Innovative Marketing, Volume 7, Issue 3, 2011

Khalid M. Dubas (USA), Lewis Hershey (USA), Inder P. Nijhawan (USA), Rajiv Mehta (USA)

Breakeven and profitability analyses in marketing management

using R software
Abstract
An extensive literature in economics and business provides guidelines for profit maximization for firms in various
market structures. However, these elaborate and sophisticated techniques and rules for profit maximization require ap-
propriate estimation of a company’s cost and revenue functions that are often difficult to obtain for many companies.
So for many businesses, an important practical tool for profitability analysis and decision making is often the breake-
ven analysis that identifies the level of price and output where a firm’s revenue equals its cost. So production and sales
beyond that point generate profit. Although, breakeven analysis is easy to understand and use, its assumptions are often
misunderstood or ignored resulting in its misuse.
The commonly used breakeven formula in business and marketing describes a special type of perfectly competitive
firm that has no pricing power, faces a horizontal demand curve, a linear total revenue curve, a linear total cost curve,
and a linear profit curve that increases indefinitely. A more typical perfectly competitive firm would instead have a U-
shaped (or inverted S-shaped) total cost curve, and a quadratic profit function; thus, two breakeven points, and it would
reach maximum profit at the point where its marginal revenue equals its marginal cost. Such firms would not require a
marketing manager since they can sell all of their production at the given market price that is determined by the market
demand and supply. However, most firms operate in an imperfectly competitive market and exercise some control over
the price of their products; they also control their product quality, promotion, and distribution. Such firms require mar-
keting managers for understanding and responding to the needs and wants of their customers and these managers can
utilize appropriate breakeven and profitability analyses.
This article evaluates breakeven and profitability analyses for firms in perfectly competitive and imperfectly competi-
tive markets. The conceptual and practical methods for profitability analysis are presented, and R, free mathematical
and statistical software, is used to analyze various situations to guide marketing managers in their decision making. The
use of this free and powerful software to facilitate analysis and decision making should empower the greatest number
of decision makers all over the world. The role of product characteristics in determining product demand, pricing, and
market shares is also presented here.
Keywords: breakeven analysis, profitability analysis, sales-costs-profit analysis, volume-costs-profit analysis, market
structure, demand estimation, product characteristics, product features.

Introduction© useful for evaluating new and existing products and

projects. The typical discussion of breakeven analysis
Business organizations strive to be successful in
in the business literature assumes a given price (P)
achieving their missions and their goals. One essential
and linear total revenue (TR) curve; so the firm has
business goal is to achieve desired profits. Marketing
a horizontal demand curve at the given market
management works within the overall business frame-
price. Its marginal revenue is equal to its average
work to develop marketing plans involving market
revenue, MR = AR. A linear total cost (TC) curve
segmentation, targeted marketing mixes (product,
is also assumed that along with a linear TR curve,
price, promotion, and place) and appropriate position-
ing/repositioning of the product for each target market generates a linear profit curve. The breakeven
segment. Of the four marketing mix elements, only point is reached at TR = TC or profit = 0. This de-
price generates revenue while the other three elements scribes a special type of firm within a perfectly
create costs (Kotler, 1999). So firms strive to increase competitive market; this firm has a linear profit
their prices as high as their level of product differentia- function that increases indefinitely with increase in
tion, market structure, and their pricing power would output that is always sold at the given market price.
allow. Successful firms accumulate a lot of informa- This is an unstable situation because the firm will con-
tion that helps them to make reasonable profitability tinue to produce as much as possible since its output is
analyses. Use of breakeven/profitability analyses, simu- always sold at the market price. Let us call this spe-
lation modeling, and yield management for pricing cial firm an “unstable perfectly competitive firm”.
is quite common in many companies and industries. Changing the linear TC curve to a U-shaped TC
curve, with upward sloping marginal cost (MC)
Perfectly competitive firm. Breakeven (cost-volume- curve, will stabilize this firm’s situation and it will
profit) analysis is often utilized to understand the sales achieve an equilibrium between its supply and de-
volume where profits begin to emerge. This tool is mand curves. A firm in a perfectly competitive mar-
ket maximizes its profit at MR = MC which is its equi-
© Khalid M. Dubas, Lewis Hershey, Inder P. Nijhawan, Rajiv Mehta, 2011. librium point and this will lie between its two brea-
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Innovative Marketing, Volume 7, Issue 3, 2011

keven points that arise due to the fact that it will have a tential. Sales and marketing literature (Palda, 1969,
quadratic profit function. A firm in a perfectly compet- 1971; Spiro, Rich, and Stanton, 2008; Perreault, Can-
itive market does not require a marketing manager. non, and McCarthy, 2011) presents numerous me-
thods for calculating market potential, sales potential,
This special case of an unstable perfectly competitive
and sales forecasts and points out that the difficulty in
firm tends to be applied across much of business and
developing an accurate sales forecast varies from sit-
marketing literature to firms that operate in imper-
uation to situation. Sales forecasts will be quite diffi-
fectly competitive markets. It is important to under-
cult to obtain for radically new products than for
stand the appropriate market structure (monopoly,
somewhat new or established products that enjoy sta-
oligopoly, monopolistic competition, perfect compe-
ble sales. Other situations would require considering
tition) of the firm under consideration and apply ap-
capacity limitations and product quality to forecast
propriate breakeven and profitability analyses for
sales and manage demand.
marketing management. Only firms in imperfectly
competitive markets would require marketing man- Here are several sales forecasting methods and their
agers to develop marketing plans, to study their cus- data sources:
tomers’ needs and wants, to achieve customer satis-
i Concept testing – respondents/potential customers.
faction, and build customer relationships that would
generate profit for their firms. i Survey of executive opinion, the Delphi tech-
nique – managers.
Purpose and scope. This paper illustrates an overall i Sales force composite – managers and salespeople.
conceptual framework for profitability analysis and i Survey of buyer intentions – customers.
breakeven analysis using examples and R software i Moving average, exponential smoothing, and
that is free and can be downloaded and installed regression analysis – historical data.
from the Internet. Specifically, the following topics i “Must do” approach and capacity-based ap-
are presented in this article: proach – company operations.
1. A generalized theoretical framework for profit i Test marketing – customers/potential users.
maximization using marginal analysis and the im- These techniques help a marketing manager to deter-
plications of pricing power on the shape of demand mine sales forecasts for a target market; however, the
curve, total revenue curve, and profit function. accuracy of these forecasts depends on the firm’s abili-
2. The main ideas of breakeven (cost-volume- ty to determine the correct marketing mix and under-
profit) analysis, its assumptions and uses. The stand the impact of the changing external environment
methods for estimating revenue (sales forecast- on the firm. It should be noted that only a firm in an
ing) and various means of collecting and eva- imperfectly competitive market would need to forecast
luating information for better decision making. sales and plan production accordingly since a firm in a
3. Yield management and price differentiation by perfectly competitive market can sell its entire produc-
organizations. tion at the given market price even without any promo-
4. Market and competitor analysis using product cha- tion at all since the customers have perfect information
racteristics and price to estimate market shares. and all companies’ products are homogeneous.
5. Use of R software for mathematical and statistic-
al analysis. Products follow a product life cycle and the marketing
6. Forecasting sales using price and marketing mix mix must be adjusted as a product goes through the
elements. various stages of its life cycle. During the introduction
stage of a product’s life cycle, the pricing policy
1. Literature review should be market skimming or market penetration.
1.1. Market potential, target sales potential, and During the later stages of its life cycle, the price should
sales forecasting. Market potential is the maximum match its competition; may use price dealing and price
possible total sales of a particular product or service, cutting (Perreault, Cannon, and McCarthy 2011). So-
under ideal conditions, for the entire industry in a spe- ny, for example, used market penetration pricing to
cific market for a specific time period. Sales potential beat Toshiba in their competition between its Blu-ray
is the share of market potential that an individual firm DVD and Toshiba’s HD DVD formats by cutting pric-
can ideally expect to achieve. Compared with sales es, establishing alliances with Samsung and Philips,
potential, a sales forecast is what an individual firm and including Blu-ray players in its PS 3 consoles.
realistically expects to achieve; typically the sales po- 1.2. Types of innovations. A product is a bundle of
tential would be higher than the sales forecast since the features (or attributes or characteristics) and it can be
former would be achieved only under ideal conditions modified by modifying its features. It is useful to de-
and a firm’s financial resources or changes in its exter- scribe different types of product innovations and indi-
nal environment may not allow it to reach its sales po- cate the degree of difficulties involved in forecasting
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 Innovative Marketing, Volume 7, Issue 3, 2011

