Brand Credit Degree, Choice Cost and Sales Model Building
Wei-liang Li1, Hui Wang2
1
Department of Business and Management Training, Shandong Academy of Governance, Jinan, China
2
Department of International Economy and Trade, Shandong Academy of Governance, Jinan, China
(1Liweiliang2001@163.com,2lynx12wang@hotmail.com)
Abstract - From the demand theorem, sales model
theory has fully discussed how price affects the sales process
and manufacturer’s competitive strategy under the
background of supply surplus, but is little concerned with
the effects of brand credit degree and choice cost on the sales
process. Building sales model based on brand economics,
using matlab to model and case studies of the variables such
as brand sales cycle, brand purchase proportion of
population, the paper provides theoretical support on how to
optimize sales process and finally the study should become
the theory guidance for corporations using brand as the core
to establish business strategy and in order to obtain higher
profits and market share .
Keywords - Sales model, brand credit degree, choice cost,
case study
I. INTRODUCTION
The sales model is about a mathematical relationship
between variables affecting product sales and the sales
cycle in the research of brand sale process, which could
effectively guide the corporations to establish the optimal
marketing strategy and sales promotion mode, and to
increase market share and profits rate. Hal R. Varian
established the optimal sales model based on price and
information to explain the retail behavior of real-world
and provided a theoretical support for the corporation
product sales[1]. The Peng SY established the sales model
in which price is a decreasing function of demand rate,
and proved the existence and uniqueness of the optimal
policy [2]. