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Information model of the economic efficiency of advertising
Alina Vinkovska1,*, Arnold Kiv1, Tatyana Koycheva1, Liliia Bodnar1, and Ivan Donchev1
1South Ukrainian National Pedagogical University named after K. D. Ushynsky, Odessa, Ukraine
Abstract. The development of the economy and trade has led to the widespread use of
advertising and the need for its constant improvement. There is a vast field of advertising theory.
This paper proposes an information model of the functioning of advertising. We introduce ideas
about useful and harmful (excess) information. The concept of user’s thesaurus is also
introduced. The effectiveness of advertising is determined by the mutual influence of useful and
redundant information. Differential equations are formulated on this basis, the solution of which
allows to establish the patterns of the influence of psychological characteristics of users and the
mode of presentation of information on the effectiveness of advertising.
1 Introduction: state of the advertising
research
The advertising research has two directions. One of them
consists in the staging of purposeful experiments and the
creation of empirical formulas describing the identified
experimental consistency. Another direction is the
development of models and the mathematical description
of these models. Then a comparison with experiment is
carried out.
In [1-3] experiments were described to examine
memory interference in an advertising context. The
processes of remembering and forgetting advertising
blocks in the human’s brain are depending on the quality
of blocks, clarity of advertisement.
At first, consumer memory for some advertising was
inhibited as a result of subsequent exposure for other
products in that manufacturer's product line and for
competing products in the same product class. It happens
preferably in the case of some kind of advertisement
which is more attractive. Next, an experiment was
performed which showed the analogous interference
effects. In the third case it was obtained that the presence
of advertising for competitive products changes the
relationship between the repetition and consumer
memory. Repetition had a positive effect only when
there was little or no advertising for similar products [4].
This effect was also studied in the works [5, 6, 21, 24,
27, 29], in which the found experimental patterns are
described using empirical formulas.
Mathematical models in this field have been
developed for a long time [6-9, 20, 31-33]. They
described empirical results in mathematical language. By
this way, fundamental patterns are obtained. In [10-16,
39] a dynamic model of the company’s sales dependence
on advertising costs is constructed. It was shown that the
advertising allows you to increase sales, but the
dependence of increasing demand from increased
advertising costs is not linear. Authors claimed that the
advertising does not work instantly, since its inception,
the information is accumulated in the minds of people
with each meeting with advertising and reaches the peak
after a certain time.
In our work, we use some representations of
information theory for the implementation of an
information approach with the aim of increasing the
effectiveness of advertising.
Presentation of advertising is essentially a message of
information to the consumer [17-19]. Therefore, the
problem of increasing the effectiveness of advertising is
reduced to considering the quality of the information
presented, the mechanisms of its creation and
presentation to the recipient, the psychological
characteristics of perception of information by the
recipient.
When creating advertising, along with clearly marked
target information, extra information is usually added to
“decorate” advertising [22, 26, 28]. This immediately
affects the perception of useful target information.
Further, in the course of the operation of advertising (in
the course of its multiple presentations), the effect of
“redundant information” arises.
This effect increases with time, prevents the
perception of useful information and depends on the
psychological characteristics of the recipient.
Information theory introduces the concept of
information usefulness. Bongard [37] connects the
usefulness of information with an increase in the
probability of achieving the goal after receiving a
message, in accordance with the formula:
𝑉 =𝑙𝑜𝑔2 (𝑃’/𝑃) (1)
Here, P and P' are the probability of achieving the
goal before and after receiving the information.
SHS Web of Conferences 65, 04022 (2019) https://doi.org/10.1051/shsconf/20196504022
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© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution
License 4.0 (http://creativecommons.org/licenses/by/4.0/).
According to formula (1), the redundant information
has zero value. However, in many cases, redundant
information turns out to be useful and even necessary
[38, 40-42].
In the case of the creation and operation of
advertising excess information harms, reducing the
effectiveness of advertising.