sales for each category. According to the Federal two categories: fixed and variable. This classification
Trade Commission, a firm can call its product new is with respect to production. However, in a business
only for up to six months after introduction to the mar- the vast majority of costs are semi-variable; that is they
ket. To be called new, it must be entirely new or vary with production but do not vary in direct propor-
changed in substantial ways. Product innovations can tion to volume. Thus, he suggests use of (1) direct
be classified as follows: costs, those costs that are incurred by producing a
product like raw materials and fuel or making a sale
1. New-to-the-world products or discontinuous in-
like advertising and sales commissions, and (2) period
novations. These are radically new products that,
costs that are incurred from the provision of capacity
if successful, create a new product category and
to make and sell and from keeping this capacity in rea-
require new skills and knowledge. These are least
diness regardless of production or sales volume. Fur-
frequent innovations.
ther, the period costs could be divided into two catego-
2. Me-too products. These products are new-to-
ries: (1) capacity costs that are required to provide op-
the-company but not new-to-the-market so his-
erating capacity and organization, while (2) discretio-
torical sales data are available for similar prod-
nary costs arise from specific management appropria-
ucts that can be used to develop sales forecasts.
tions. Thus, like direct costs, the period costs can be
These are more common innovations.
influenced in the short run by management. Therefore,
3. Product modifications involve modifying exist- each organization should categorize its own costs and
ing products. break them into their variable and fixed components
4. Product line extension involves adding more for breakeven analysis. He recommends incorporating
products to a product line. breakeven analysis concepts into the regular account-
5. Product positioning/repositioning. Here the prod- ing and record keeping system by creating a chart of
uct is positioned/repositioned in the customer’s accounts and reporting financial results to manage-
mind by changing its advertising message and/or ment. Direct costing emphasizes the contribution ap-
product features. proach, so the contribution of each segment is meas-
Sales forecasting for new-to-the-world products is ured. This eliminates allocation of costs from outside a
most difficult while it is easier for other types of in- responsibility center using arbitrary methods. Direct
novations since comparable data on similar or com- cost system can transform managers from critical spec-
peting brands are often available for comparison. tators to active participants in the management ac-
counting process as they carry out planning, organiza-
1.3. Breakeven and profitability analyses. Several tion, and control activities.
authors in business and marketing literature discuss the
uses of breakeven analysis and all of them utilize the He notes that revenue projection is a prerequisite for
unstable perfectly competitive firm’s breakeven analy- every modern management control technique. For ex-
sis formula and/or diagram and apply them to all situa- ample, sales forecasts are required for budgeting, pro-
tions – including imperfectly competitive firms. Harris duction planning and inventory control; non-manufac-
(1978) discusses the unstable perfectly competitive turing organizations may express revenue as profes-
firm’s breakeven analysis, a plot of TR, TC, FC, and a sional fees, rents, interest earned, merchandise sales, or
computer program in BASIC language for a main- royalties, etc. Individual segments of an organization
frame computer and numerous applications of breake- plan their operations based on revenue potential. He
ven analysis. Since 1978, breakeven analysis has been notes the following difficulties in revenue projections:
more widely discussed and utilized in business litera-
ture and numerous breakeven analysis calculators are i Revenue forecasting is not an exact science.
now available free online. Harris recommends use of i The goals set are not reasonable.
breakeven analysis for the following situations: i Company’s personnel perform better or worse
than expected.
i Profit planning or budgeting. i Unexpected changes in external environment.
i Problem analysis at the level of a segment or
whole business when financial results are unsa- He suggests the following steps for successful im-
tisfactory. plementation of breakeven analysis:
i Making quick assessment in advance of major i Proper understanding of breakeven formula and
changes like opening or closing plants, adding chart.
or eliminating sales territories or product lines. i The importance of proper terminology.
Breakeven analysis is one of many techniques that i The attainment of reasonable accuracy.
have been developed to help management plan, coor- i The need to track results.
dinate, and control business operations for success. He i The relation of breakeven techniques to direct
notes that the basic breakeven analysis shows costs in costing.
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i Start with past sales data for revenue projection. i The desired variable cost per unit or fixed costs.
i The estimate is usually for one year or less. i Breakeven analysis is important when beginning a
i Dollar or unit sales can be used as overall base new activity like starting a new product, or a new
to measure activity. line of business, or expanding an existing business.
i A stable price is usually assumed. i Financial managers use breakeven to determine
i A constant sales mix is also assumed. the feasibility of a proposed investment. Would
i Management should participate in revenue pro- the lower interest payments over the life of a
jection. new loan cover the costs of refinancing the ex-
i Projection of sales should be within normal isting higher interest loan?
range of operations where volume-cost-profit i Management executives: Have the company’s
relationships are predictable. breakeven possibilities improved or deteriorated?
i Marketing managers: Will a new marketing cam-
For sources of information for revenue projections, paign generate sufficient sales to cover the costs of
he recommends use of historical information and ex- the campaign? Would the introduction of a new
ternal sources of information from trade associations, product add to the company’s profitability?
government publications, trade journals, financial i Production managers: Would modernization of
newspapers, professional marketing studies, chamber production facilities pay for themselves in cost
of commerce publications, business associations, and savings.
sales people.
The literature in business and marketing (Grewal
Siegel, Shim, and Hartman (1992) describe the un- and Levy, 2011; Shim, and Siegel, 2000; Siegel,
stable perfectly competitive firm’s breakeven analy- Shim, and Hartman, 1992; McBryde-Foster, 2005)
sis and related formulas as follows: presents the following assumptions for breakeven
i Breakeven formulas are useful for all businesses. and profitability analyses and all these authors util-
The three most common breakeven formulas are: ize the unstable perfectly competitive firm’s breake-
(1) to determine breakeven point; (2) the margin ven analysis:
of safety; and (3) the cash breakeven point. i Sales price per unit is constant during the period
i Breakeven analysis is used to organize thinking on of analysis.
important broad aspects of any business whether a i Variable costs per unit are constant during the
hotel or an airline flight by determining the level period of analysis.
of sales required to breakeven. i Total fixed costs are constant during the period
i The margin of safety is a measure of operating of analysis.
risk, the larger is the ratio the lesser is the risk in i Everything produced is sold so there is no in-
reaching the breakeven point. Margin of safety = ventory.
[(expected sales – breakeven sales)/expected i The company sells one product or a constant
sales] x 100. mix of products.
i The cash breakeven point is useful when a com-
Scheuing (1989) utilizes the unstable perfectly com-
pany has low cash on hand or the opportunity cost
petitive firm’s breakeven formula to select among
of holding excess cash is too high. The cash brea-
alternative marketing mixes for a firm. These market-
keven point is less than the usual breakeven point
ing mixes include alternative advertising budgets and
since noncash expenses are deducted from fixed
alternative distribution cost allowances. He goes on
costs. Cash breakeven point = sales = variables to discuss breakeven management by using three
costs + fixed cash cost. It should be pointed out tools: (1) increasing revenues by increasing price; (2)
that elsewhere in the literature, the cash breakeven reducing fixed costs; and (3) reducing variable costs.
formula is also presented as (Fixed costs – Depre- He notices that “Raising the price of the new product
ciation)/Contribution margin per unit. appears to be the “quick fix” for the break-even prob-
They present these uses of breakeven formula and lem, increasing revenue in a hurry without much ef-
analysis: fort.” He then discusses the price elasticity of demand
and states that increasing price should be linked with
i The sales volume required to breakeven. the price elasticity of the demand curve and that a
i The sales volume necessary to earn a desired firm may use price differentiation to increase its rev-
profit. enue. He provides an excellent example of the use of
i The effect of changes in selling price, variable price discrimination to increase sales revenue and
cost, fixed cost, and output on profit. profit for an imperfectly competitive firm. While he
i The selling price that should be charged. utilizes a downward sloping demand curve for this

