "Investment i n Organirat~onalCapital
Mona8cr'al and Decasion Economics 28, no 2 (March, ZOOi!.
"
107-113.
PROPERTIES OF REAL NUMBERS
~
~
~
~
~mportantpropertlrs of real numbers. These pr()pertic5 are
hi^ sectlon rcrlerss
basic~ to
~understanding
~
~uf ho\r ~to manipulate
~
~numerl~alvalues.
Transitive Property
If X, Y, and Z are real numbers. then
Mjnlzberg. H e n r y "Productivity Is Killing A m e r t c i n
Enterprise'' Hanerd Businrss Rei,,en 85, no. 7, 6 f l u l y 1.
ifX=YandY=Z,X=Z
2007): 25.
SIone, Ruben E.. Iohn T. Mentzer, 1. P a u l Dlrtmann. ‘,*re
You the Weakest Lmk in Your Companfs Supply Chaln?"
Harunrd Business R ~ v ~ 85,
E u no.
~ 9 (September 1. 2007)
116127
hi^ means that if two numbers are both equal to a third number. they are equal to each
other. For example, if X = Y and Y= 5, then X = 5 .
Commutative Properties
It X and Yare real numbers, then
X+ Y=Y+XandXY= Y
X
that YOU can add or multiply numbers in any order. For example, 2
hi^
3 t 2 = 5 and 2(3) = 3(2) = 6.
3=
Part 1: Overview ofManagpllal
Associative Properties
If X,Y, and Z are real numbers, then
do not iIaairran nth root that is a real number. For example, because the second power, or
X t ( Y + Z l = ( X +Y)+ZandX[YZ)-(XY)Z
This implies thjt I j X - ' = X' In generdl, n.l>enevcr wr move a nljrnher raised to power
from the numerator (top) to the dei~ominator(bottumj of an expression, the sign of
the exponent, or power, 15 mult~pliedby 1 , and i-ice-vrrs,i For ezdmple. l ' ( 2 x 2 i21 =
Distributive Properties
1,'2i=2-'=0.125.
If X, Y. and Z arc real numbers, then
X(Y+T)=XY+XZand(X Y)Z=XZ+YZ
This means that within the context of an equation, the order of addition or n ~ u l t i ~ l i c a t i o ~
is ~mmaterial,that is, it is possible to first multiply and then add, or vice versa. F~~
example. 3(4 + 5) = 314) + 3 ( 3 = 27 and 3(4 5) = 3(9) = 27.
+
Inverse Properties
For each real number
Y,there is a number
~ the 111,li.r.i' 1s the rn,lri,il sijir!, and X 1s
The s j m b ~ ~':l 1s c.iilcii a ~~idlcu!H L r l 1s
the rdd!<and For con~enienre,the index IS usually un~ittedIn the case c>f principal squJre
ri~pts,so $Yis \vrittm instead o i i ~
Thereiorr, . l h -I 6 = 4. It Xis positive and rn and I !
are mtegers whizre 12 is ,lljo positrvi,. then
-
.o = 9: ' =- 7.
F~~example, ;2' 2 j : = 2: = 4.
The basic nlle for ~nultiplicatiunis X" x X" = X;"' ' and for division is X"!X"= .Y" '. For
example,33 ,3' = 3": = 3 = ,743, and 3'i.i' = 3' '= 3 = 3.
- X, called the additive inverse or neptke of X,
X+(-x)=O
For example, because 5 + ( - 5 ) = 0, the additive inverse of 5 is -5. Similarly, the additive
rnverse of -5 is 5. For each real number X, there also is a unique number, X-1, called the
multiplicative inverse or reciprocal of X, where
A statement that relates two algebraic expressions is called an equatiori. The two
expressions that make up an equation are called its rnenrbcrs or sldes. They are often
separated by the symbol =, rvhich is called an equailiy or eqlials sipn. In solving an
equation or finding its roots, we often manipulate the original equation in order to
generate another equation that will be somewhat easier to solve.
Equivalent Operations
xX-1=L[= I
X X
The expression 1 /X can be written X-', so x (I/X) =
X-1
= X / X = 1. F~~ examplr,
4(1/4) = 4 x 4 ' = 4/4 = 1. This property holds tor all real numbers except 0, for which the
reciprocal is undefined.
x
Exponents and Radicals
Exponents and radicals can be thought of as abbreviations In the language of
mathematics. For example, the product:
XxXxX=X'
In general, for a positive integer n, X' is an abbreviation for the product of xs.
xn,
the letter X is called the base and the letter n the exponent (or power). y = p, x i s
the nth root of Y . For example, 2 x 2 x 2 = Z3 = 8 and 2 is the third root of 8.
