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David B. Montgomery** and Glen L. Urban**

248 — 67
March, 1967






David B. Montgomery** and Glen L. Urban**

248 — 67 )
March, 1967

Comments and criticisms are solicited, but this paper may not be cited
or reproduced without the written permission of the authors.

** The authors are Assistant Professors of Management in the Alfred

P. Sloan School of Management, Massachusetts Institute of Technology



David Bruce Montgomery
Glen Lee Urban


All Rights Reserved


This paper is a working draft of Chapter 4 in

Management Science in Marketing


David B. Montgomery

Glen L. Urban

Sloan School of Management
Massachusetts Institute of Technology



Advertising and promotional expenditures have become significant in
the marketing of many products. In 1966 about 16 billion dollars was
spend on advertising alone. This expenditure is made because advertising
has a vital communication function to play in marketing as part of the
overall communication mix the firm utilizes to inform and convince
customers of the desirability of its products. The discussion in this
chapter will be largely restricted to advertising decisions, but the
management science techniques discussed are also relevant to other
promotion and communication decisions.

The marketing manager faces many decisions in advertising. Some
of these decisions are shared with his advertising agency, but he and
his technical advisors should have an understanding of each decision
area in order to insure the quality of the decisions. In advertising,
decisions must be made regarding the goals of the advertising expenditure,
the appeals to be used, the size of the overall budget, the media to be
used, and the copy to be employed. These decisions are interrelated.
For example, the media schedule cannot be determined until the budget is
specified, but the effectiveness of the schedule may affect the budget
necessary to achieve the specified goals. It would be desirable to specify
all these decision solutions simultaneously, but this is an extremely
complex problem. To relieve this complexity, advertising decisions may
be placed in a hierarchy. In Figure 4-1, an order of decision making is


outlined. In given decision situations, this hierarchy may be varied.
For example, the budget may be determined before the specific appeals are
identified, but the budget decision must be made with some estimate of
the probable effectiveness of the appeals that will be created. Likewise,
media decisions will reflect copy considerations, since the size of the
ad will be a factor in determining media schedules. For purposes of
exposition this hierarchy will be utilized in this chapter. As decisions
are discussed, the interrelations between them will be developed.
In Figure 4-1 certain of the important interactions which are exceptions
to the hierarchy are denoted by dashed lines.


Define Advertising Goals


— >

Determine Appeals



Determine Budget


Develop Media Schedule

( 1

^Detailed Copy and Format Specification


Final Campaign Specifications



4. 1 Determination of Advertising Goals

In its widest context advertising should be viewed as an investment,
so the goal of advertising should be to maximize the returns on the
investment. This implies a measurement of the profit implications of
advertising expenditures. This is the most desirable goal, but the
problems in identifying profit effects are considerable. In an effort
to express the goal of advertising in measurable terms, several alter-
native criteria have been suggested. In Table 4-1 a list of possible
advertising goal criteria is given. The criteria are listed in order
of increasing relevance to the investment decision, but this listing also
is one of increasing measurement difficulty.

I. Exposure

A. Total Exposure

B. Frequency (Impact)

C. Reach (Coverage)
II. Awareness

III. Attitudes
IV. Sales
V. Profits



The first criteria possibilities pertain to the exposure to advertising.

The exposure criteria refer to a relevant segment of the total population.


The relevant segment is a target group of people who are potential and
desired customers. For example, a target group may be all men between
25 and 35 with incomes above $8000. The exposure criteria attempt to
measure various levels of exposure to advertisements within given target
groups. The definition of target groups is necessary before meaningful
advertising goals can be established. This relates to overall marketing
strategy decisions. In the remainder of this chapter it will be assumed
that the target group (or groups) is known.

The three principal exposure criteria which have been proposed are
total exposures, frequency (impact), and reach (coverage). While these
have been termed exposure criteria, a more descriptive term might be
"potential" exposure. This more descriptive label reflects the fact that
exposure measures generally reflect exposure to the medium which contains
the advertisement. This is something different than actual exposure to
the ad. For example, a subscriber to a particular issue of Time magazine
will have had potential exposure to all ads in that issue, yet he may,
in fact, only have been actually exposed to a few of those ads - those
in the pages which he happens to glance at or read. Special studies
may be used to estimate the extent of this audience shrinkage. Data
from these studies may then be used to adjust exposures. In the remainder
of this discussion the term exposure will be used to denote either
potential or adjusted exposures. Time, cost, and feasibility constraints
will dictate which is used in any practical situation.