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 Innovative Marketing, Volume 7, Issue 3, 2011

illustration, he uses the breakeven formula for the under their heading “Marginal Analysis Consid-
unstable perfectly competitive firm. Further, his illu- ers Both Costs and Demand”.
stration generates a quadratic TR curve that produces i Their marginal analysis includes two breakeven
two breakeven points that he does not relate to his ear- points as is expected with a quadratic profit
lier discussion of breakeven analysis that used an unst- function, however, they do not link it with their
able perfectly competitive firm. This is another exam- earlier discussion of breakeven analysis.
ple of the confusion created by using the incorrect i They emphasize that managers should not strive
breakeven formula for an imperfectly completive firm. to identify the precise price that will maximize
Perreault, Cannon, and McCarthy (2011) discuss the profit but to get an estimate of how profit might
uses and limitations of breakeven analysis for an vary across a range of relevant prices. They
unstable perfectly competitive firm (described in present many approaches to help managers un-
Table 1, below). derstand the likely shape of their demand curve
for a target market.
i They note that it is popular, easy to use, and
helpful in evaluating alternatives. While books in economics are typically very clear
i They note that each price has its own breakeven about a typical firm’s goal as profit maximization
point (BEP), so it is helpful to calculate a BEP and how to achieve it under various market condi-
for each of several possible prices and compare tions, few books in business or marketing success-
the BEP for each price to the likely demand at fully clarify the basic assumptions and limitations of
that price and reject those BEPs for which the breakeven and profitability analyses even though
demand is expected to be far below the BEP. there is significant business and marketing literature
i They provide a formula for calculating BEP in on elaborate pricing and profitability models. Typi-
dollars, so TR = TC, and a breakeven formula cally, the books in marketing and business do not
for target profit that is added to the fixed costs specifically identify the various types of market
to obtain the target sales volume. structure and their marginal conditions (MR = MC)
i They note that managers can lower BEP by reduc- to achieve maximum profit. Their formulas and
ing the fixed costs or by lowering the variable cost graphs for breakeven analysis typically consider the
per unit so the profits would start faster. case of an unstable perfectly competitive firm and
They do not discuss that this particular breakeven apply them to the most common situation of an im-
formula describes a price-taker firm that can sell all perfectly competitive firm. Such authors typically
of its output at the given market price so it is faced ignore that two breakeven points exist for a quadrat-
with only one price level. However, they do ic profit curve. The appropriate breakeven formula
recognize the following: for a perfectly competitive firm and for an imper-
fectly competitive firm would be their quadratic
i Breakeven analysis is too often misunderstood. profit set equal to zero. This quadratic equation will
i Beyond the BEP the profits grow indefinitely. produce two breakeven points (roots) within which
i The straight-line TR indicates that TR grows would lie the maximum profit and the correspond-
indefinitely so any quantity can be sold at the ing price, quantity and other marketing mix ele-
assumed price but this is usually not true. Most ments. Some authors seem to associate marginal
managers do not have TR curves that increase analysis (MR = MC) for profit maximization with
indefinitely. imperfectly competitive firms only that face a
i The straight-line TR curve means that the firm downward sloping demand curve although a perfect-
has a perfectly horizontal demand curve at that ly competitive firm would also use marginal analy-
price, but most managers face a downward slop- sis to maximize its profit at MR = MC; it would
ing demand curve. have a horizontal demand curve.
i Breakeven analysis is useful for analyzing costs
and evaluating what might happen to profits in 2. Methodology
different market environments. This paper utilizes a general framework for profit
i It is a cost-oriented approach that does not con- maximization for a firm in a perfectly competitive
sider the effect of price on the quantity that con- market and another firm in an imperfectly competi-
sumers will want, i.e., the demand curve. tive market. Breakeven analyses are utilized in both
i To identify the most profitable price, marketers cases. Various situations involving different shapes
should estimate the demand curve and then use of relevant functions and their implications on profit
marginal analysis to equate MR = MC. and marketing mix decisions are analyzed. In addi-
i They present the behavior of an imperfectly tion, several examples involving data and graphs are
competitive firm (described in Table 1, below) provided to illustrate important concepts.

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Innovative Marketing, Volume 7, Issue 3, 2011