number
raised to the first power equals itself, X1= X (e.g., 7 = 7), and any number raised to
the zero Power equals one--that is, X0= 1 for X # 0 (0' is not defined). some numbers
There are three op~rationsthat can be performed on equations without changlng their
solution values; hence, the original and subsequent equations are called t.quiaalenf. These
operations are as folloxvs:
Addition (Suhtrachon) Operation. Equivalence is maintained when adding (subtracting)
the same variable to (from) both sides of an equation, where the varlable is the same as
that occurring in the origlnal equation. For example, if hX=20+2X, subtracting 2X from
both sldes gives the equivalent equation 1X=20
Multiplication (D1:'ision) Operation. Equivalence 1s maintained when multiply~r~g
(dividing) both sides of an equation by the same nonzero constant. For example, if
4X=20, dividing both sides by 4 gives the equivalent equation X=5.
Replacement Operation. Equ~valenceis maintained when replacing e~therside of an
equation by an equivalent expression. For example, if X(X-41=3, replacing the left side
by the equivalent expression X-4X gives an equivalent equatlon Xi -4X=3.
It is worth emphasizing that each of these operations can be applied to any equation
with the effect that ihe resulting equation wiIl be mathematically identical to the origmal.
Equations may take a wide variety of functional forms. Three of the more kequently
encountered are described next
may seem a curious number to adopt as the base in an exponential function,
in economrc studies of compound growth or decline.
Linear Equations
uy
An equation linear in the variable X can be written as
~~garithrnic
Functions
O X + ~ = O
For the purposes
of economic analysis, multiplicative or e~ponenhalrelations often are
hansbrnled into a Linear logariihmii farm, where
where 0 and b are constants and a is called the slope cceficicni and b the intercept.
A linear equation is sometimes referred to as a first-degree equation or equal,on
dl.gree I. To solve the linear equation 2X + 6 = 14, we apply the subbaction and divisi
operations to find 2 X = 8 and X = 4 .
Y=logbXifandoniy ~ f i =b v
H~~~ Y is a logariilrm!c funct~nilt o thc !'ace t.. Y = logb X
Quadratic Equations
An equation qvadratlc in the variable X can be written as
aX1+bX+c-o
where a, b, and c a~ constants and n to.Here a and 5 are slope coefficientsand is the intemp.
A quadratic equation is iometimes referred to as a second-degree ~ p a t l o l tor ~
~of
d e ~ e 2.
e Whereas h e a r equations have only one root, quadratic equations sometimes have
two jiffepnt mob. The solutions to quadratic equations are easily found though
of the quadratic formula. l f a F + bX + c = 0 and a, b, and r a* constants where
then
~
~
l
i
1s
the logarithmic fornl of
the
exponential
exponential
lo3=
s1,000
= i.'.F~~
For examp;?,
much of log,
thc work
1,0110
i r=~n3 ~isa nthe
a ~ logarithmic
e r i econom~cs,
al
equivalent
log.lrithms
of the
are
written using either the base 10, called ~ ( 7 r n r n i 1 niugarithms, or the base c ( = ~ a p e r i a n
constant = 2.71828 .), called naiiural lnplrrthini. Nstrlr,il laxarithms kypca!l: ?re denoted
by the notation "In" rather than "log c."
Some rmportant basic propertie5 oi logankhms are as fo1loti.i
~ r o d uProperty.
~t
The logarithm of a product is the sun1 of logarithms:
~
~
InXY=!nX+lnY
-
-
F~~ example, ln (1 ln(3 x 2)= l n 3 +In ? = 1.099 0.693 1.792.1t is important to note that
the logarithm of a sum is not the sum of logarithms.
Qrrotze~ltProperty The logarithm of a quotient is the difference of logarithms:
The solutions for the values of X are called the roots of the quadratic equation, F~~
example, if 2 X - 15X+18=0, then X = +i5+juTzi-4(~))/2(2)=(15i9)/4=6
and 1.5.In n1arlY instances, one or both of the solved values for a quadratic equation will
be negative. If the quadratic equation is a profit function and X is output, for
any root X<0, implying negative output, will be mathematically correct but meaningless
from a n economic standpoint Therefore, when applying the quadratic formula to
problems in managerial economics, one must use judgment to identify those solution
values that are both mathematically correct and economicall" relevant.
For example, In 1.5 = I n 3 / 2 = ln 3 -In 2 = 1.099 - 0.693 = 0.406 Here note that the
logarithm of a quotient is nab the quotient of logarithms.
Pow.r Property. The logarithm of a number X raised to the exponent ti, X;.. is the
exponent tinlrs the logarithm of X'
Multiplicative Equations
For example, In 9 =In 32= 2 In 3 = 20.099) = 2-198.