The total exposure is the sum total of the number of times any


advertisement relating to the product is seen or heard by target group
members in a given period. Letting

A. = number of target group members in the audience of

medium i (i=l I)

N. = number of advertisements in medium i during the time

period of interest,
the total exposure to the N N insertions in the respective media

is given by

T = E A.N. ,
^ i=l ^ ^

where T denotes total exposures,

The frequency or impact is the average number of advertisements for

the product seen by each member of the target group during the given

period. If there are M individuals in the target group, the frequency

is just

F = T /M

where F denotes frequency. Frequency is an important criterion measure

whenever the response to the product's advertising is thought to have an

"S-shaped" relationship to cumulative exposures or whenever there is

a threshold number of exposures required in order to trigger the desired

response (purchase) on the part of target group members.

The reach or coverage of advertising is defined as the total number

of people exposed to at least one advertisement relating to the product

in a given time period. The two subcategories of reach are cumulative


audlence and net coverage. They are defined as :

Cumulative audience = the reach of two or more issues of a given medium,
Net coverage = the reach of a combination of single issues of two or
more media
For example, cumulative audience would refer to the total number of target
group members who will be exposed at least once when successive weekly
insertions are made in Life magazine. Net coverage would refer to the total
number exposed at least once when insertions are made in single issues
of Life and Time . In order to encompass both cumulative audience and net
coverage in the discussion below, a medium will be defined as a single
insertion. For example, two successive insertions in Life could be
considered as two separate media in this discussion.

Reach measures the number of different people in the target group who
are exposed one or more times to a given campaign in a set of media.
For the case of two media, say media 1 and 2, the reach of a single
insertion in each medium will be

R = A^ + A^ - A^2

where R = the reach or number of persons exposed to one or

more of the two insertions
A, „ = the duplication between medium 1 and medium 2
and A, and A„ are as previously defined. Note that A „ measures the extent
of overlap in exposures within the target group between the two insertions.
That is, A^ „ represents the number of target group members who will be
exposed to both ads. For insertions in three media, the reach will be

R = A^+A2+A3-A^2-^13-^23^^23


where ^i?-? ~ ^^^ triplications among media 1,2, and 3

(i.e. the number of target group members who

will be exposed to the ads in each of the

three media) .

In general, for I media the expression for reach will be

R = S (-l)^'^A

1 I

where A = E A. = total target group members in the audiences

i-1 ^

of media 1, . . . , I

2 ^ ^

A = E E A. . = the total of all pair wise duplications

i=l j=l ^^

of the I media

3 I I I

A = E E E A. ., = the total of all triplications
1=1 j=l k=j

A = E E .. . E A. .
1=1 j=l q=p

These results follow from set theoretic considerations.

The equation for the reach of I media requires a great deal of data.
For example, for 1=5, it will be necessary to know (or have estimates of)
the target audience overlap between each pair of media, each triplet of
media, each group of four media in addition to the overlap among all five
media and their individual total audiences in order to determine the reach
of simultaneous insertions in each of these five media. The measurement

problem involved is tremendous. Fortunately, it appears that short cut

estimation procedures are useful. Agostini , utilizing an extensive

French study of audience duplication, triplication, and up to 15-tuplication,

found that the total reach for magazine insertions may be estimated by

, ^*^

2 1

This formula was found to be an excellent approximation to total reach

for French magazines when K=1.125. The relation is also approximately

true for American and Canadian magazines. For a theoretical discussion

see Claycamp and McClelland. The Agostini formula is particularly

useful in estimating reach for media where data for higher than second

order replications among the media audiences is not available.

The criteria relating to exposure are relatively simple to measure

since they depend only on readerships of various media, the number of

insertions, and the total number in the target group. Making advertising

decisions on the basis of exposure, however, assumes a direct relationship

between the ultimate advertising returns — profits — and exposures to



Exposure merely relates to the potential for having seen and noticed
a particular ad. Awareness, on the other hand, implies some ability to
recall an advertising message. Measures of ad awareness are available
commercially through such services as Starch and Gallop-Robinson. These
services use recall and aided recall techniques in surveys of potential
readers of ads in order to determine the extent to which particular ads
are noticed and remembered. Since awareness is somewhat closer to the
ultimate sales and profit goals of advertising, it would seem that it
might be a better prediction of the sales and profit effects of advertising


than exposure measures.


Attitude changes may be used as the criterion by which advertising
performance is judged. The firm may monitor attitudes related to specific
product attributes or to overall attitudes such as brand, total product,
and corporate images. Advertising may then be designed and evaluated in
terms of attitude changes which the firm believes will ultimately enhance
sales and profitability.