R software is used here for analysis; this software is different marketing mix to each market segment
free and can be downloaded and installed from http:// while they position/reposition their products appro-
cran.r-project.org/. Six manuals on R are available in priately to offer intended value propositions.
PDF format at this website and also in R itself in the
3.2. Price discrimination. Firms in an imperfectly
pull down menu under Help. In addition to the base R
competitive market with product differentiation and
software, a lot of free packages can be downloaded
market segmentation may use price discrimination
from the Internet and installed in R software. R can be
run from the command line interactively or in a batch (Scheuing, 1989) to maximize their revenues or prof-
mode; it can be run on the web, or in a GUI with the R its. Consider the airlines industry that is highly com-
Commander (Rcmdr) package. R is a good substitute petitive and many airlines have gone bankrupt or
for SAS, SPSS, Maple, MATLAB, and Mathematica. merged with other airlines in order to survive. These
R software can solve optimization problems usingcal- airlines typically do not charge the same price for a
culus or the more general numerical analysis methods. seat to all passengers; they utilize yield management
We present several numerical examples to illustrate concepts and software (Smith, Leimkuhler, and Dar-
the models and provide the essential commands in R row, 1992) to maximize their revenues by charging
software and its output. different prices to different passengers based on the
time and day of a reservation, weekend stay at the
3. General framework destination, nonstop flight, senior citizen status, child
Business organizations must earn some target profit if status, stay exceeding 45 days at the destination, elec-
they are to survive and prosper. Marketing managers tronic versus paper ticket, first class versus coach
operate within the general framework of the corpo- class, etc. Similarly, universities typically charge dif-
rate/business plans to carefully develop and imple- ferent prices based on in-state versus out-of-state sta-
ment marketing plans for organizational success. The tus, online versus in-class courses, summer versus
general framework of the marketing management fall/spring courses, scholarship versus no scholarship
process can be summarized as follows (Kotler, 1999): status, tuition waiver versus no tuition waiver status,
graduate versus undergraduate status, etc.
R Æ STP Æ MM Æ I Æ C,
3.3. Market structure and profitability analyses.
where R is the research (i.e., market research), STP is
It is important to select the correct market structure
the segmentation, targeting, and positioning, MM is
in which a firm competes. A firm’s market structure
the marketing mix (or 4 Ps, i.e., product, price, place,
could be any of these types: perfect competition,
and promotion), I is the implementation, and C is the
monopolistic competition, oligopoly, or monopoly.
control (getting feedback, evaluating results, and revis-
Although, there are significant differences among
ing or implementing STP strategy and MM tactics).
these market structures, generally, the firm would
3.1. Product differentiation and promotion. To achieve equilibrium, i.e., maximum profit at MR =
better compete in their imperfectly competitive MC. Firms in each market structure would have qu-
markets, firms often strive to differentiate their adratic profit functions and two breakeven points.
products from those of their competitors by using However, an unstable perfectly competitive firm
quality improvements and promotions; they estab- would have only one breakeven point which is the
lish well-known brand names to increase their price most frequently used situation in business and mar-
control. The steepers are their downward sloping keting literature and incorrectly utilized across all
demand curves, the higher is their ability to charge other market structures. Table 1 summarizes the be-
higher prices for their products. Further, successful havior of an unstable perfectly competitive firm and
firms typically segment their markets and offer a that of an imperfectly competitive firm.
Table 1. Breakeven and profitability analyses
An unstable perfectly competitive firm
Imperfectly competitive firm
(profits increase indefinitely)
Downward sloping to the right
Demand curve Horizontal demand curve at the market price. P = a + bQ, a > 0, b <0, where a is the maximum price and b is the change in
price per unit sold.
Pricing power No pricing power. The firm has some pricing power.
Information Perfect information, so no need for promotion. The firm promotes its product.
TR TR = PQ TR = PQ = aQ + bQ2
TC = F + VC TC = F + vQ. TC = F + vQ,
Ȇ = aQ + bQ2 – F – vQ, or Ȇ = bQ2 + (a–v)Q – F
Ȇ = (P-v)Q – F
Let A = b, B = a-v and C = -F, then Ȇ = AQ2 + BQ + C.
Ȇ is a positively sloped function that intersects the
Ȇ = TR - TC Ȇ is a quadratic function that reaches a maximum point then begins to de-
vertical axis at – F and intersects the horizontal axis at
cline for additional sales. Maximum profit is at MR = MC which lies between
F/(P-v) and increases indefinitely as sales increase.
the two breakeven points

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Table 1 (cont.). Breakeven and profitability analyses

An unstable perfectly competitive firm
Imperfectly competitive firm
(profits increase indefinitely)
Set Ȇ = (P-v)Q – F = 0 to obtain Set Ȇ = AQ + BQ + C = 0 to obtain its roots (breakeven points)
2
Breakeven quantity
QB = F/(P-v) QBi = [-B ± ¥(B2 – 4AC)]/2A, where, i = 1, 2; A = b, B = a-v and C = -F.
Target profit quantity, QT. QT = (F + Target Profit)/(P-v) Target Ȇ = AQ2 + BQ + C will imply QTi., where, i = 1, 2; A = b, B = a-v and C = -F.

Table 2. Demand schedule and corresponding costs, revenues, and profit

P ($) QE (units) TR = P*QE F = $100 VC = 2QE TC = 100+2QE Profit = TR-TC
7 0 0 100 0 100 -100
7 20 140 100 40 140 0
7 40 280 100 80 180 100

The behaviors of two types of perfectly competitive The following relationships exist among price (P),
firms and an imperfectly competitive firm. average revenue (AR), and marginal revenue (MR)
Case 1. Unstable perfectly competitive firm í horizon- functions of this firm. P = $7; AR = $7, Q  0; and
tal demand and linear profit curves. MR = $7. Therefore, P = AR = MR = $7. The infor-
mation in Table 2 is used to produce Figure 1 where
Consider a hypothetical firm that produces and sells quantity demanded is measured on the horizontal axis
widgets. Here, P is the price in dollars per unit, Q is and TR, TC and profit are measured in dollars on the
the number of units produced and sold (no inventory), vertical axis. The breakeven point is reached at QB =
TR is the total revenue, F is the fixed cost, v is the va- 20 units and the target profit of $100 is obtained at Q
riable cost per unit, VC is the variable cost, P – v is the = 40 units. These plots are produced by using the fol-
contribution margin per unit, TC is the total cost, and lowing R code and are given in Figure 1 below:
Ȇ is the profit. In this situation, the company first rece-
ives the order then produces the product so there is no P < -7; v < -2; F < -100; Q < -c(0,100); TR < -
inventory. This situation could be approximated by function(Q){P*Q}; TC < -function (Q) {v*Q + F}; PI <
some web-based companies that produce their prod- -function (Q){(P - v)*Q - 100}; curve(TR, -10, 80, ann
ucts after they receive customer orders. In this case, = FALSE, las = 1, cex = 1); curve (TC, -10, 80, add =
TR and TC curves are linear so the profit curve is also T); curve (PI, -10, 80, add = T); abline (h = 0, v = 0);
linear and there is only one breakeven point at the in- QB < -F/(P - v); QB; abline (h = 140, v = 20, lty = 2);
tersection of TR and TC curves which corresponds to title (xlab = ”Quantity (units)”, ylab = ”TR, TC, Profit
the point where the profit curve intersects the horizon- ($)”, main = ”Figure 1. Breakeven Analysis: Unstable
tal axis. This is a special case of a perfectly competi- Perfectly Competitive Firm”, cex.main = 1, sub =
tive firm since TC is linear which along with linear TR Case 1: Horizontal Demand Curve (not shown) and
curve generates a linear profit curve that increases in- Linear Profit Curve.”, cex.sub = 1); text (40,300,
definitely as production and sales increase. This is an substitute (TR)); text (40,200, substitute (TC)); text
unstable situation with no equilibrium. (40,100, substitute (Profit)); text (15,155, substitute
(“BE pt”)); text (15,15, substitute (“BE pt”));
Let price, P = $7/unit, variable cost, v = $2/unit,
fixed costs, F = $100, and target profit = $100. Q =
QE is expected sales volume.
The first two columns in Table 2 show the demand
schedule where the price per unit is fixed thus giv-
ing rise to a horizontal demand curve at price =
$7/unit, where units are plotted on the horizontal
axis and price on the vertical axis. This horizontal
demand curve describes the behavior of a typical
small “price-taker” firm in a perfectly competitive
market selling an undifferentiated product at the
given market price to customers who have perfect
information about the market so no promotion is
required. This firm can sell its entire production at
the market price and would be unable to sell at a
higher price and there is no incentive to sell below
the market price. Fig. 1. Breakeven analysis: unstable perfectly competitive firm

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Innovative Marketing, Volume 7, Issue 3, 2011

3.4. Perfectly competitive firm – downward sloping dratic formula provides the two roots (breakeven
demand & quadratic profit curves. A firm in a per- points) for this profit function.
fectly competitive market faces a horizontal demand
QBi = [-B ± ¥(B2 – 4AC)]/2A,
curve. This implies no pricing power since the firm is a
price-taker and it can sell its entire (homogeneous) where, i = 1, 2; A = b, B = a-v and C = -F.
production at the market price thus its TR is a positive-
Enter these values in the breakeven formula (qua-
ly sloped straight line that increases indefinitely. A
dratic formula) to obtain the following:
more typical perfectly competitive firm will have a U-
shaped (or inverted S-shaped) TC curve that along QBi = [-8 ± ¥(82 – 4 (-0.10)(-100))]/2(-0.10), or QBi
with a linear TR curve would generate a quadratic = = [-8 ± ¥24]/-0.20, therefore the two breakeven
profit curve and two breakeven points. The quadratic points (roots) of the profit curve are as follows:
formula can be used to solve for the two roots or brea-
QB1 = 15.51 units and QB2 = 64.50 units.
keven points of the profit function. These roots may or
may not be distinct, and they may or may not be real. By entering these quantities in the demand curve, the
If the expression under the square root, called the dis- two corresponding prices are obtained as follows:
criminant, is zero then there is only one real root. If the
PB1 = $8.45 and PB2 = $3.55.
discriminant is negative then there are two distinct
non-real or complex roots. If the discriminant is posi- This situation can be depicted by plotting the quadratic
tive then there are two real roots. Therefore, this analy- profit curve that intersects the horizontal axis at the two
sis is restricted to those situations where the discrimi- breakeven points: QB1 = 15.51 units and QB2 = 64.50
nant is zero or positive so one or two distinct real roots units. At these two breakeven points, the TR = TC.
are obtained. In this stable situation, an equilibrium
between supply and demand is achieved since the
profit function is quadratic and MC slopes upward to
intersect MR = AR curve, indicating maximum profit
(MR = MC) that lies between two breakeven points.
The linear TR curve is based on a horizontal demand
curve at a given price level that is determined by the
market supply and demand.
Case 2. Imperfectly competitive firm – downward
sloping demand curve.
An imperfectly competitive firm has some control over
its price and is faced with a downward sloping demand
curve, a quadratic profit function that implies two
breakeven points, so the maximum profit (MR = MC)
and target profit would lie between these two breake- Quantity (units)
Case 2: Downward sloping demand curve and Quadratic Profit Curve.
ven points. Most real world markets are imperfect
where buyers and sellers do not have perfect informa- Fig. 2. Breakeven analysis: an imperfectly competitive firm
tion, firms use promotion to inform and persuade cus-
In Figure 2, the quantity is plotted on the horizontal
tomers, products are differentiated, and firms compete
on price as well as on non-price variables of the mar- axis while TR, TC and profit are plotted on the ver-
keting mix. In fact, much of marketing management is tical axis. Both breakeven points and the maximum
about customer satisfaction and customer relationship profit (at MR = MC) are also shown. Figure 2 and the
management in an imperfectly competitive market. two breakeven points or roots of the profit function
were obtained by using this R code:
This example is adapted from Scheuing (1989) and
Kotler (1967). Consider a company that produces v < -2; F < -100; P < -c(0,10); Q < -c(0,100); P < -
and sells widgets and faces a downward sloping li- function (Q){10-0.10*Q}; TR < -function(Q){(10 -
near demand curve, Q = 100 í 10 P, the inverse of 0.10*Q)*Q}; TC < -function(Q) {v*Q + F}; PI < -
which (with Q on the horizontal axis and P on the function(Q){-0.10*Q^2 + 8*Q -100}; curve(TR, 0,
vertical axis) is P = 10 – 0.10 Q, so a = 10 and b = 100, ann = FALSE, las = 1, cex = 1); curve (TC, 0,
-0.10. If v = 2, and F = 100, then 100, add = T); curve (PI, 0, 100, add = T); polyroot
(c(-100,8,-0.10)); abline (h = 0, lty = 2); abline (h =
Ȇ = AQ2 + BQ + C,
131.018, v = 15.5051, lty = 2); abline (h = 228.9569, v
where A = b, B = a í v and C = -F, or A = b = -0.10, = 64.4949, lty = 2); abline (h = 60, v = 40, lty = 2); title
B = a í v = 10 í 2 = 8, and C = -F = -100. The qua- (xlab = ‘Quantity (units)”, ylab = “TR, TC, Profit ($)”,