In the majority of works devoted to study the
properties of advertising, it is believed that over time (an
increase in the number of repeated presentations of
advertising) there is an accumulation of information (I)
perceived by the recipient (for example, [1-4]).
In fact, from the very beginning the advertising
presents the necessary information for the recipient, and
at subsequent presentations the new information is not
added. Therefore, to talk about the accumulation of
information for the recipient over the time of the
functioning of advertising (increasing the number of
presentations) is not entirely correct. That is why we
introduce the concept of “enhancing of the information
impact” which is not equivalent to the idea of the
accumulation of information.
2 Description of the information
approach in the advertising research
Usually the first perception of a new advertisement is
surface, inaccurate and not fully understood [25, 30, 34-
36]. Although the new information is not added,
subsequent presentations of this ad lead to the fact that
its content becomes more conscious, understandable,
more deeply perceived.
For a quantitative description of the process of
perception of advertising information, we found it
convenient to identify the process of deeper “mastering”
advertising with the accumulation of additional
information and introduce a function of the information
accumulation I = f(t). We assume that the number of
advertisements presented (n) is proportional to time (t).
With a large number of presentations of advertising,
its content is completely assimilated by the recipient and
after some time begins to be perceived as redundant
information. In this case, the accumulation of redundant
information adversely affects the perception of useful
information.
Thus, the perception of advertising depends on the
mutual influence of useful and harmful (redundant)
information. It is obvious that at the initial stages of the
functioning of advertising, the influence of useful
information prevails, but over time, as the accumulation
of excess information, the latter dominates. The period
of time after which the information begins to be
primarily perceived as excessive depends on the
psychological characteristics of the recipients and on
their thesaurus.
But not only redundant information with a large n
can adversely affect the perception of advertising. At the
very beginning of the presentation of advertising (when
it is created) it can contain harmful information that has
a negative impact on the perception of advertising.
Therefore, from the very beginning, the model should
take into account the impact on the recipient of positive
and negative information, as well as the interaction of
these two types of information. We will consider
positive information (contributing to the achievement of
the goal of advertising) with a plus sign and negative
information (reducing the effect of positive information)
with a minus sign.
3 Formulation of equations and
discussion of results
Naming by I1(t) and I2(t) the functions of accumulation
of positive and negative information, we write the
kinetic equations:
= (2)
= (3)
In equations (2) and (3) T is a thesaurus of recipients;
β is a coefficient of influence of the negative information
on the positive one and is a coefficient of influence of
the positive information on the negative one. It is
presumed that β, β' < 1. From equations (2) and (3) we
go to equation (4)
= { } . (4)
The last equation has a solution:
= +
(5)
where C1 and C2 are constants that are determined by
initial conditions.
Using (4) one can write expression for I2:
I2= 1
β T- ββ'C2et (6)
With initial conditions:
(0)= (0)= 0 ; (7)
we obtain:
=
; =
(8)
As a result, we get:
=
1 (9)
=
1 e (10)
For large enough time periods one can write:
=
[] (9’)
=
(10’)
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These results show that an accumulation of both
kinds of information (I1 and I2) depends on their mutual
influence. It is important that parameter values β and β'
change in the process of advertising functioning. The
competition of information I1 and I2 accumulation
processes leads to the conclusion about two stages of
advertising evolution. At the first stage, accumulation of
I1 information prevails and at the second stage
accumulation of I2 information prevails.
Considering solutions (9’) and (10’), we take into
account that these dependencies obtained are determined
primarily by the exponent. We also take into account that
at the first stage, β is small compared to β', and
practically does not change. There is only a gradual
increase in β'. This leads to the quality result illustrated
in Fig. 1.
Fig. 1. Schematic illustration of I1 information accumulation at
the first stage of functioning of an advertisement. The curve 1
corresponds to I1 accumulation and the curve 2 to I2
accumulation. The curve 3 is an accumulation of a total
positive information received by the recipient.