An interesting conceptual model of the progress of a consumer from
unawareness through attitude change to ultimate purchase has been given
by Lavidge and Steiner . They postulate the hierarchy of effects illus-
trated in Figure 4-2 . The consumer is seen as passing from a lack of
awareness about the firm's products to a state of awareness of the firm's
offerings. Awareness is followed by knowledge of the product's character-
istics. Advertising plays an informative role in both of these steps.
In terms of liking, preference and conviction, advertising plays the role
of persuader. It is at these steps that attitude change would seem to
be an appropriate measure of advertising effectiveness. The final step,
purchase, relates to the sales criterion discussed below.

While considerable progress has been made in attitude measurement ,
there are limitations in its use as a criterion of advertising performance.
It is a relatively costly and time consuming procedure and the representative-
ness of the sample from which attitudes are obtained is often open to
question in terms of generalization to the population of potential customers.










In addition, the link between attitude change and sales is not direct in
that it is known that attitude change may follow a purchase rather than
precede it. '


Several researchers have used sales as a criterion to


evaluate advertising expenditures. For example, Benjamin and Maitland
analyzed four different models of sales response to advertising using data
from five separate advertising campaigns. Although none of the models


provided a uniformly good fit to the data , the best sales response to

advertising relation was given by a logarithmic equation of the form

R = a £n A + b
where R = sales response to A

A = advertising expenditure

a,b = constants.
This relation was initially proposed on the basis of ^ priori reasoning
which suggested that advertising might be considered analogous to a
psychological stimulus and hence might be expected to have a logarithmic
relation to sales response, a relation which is common in psychophysical
research . The empirical results which they obtained suggested that

a. there is a threshold value of advertising expenditures
(A) below which there is no appreciable response

to advertising

b. saturation (diminishing returns to advertising) eventually
sets in

With reference to item a recall the discussion of the potential importance

of frequency as an exposure criterion when there is likely to be such a

threshold effect.

Banjamin and Maitland have gone on to link the sales response to

profit. If

r = profit margin per unit of product sold

X = a proposed percentage increase in advertising,

then the increment in R, (AR) , resulting from an increment in A,(AA), will be

AR = a Jin



and the criterion for increasing advertising by x per cent is

r a ^n(l^) - ffg - '^
where A is expressed in terms of cost and K is a prescribed minimum
increase in revenue.

In a later paper Banjamin, Jolly and Maitland proposed a time response
function to an advertising pulse based upon an equation of the form

R = a e"^*^ (1+ct)'^
where R = weekly sales response following a single

advertising pulse,

t = time in weeks measured from the time of the
advertising pulse,

a,b,c, and d are constants which must be estimated.
The model was again posited on a priori grounds, this time by analogy to
epidemiological phenomena such as infection, incubation, and immunity.
The appeal of this epidemic analogy to advertising response is based upon
the intuitively appealing notions that:

1. Advertising is concerned v/ith the spread or diffusion of an idea,

2. Some people may not be susceptible to the idea,

3. It takes time for an idea to take root, and

4. The ideas in an ad need not be simultaneously communicated to all
persons in the community - i.e. there may be word of mouth trans-
mission of the initial message.


While the fit of this model to their data was not especially good , they

concluded that "the data suggest a response distribution over time with a


very sharp rise to a maximum and a subsequent gradual decline."

A significant problem in the measurement of sales response to adver-
tising is the likelihood that the sales response to an advertisement may

continue over many periods, perhaps even years. Palda in an analysis

of the cumulative effects of advertising for Lydia Pynkham's found that

there indeed is such a carryover effect . Behavioral mechanisms which

may result from
may generate such carryover effects / the fact that consumers may learn

to buy the advertised brand or product or the ad may convert them to

1 fi
hard core loyal customers for the firm

The attempts to establish sales-advertising relationships have been
plagued by statistical problems related to isolating the effects of
advertising. The problems involved in using historical data have been
lucidly discussed by Ouandt . After reviewing the pitfalls in using
cross-sectional models, single equation time series models, and simul-
taneous equation time series models, Ouandt concludes that there is a
need to return to classical experimentation in order to measure the sales

1 Q

effects of advertising. Buzzell reported such an approach at du Pont.

In spite of the measurement problems involved, sales and profit
represent the best criteria for advertising goals if their dependency on
advertising can be established.

Summary on Advertising Goals

In selecting the criteria to be used in setting goals for advertising
a compromise is necessary between the accuracy of measurement and relevance
of the criteria in achieving the overall objective of maximizing the profit


produced by the advertising investment. If results and decisions are not to
be judged on the basis of profits, then one must explicitly or implicitly
assume a relationship between the response measured (e.g. exposure, aware-
ness, attitudes) and profits. Given a relationship between profits and
the criteria listed in Table 4-1, the overall goal of maximizing profits
can be translated into more measurable criteria such as reach, frequency,
awareness, attitudes, or sales. For example, the goal for advertising in
a target group may be to create a specified level of awareness. This is
meaningful if level of awareness was determined by a consideration of the
relationship of advertising to awareness and awareness to attitudes ^'^•d attitudes
to sales so as to maximize the return on the advertising investment. The
use of the more easily measured criteria will become more practical as
lower levels of the decision goal hierarchy (see Figure 4-1) are reached.