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 Innovative Marketing, Volume 7, Issue 3, 2011

main = “Figure 2. Breakeven Analysis: An Imperfectly gression estimates; the regression coefficients for the
Competitive Firm”, cex.main = 1, sub = (“Case 2: three marketing mix elements are statistically signifi-
Downward sloping demand curve and Quadratic Profit cant and have correct signs. However, the intercept
Curve.”), cex.sub = 1); text (40,250, substitute (TR)); shows that the mean effect of excluded variables
text (40,190, substitute (TC)); text (40,70, substitute is positive and significant implying that the model
(Profit)); text (15,145, substitute (“BE pt 1”)); text is probably misspecified. In order to properly spe-
(65,240, substitute (“BE pt 2”)); text (15,10, substitute cify this model, this company should search for
(“BE pt 1”)); text (65,10, substitute (“BE pt 2”)). some important excluded variables and include
them in this model. Regression analysis using
These examples utilized linear TC curves but a more dummy variables is another alternative method
general TC curve would be U-shaped (or inverted S- that should be explored.
shaped) indicating economies of scale and diseco-
nomies of scale. A more complete analysis of the Table 3. Marketing mix selection using breakeven
demand and cost curves for profitability and brea- and profitability analyses
keven analyses should include all relevant factors No. P ($) A ($) D ($) QE (units)
and their impact on demand and cost. Such factors 1 16 10000 10000 12400
include prices of complementary and substitute 2 16 10000 50000 18500
products; buyer’s income; promotional expenditures 3 16 50000 10000 15100
and other expenses including those for market re- 4 16 50000 50000 22600

search, training of marketing personnel, product 5 20 10000 10000 5500

6 20 10000 50000 8200
quality, distribution decisions, etc.
7 20 50000 10000 6700
4. Marketing mix selection and 8 20 50000 50000 10000
demand estimation 9 24 10000 10000 3500
10 24 10000 50000 6200
4.1. Marketing mix selection. Consider the follow- 11 24 50000 10000 5500
ing example that is adapted from Kotler (1967) and 12 24 50000 50000 8500
Scheuing (1989) to illustrate estimation of demand
curve, and use of breakeven and profitability analyses Let the variable costs per unit, v = $10, overhead
to determine an appropriate marketing mix for a costs allocated to the product under consideration,
company in an imperfectly competitive market. O = $38,000, so the fixed costs are F = O+A+D. Us-
ing the quadratic formula, the two breakeven points
The expected quantity demanded for the company’s (roots) can be calculated for the profit function. The
product (QE) is forecasted based on its price (P), first breakeven point will be of higher significance
advertising budget (A), and distribution budget (D) than the second breakeven point because it would
using historical data and input from salespeople and be achieved first. The marketing mix that is asso-
management. Here, the three marketing mix ele- ciated with the first breakeven point should serve
ments have these levels: P = $16, $20 or $24; A = as a point of departure in marketing mix selection.
$10,000 or $50,000; and D = $10,000 or $50,000. This initial decision could be improved by explor-
ing the marketing mix that would maximize profitat
The following R software code for regression analy-
at MR = MC.
sis and the data in Table 3 produced these results:
Multiple linear regression example 4.2. Estimating product demand and market
shares. The above example about marketing mix
fit < -lm(QE ~ P + A + D, data = mktmix) selection did not specifically consider the product
summary (fit) # show results element of the marketing mix decision. It can be
QE = a + b A +c D + d P assumed here that the product under consideration
was a mid-level product based on its features. A
QE = 33,360 + 0.0059 A + 0.1054 D – 1,403 P more comprehensive marketing mix decision would
(0.00001) (0.001) (0.01) (0.05) consider product aspects as well. The discussion
below elaborates upon the product aspects using
Here, multiple R = 0.8567, adjusted R2 = 0.803, F-
2
Apple’s iPad and iPad 2 as an illustration.
statistic = 15.95 with 3 and 8 degrees of freedom, and
p-value = 0.0009756. Thus the regression model is Table 4 shows that Apple’s most basic iPad 2 (16
statistically significant and it is the best prediction GB+Wi-Fi) sells for $499 and it includes all features
model based on these three independent variables. except higher storage and 3G that cost more. All
The p-values are given in parentheses below the re- iPad and iPad 2 have Wi-Fi.