This situation persists at the first stage of the
functioning of advertising. I2 slightly decreases an
accumulation of I1. Expression (10’) does not adequately
describe the situation at the first stage, since the amount
of redundant information is still small
The situation changes at the second stage of the
functioning of advertising. Over time, the nature of the
mutual influence of the two types of information
changes. The effect of I2 on I1 increases, and the
influence of I1 on I2 drops. At the second stage of the
functioning of advertising negative (redundant)
information predominantly increases. This means that
the effect of positive information will be reduced and
although I1 according to formula (9) continues to
increase, but the “effective” value of I (I1+I2) decreases.
In fact, I1 turns into I2, because the accumulation of
redundant information in accordance with the model
reduces the “quality” of positive information, therefore –
its quantity. The noted patterns are qualitatively shown
in Fig. 2.
The perception of useful information throughout the
operation of advertising (in fact, its effectiveness) is
demonstrated in Fig. 3.
Based on the expressions (9) and (10) for the relative
effectiveness (δ) of advertising can be written:
=
(11)
I+ I= T
(e1) (12)
=
/
(13)
=
(14)
Fig. 2. Schematic illustration of accumulation of a total
information received by the recipient at the second stage. The
first and the second curves correspond to the accumulation of
positive information for two values parameters (
>
),
parameter β does not change. The third and the fourth curves
correspond to accumulation of negative information for two
values of parameter β (<), does not change. The fifth
curve corresponds to accumulation of total positive information
received by the recipient.
Fig. 3. Schematic illustration of total positive information
received by the recipient during two stages of functioning of
advertising.
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Formula (14) in accordance with our model shows
that relative effectiveness of advertising depends on the
influence of the value of parameter . As we noted
above, formula (9’) describes the accumulation of
positive information at the first stage of the advertising
operation and formula (10’) is applied to the second
stage.
Due to the quality of advertisement the action of the
advertising can be started in the different moments of
time. This means that advertising can be disconnected
for a while and then re-presented.
If the action of the ad starts at the moment t1 the
initial conditions will be formulated as:
()= 0; ()= 0 (15)
In this case using expressions (5) and (6) we obtain:
+
= 0 (16)
= 0 (17)
= 0 (18)
=
(19)
=
(20)
As a result, constants and , in contrast to (8), are
follows:
=(
); =
(21)
Substituting these constants to (5) and (6) and using
the formula (11) we obtain:
=
+
(22)
In this case the relative effectiveness of the
advertisements significantly depends on the time when
the advertisement does not act. We also see that in
contrast to formula (14) in the last case the relative
effectiveness depends on the thesaurus of recipients.
4 Conclusion
The effectiveness of advertising is determined by the
perception of positive information by the recipient.
Analysis of the information model of advertising leads to
the conclusion of a two-stage process of functioning of
advertising. This is due to the influence of redundant
information on useful information that should be
perceived by the recipient. Excess information appears
as a result of multiple presentation of the same
advertising material. We claim that in the case of the
advertising operation the redundant information is
always harmful.
It is significant that the accumulation of both types of
information occurs differently at different stages of the
functioning of advertising. In the first stage, mainly
positive information is accumulated. The accumulation
of redundant (negative) information begins with a
sufficiently large number of presentations of advertising
(in the second stage). In this case, the accumulation of
positive information continues, but it is suppressed by
the predominant accumulation of negative information.
In Figure 1, the vertical line conventionally separates
the two stages of the functioning of advertising. The
position of this line depends on the psychological
characteristics and the thesaurus of the recipients. Thus,
when creating advertising, it is important to evaluate the
period corresponding to the first stage of the functioning
of an advertisement, for which a special psychological
research is necessary. The effect of advertising depends
not only on the quality of advertising, but also
significantly on the thesaurus and psychological
characteristics of the recipient.
The dependence shown in Fig. 1 is of the identical
form as the experimental curves [3].
The obtained results show that for different initial
conditions the advertisements act in different ways
relatively their effectiveness (δ). It means that in the real
conditions of advertisement operation its effectiveness
can change not only in accordance with mentioned
stages but under influence of other factors, such as
turning off and subsequent turning on of the
advertisement.
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