Assuming that the overall goal of advertising is to maximize profits,
this section has discussed how this overall goal could be expressed in
terms of criteria that are more measureable. The price paid for the ease
of measurement of the criteria is a difficulty in tracing the explicit
effect of the criteria on advertising profits. Ignoring the problem of
linking lower level criteria to profits is not satisfactory. A better
approach is to attempt to make the relationships explicit rather than
treating the relationships as implicit assumptions.

4.2 Creating Advertising Appeals

With a satisfactory set of overall goals and subgoal criteria in mind,


the next problem is to generate an appeal that will be most effective in
achieving these goals. The creation of appeals to be used in advertising
is based upon a sound understanding of the firm's consumer market. In
particular the behavioral characteristics of the firm's target group for
this campaign must be clearly identified and understood. These character-
istics will include the psychological, sociological, and social-psycholog-
ical factors affecting their behavior. Theories of consumer behavior based
on notions of perceived risk, cognitive dissonance, images, social norms,
economic utility, and personality will be relevant to this decision. It
is not within the scope of this book to discuss these topics. Management
science applications have largely been outside this area. This is perhaps
because the factors do not lend themselves to quantification and because
the problem is largely an exercise of behavioral science knowledge and
creative intuition. Management science can be useful in evaluating alter-
nate campaigns, but the creation of viable alternate appeals has largely

remained outside the scope of management science efforts up to this time.

There is no conflict between the creative and research or management science
aspects of this problem. Both functions are compatable; research and eval-
uation techniques will help place appeals in relative positions of effect-
iveness as well as suggest new appeals. The management scientist and the
behavioral scientist must both display creativity in the generation and
evaluation of the appeals.

4. 3 Determination of the Advertising Budget

Once the appropriate appeals for a potential campaign have been


detennined, the overall level of commitment to the campaign must be estab-
lished. While the selection of appropriate appeals may have required
preliminary judgment as to the approximate size of the campaign, the
optimal advertising budget must be determined at this stage.

The advertising budget will be optimized with respect to the goals
which have been established for the campaign. While several goal criteria
are available (as discussed in Section A.l), budget determination generally
has a sales or profit goal as the optimization criterion. It should be
emphasized once again that long run profit maximization is the ultimate
goal even though a more measureable subgoal may be used as the explicit

A Simple Model

In the simplest case current advertising is the only variable
affecting current period sales. That is,

q = f(A)
or quantity (q) sold in the current period is a function of current period
advertising (A). Letting p denote unit price, Pr denote total profit,
and C(q) denote the total cost of producing and marketing (exclusive of
advertising) q units during the current period, the total profit may be
expressed as

Pr = pq - A - C(q)

= p f(A) - A - C(f(A))
If q=f(A) and C(q) - C(f(A)) are dif ferentiable functions and if there are
decreasing returns to advertising at some level of A, then classical


optlmization procedures may be used to solve (4.?-l) for the profit max-

imizing budget level of advertising . If variables other than advertising

affect demand, a multivariate version of this simple model may be developed

Dynamic Models

If the advertising decision made in the present period will have

impact on sales and profits in future periods, the budget problem becomes

more complex in that it takes on dynamic aspects. A simple model for

determining an advertising budget in the presence of carryover effects

is given by Julian Simon. He assumes that revenues realized in future

periods due to an advertising expenditure in the present period will

decrease by a constant rate per period into the indefinite future. In

addition, there will be sales revenue realized in the present period even

if the present advertising budget is zero. This is due to the carryover

effects in the present period of previous advertising. If b denotes the

retention rate of sales revenue per period (i.e. b = 1-f constant rate of

revenue decline per future period]) and i denotes the firm's cost of

capital, the discounted present value in period t of all present and future

revenues generated by an advertising expenditure of A in period t is given by

PV(A ) = [AR(A )]


where AR(A ) represents the incremental net sales revenue generated in the
present period (period t) by the expenditure of A for advertising. The


sales revenue is the net of incremental gross revenue and production
costs. Profit from advertising in the present period is given by

Pr = PV(A^) - Aj.

The profit maximizing rule is to continue advertising in period t until the
increase in PV(A ) due to AA is just equal to AA . It should be noted
that this model concentrates upon a single period budget decision.

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Online LibraryDavid Bruce MontgomeryAdvertising decisions → online text (page 1 of 4)