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Innovative Marketing, Volume 7, Issue 3, 2011

Table 4. Prices and features of iPad and iPad 2

iPad prices in 2010 at its iPad prices in 2011 at iPad 2 prices in 2011 at its
No. iPad specs iPad 2 specs
introduction iPad 2 introduction introduction
1 16 GB+Wi-Fi $499 $399 16 GB+Wi-Fi $499
16 GB+Wi-Fi, 3G (AT&T or
2 16 GB+Wi-Fi, 3G AT&T $629 $529 $629
Verizon)
3 32 GB+W-Fi $599 $499 32 GB+W-Fi $599
4 32 GB+W-Fi, 3G AT&T $729 $629 32 GB+W-Fi, 3G (AT&T or Verizon) $729
5 64 GB+W-Fi $699 $599 64 GB+W-Fi $699
6 64 GB+Wi-Fi, 3G AT&T $829 $729 64 GB+W-Fi, 3G (AT&T or Verizon) $829

iPad was a breakthrough product that, upon its in- crete choice problem. Following Lancaster (1971),
troduction in 2010, created or redefined tablets, a information from Consumer Reports can be used to
new product category, it sold 15 million units during construct expected market shares for various brands by
that year. iPad 2 includes many more and better fea- using rank data. Williams (2011) reported that Con-
tures than iPad but is offered for sale in 2011 at the sumer Reports compared several iPad tablets with
iPad prices of 2010, while each iPad now sells at those of its competitors (Dell, Archos, Samsung, Mo-
$100 less than its introductory price in 2010. Apple torola and View Sonic) on 17 criteria and concluded:
also sells software through its App Store, accessory “The Apple iPad 2 with Wi-Fi plus 3G (32G), $730,
products, and upgrades that generate additional rev- topped the Ratings, scoring Excellent in nearly every
enue for the company for this product category. category.” Such information, along with actual sales
iPad offered six product variations based on three data, and their own marketing plans can help marke-
levels of capacity (16 GB, 32 GB, 64 GB), one type ters determine their present/future market shares and
of color (black), and two Internet options (Wi-Fi, estimate demand for their products compared with
3G-AT&T). iPad 2, however, offers eighteen prod- those of their competitor’s.
uct variations based on three levels of storage (16 Conclusion and future research
GB, 32 GB, 64 GB), two types of color (black or
silver), and three Internet options (Wi-Fi, 3G- This paper presented a general framework for select-
AT&T, 3G-Verizon). The choice of 3G carrier adds ing marketing mix elements for profit maximization
$130 to the equivalent Wi-Fi only version. The and utilized R software for analyses. Managers can
charges for signing up with the wireless carrier are utilize a similar approach to facilitate their own mar-
separate and are paid to the carrier. keting mix decisions. Breakeven and profitability
It is estimated that the bill of materials and the cost of analyses are powerful tools for managerial decision
manufacturing the 32 GB+Wi-Fi+3G iPad for Apple is making; however, often these tools are not properly
estimated to be between $270 to $320 (Murphy, 2011). used. Firms compete under different market struc-
Since this product sells for $729, it would leave $409 tures and their optimal decisions vary according to
to $459 for Apple to cover its marketing and manage- their market structures and other relevant environ-
ment costs and the rest would be its profit margin, so it mental factors. The simplest case is that of an unsta-
is very profitable for Apple (Snell, 2011). ble perfectly competitive firm that has an indefinitely
increasing profit curve that generates indefinite profit
Lancaster (1971) presented a new approach to esti- after the breakeven point. Unfortunately, this simple
mate demand based on product characteristics instead case has been applied across the business and market-
of consumer preferences as used in the traditional ing literature for situations involving imperfectly
approach to demand estimation in economics. So for competitive firms where a different profitability and
iPad 2, instead of considering 16 different demand breakeven analysis would be more suitable. A per-
curves, we may consider only storage, wireless carri- fectly competitive firm faces a horizontal demand
er, and price to estimate demand. This approach curve at the given market price and would not need a
would be much more efficient and revealing than the marketing manager; there is no need for promotion
traditional approach to estimating demand based on since the customers have perfect information; and the
consumer preferences for all product choices. Under- firm can sell its entire production at the market price.
standing product demand based on properties or cha- A horizontal demand curve is valid for perfectly com-
racteristics of products is closer to conjoint analysis, petitive firms that sell homogeneous products; it is
which is a frequently used method in marketing invalid for imperfectly competitive firms that sell dif-
theory and practice. To develop a characteristics-based ferentiated products, compete with small or large com-
demand curve, products from Apple and those from its petitors, and their customers have less than perfect in-
competitors would be analyzed. The consumer buyer formation about the products and firms so the firms
would typically choose only one tablet so this is a dis- promote their products to influence customer demand.

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 Innovative Marketing, Volume 7, Issue 3, 2011

A proper understanding of customer demand is a petition, economy, government regulations, tech-

critical aspect of marketing management since cus- nological changes, etc., would influence these de-
tomer satisfaction is critical for marketing success. cisions.
So to make the most profitable price, quantity, and
marketing mix decisions, managers should estimate Many firms sell more than one product and for a mul-
their demand curve. Even a rough estimate of the tiproduct firm, its one product may be in a monopoly
demand curve is better than no estimate at all. Typ- situation, while another may be in an oligopoly, and
ically the demand curve would be downward slop- still another may be in a monopolistic or perfectly
ing to the right. Price sensitivity or price elasticity competitive market. Over time, the market conditions
of demand should be considered in setting the right may change so a monopoly situation may become an
price for a product. A company that plans to intro- oligopoly, a monopolistic competition, or a perfect
duce a new or a modified product to the market competition as other companies enter or leave the
must answer some important questions regarding market and the market structure changes. Enlightened
its breakeven and profitability analyses. Many fac- marketing managers should consider the social costs
tors, like its marketing mix, market demand, com- and benefits of their decisions as well.
References
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