An equation multipliurtiv~in the variables X and Z can be
lnX=ln~-ln~
Y
InX"= lnX
Using the properties of logarithms, we see that there is a simple logarithmic
transformation for any multiplicative or exponentla1 function. For example, the
logarithmic transformation of the multiplicative equation Y =~X'Z' can be written as In
Y = l n 5 + 2 In X + 3 In Z. Here we have used the natural logarithm of X, although the
transformation would be the same using common logs or logs to any other base.
It is important to recognize the symmetry between the logarithmic and exponential
functions. It is an important property of each that
as
Y = aXbnZbz
where a is the constant and b, and b, are exponents.
For example, Y = 5XZ"here
X = 3 and Z = 4 has the solution Y = 5(3l)(4))= 5(9)
(64) = 2,880. Multiplicative equations are often employed in managerial economics,
particularly in demand, production, and cost analyses.
Ine'=Xande'"X=X
Exponential Functions
Certain multiplicative functions are referred to as exponential f ~ ~ t~h~
i function
~ ~ ~
Y = e r where b > 0, b# 1, and X is an). real number, is referred to as an exponential function
to the base b. Exponential functions ohen are constructed using e, the ~~~~~i~~constallt
(=2.71828 as a base. Thus, for example, the equation Y = $ means y=(2.71828 ...)1.
.
j
In words, the logarithm to the base e of the number e raised to the power X equals X.
Similarly, the number e raised to the power In X equals X. For example, In e' = 1 and
eln'= 1. This means that any number or equation transformed into logarithmic form
through use of logarithms can be converted back into original form through exponentla!
transformation. For exampie, recall from earlier discussion that the multiplicative
equation Y = 5XZ1 has the logarithmic equivalent In Y =In 5 2 In X t 3 In 2. It follows
+
i
Pan 1 :Overvier ofManagerial kooa
that if X = 3 and Z = 4, then Y = 5(32)(43)= 5(9)(64)= 2,880 and ln y = ln 5 + 2 in
+
4 = 1.609 + 2.177 +4.159=7.965. Equivalence requires that in 2,880 = 7.965 an
e"g65= 2580, which is indeed the case.
The practical relevance of tl% symmetry between logarithms and exponential functions
is that, for example, a multiplicative dentand relation can be
linear logarithmic
form using widely available computer software regression packages and
back into
original form t h u g h exponential transformation for purposes of numerical elra]uation.
CONCEPT OF A MARGINAL
A nlarginal 15 defined as the change In the value of the dependent variable associated
wit11 a l-tlnit change m an independent variable. This relationship can be more precisely
specsied by examining the nature of a change in a function. Consider the unspecified
function Y = f ( X ) ,which is read "Y is a function of X." using (delta] to denote change,
the change in the valur of th.e indepcndcnt va;iable, X, is
by the notation ~x and
the change in the dependent variable, Y , 1s given by AY.
The ratio AYIAX provides a very general specification of the marginal concept.
Sr&3
AX
x, - x :
This measure of the m.7iginal is shoh.n tn Figure 2A.l ai tile slope of the line connecting
points A and D, iVe can see that this inehure uf tlie nla~ginali, ci~rlhi~irrablv
smaller
than the estimate one ~\.ouldobtain looking at the change (Y2-Y.l/(X,-.Y,), the slope
of a straight line connecting polnts 4 and B, and larger than tlie m ~ r g i ~ found
al
for the
change ( Y , - Y , ) / ( X , X , ) , theslope of a straight line connecting pointsC and D.
The problem is that 0 , - Y \ ) / ( X , X I )measures the avrrdge change in Y for a I-unit
change in X between points A and D.Since this "average" marginal value m<ly differ
significantly from the actual marginal at a point such as D, it has lirnite~i\ . a h tor
decision making and cou!d, in fact, lead to incorrect dcosions.
If a decision maker wanted to know Iiolv Y varies for changes in X arnund point D,
the relevant marg~nalwould be found as AY/AX for a very small change in X around X,.
The mathematical concept for measuring the nature of such very in~allchanges i n called
a derlual~r~c,
A derivative, then, is simply a precise specification of the marginal value at a
particular po!nt on a tunction. The mathematical notatlon for a derlvati\,e 1s.
The change in y, AY, divided by the change in X, AX, indicztes the change I n the
dependent variable associated with a I-unit change in the rralue of X .
Figure 2A.1, which graphs a function relating Y to X , illustrates this relation. F~~
values of X close to the origin, a relatively small change I n x
a large change in y.
a=limAY
dX
W
l
.
-0
which is read, "The dcnvative of Y w ~ t hrespect to X equals the limit of the ratin I Y i ' A S ,
as AX approaches zero.""
This concept of the derivative as the limit of a ratio is precisely equivalent to the slope
of a curve at a point. Fisure 2A.l also presents this ~ d e aNotice
.
that the nz,ernge slope of
the curve between points A and D is measured as
Y
x
Y 4 Y l
x,-x:
and is shoivn as the slope of the line connecting the two points. Sim~larly,the alrerage
slope of the curve can be measured ovrr smaller and smaller ~ntervalsot X and shorun
by other chords, such as those connecting pornts B and C wlth D. At the I~mit,as AX
apprmiches zero around p o ~ n tD, the ratio AY'AX m equal to the slope of a Lint. drawn
i If the value oi a lunchon Y =KSlappmaches n constant Y' as rhe value u f the ?ndrpendentranable. X ,
approaches X', ?-IS called the h m ~ of
t the huuhon/(X, as X approaches X'. Thls ivould be writti." 2s !IT
KXI = Y Fcr example, Y = X-4, ttiel1m8t of this hnctlon asXaf;~raaches5 as I. lhill 15.!1$X-41=
1
T h s savs that the value or X oppruaches but dmsnot qute reach 5, the value of the iuncnsn Y=X-4
of a limit I, exnnnmed in detall In an? tnmductom calculus
comes closer and closer to 1 f i r
textbook
I
1
Y = oXb
& = b a xWl!
A
dX
F~~
giren the function
Y=2XJ
b y = j,
RULES FOR DIFFERENTIATINGA FUNCTION
Determining the derivative o i a function is not a particularly difficult task; it
inl'olves ap~]?'ing a basic formula to the function. This section presents the basic formulas
or rules for differentiation. Proofs are omitted here but can be found in any lntro&,ctoly
calculus texthook.
The derivative of a constant is always zero; that is, if y is a constant:
This situation is graphed in Figure 2A.2 for the example Y=2. Because y is defined as a
constant, its value does not vary as X changes and, hence, d Y / d X must be zero.
LY
,X83-11= 6 s
poxcer tuniticins shuuld ilarit!- th15 rulc. The dcrlyntii-r
T~~ furtlIer
f f n r t j o n Y = l' 15 six m a:
tile
dY =: 3 ,x2
dX
~h~ ckponrnt, 3,is nlult,pl;e,j by tile implicit ci~rtflcient I . , i r d i r t~ ~ l by
n ~the variable,
r a ~ s r dt i ) thc wcond power.
Finall!; the der~vatlueoi the function Y=O.SX is
2
%
r r u ~ t l f ~ l rby
d the coefficient. 0.5, times the variable, X,
1,
7 h e implicit
to the zero power Because any number raised to the zero power equals 1. the
result IS 0.5.
help c l a r ~ i ythe power function concept In Figure 2A.3, the
~~~i~~ a graph
last two poi,rer functions glren above, Y = X 3 and Y=0.5X, are grapllrd Consider first
Y=o,.;x ~h~ derlvatlve oi ti,Lb function, d ~ : d X = O . r ; , is a constant. indicating that
the sloFr of the iunction is a constant, This can b e readily seen from the graph. The
deri,.at,ve measures the rat? of change. ~f the rate of change is constant, as it must be if
the basic function is ]inear, the derivative of the functlon must be constant The second
function, Y=XJ, rises at an increasing rate as X increases. The dermative of the function,
d \ . / & y = 3 ~ , also increases as X becomes larger, ~ndicatingthat the slope of the function
is increasing or that the rate of change is increasing.
Sums and Differences
~h~ following notation is used throughout the remainder of this section to express a
number of other important rules of differentiation:
~ = g ( n : U i san unspecified functlon, g. ofX
v=h(n:vis an unspecified function. h, ofX
Pan I Overrlrw olMamgerlal E
Substituting X:-1 for u in the derivative results in
M= A
dx
21X2-IllR
Because U = X - 1,
in Chapter 5 and discussed throughout the remaining chapters.
usingthe h c t i o n
of h1icti011 rule, dY/dX=dY/du
-
dU/dX,
50
& - & dll
d x P d u X dX
~~t U =X - 2. Then Y= 1 /U. and the quotient ~ l ).;elds
e
Substitutingfor U creates the expression
M
dU, U x O - U2
1x1
dl-M
&=_A
d x - d l J x dx
(
x
.
-
~
=2-4X3
Step 2:
Substituting (X- 2 ) for LI yields
M =1
dU
Step 3:
(X1- 2)*
Because U = X - 2 .
M-M
&
dx- d ~ dX
= (2 - 4X3) X 6X2
= 1 2X2 - 24X5
Therefore,
d L = d v x d l i , - L X 2X
dX dU dX
iX2-2)=
y
Let U = X - l . T h e n Y =
=;*q
tn=U12.
Y = (2X + 3)'
&=lU-?,z
dU 2
=i
2UIR
Let U= 2X +3. Then Y = U1 and
M=2U
dX
I
~
~
~
~
Because U =2X+3,
and
Thus,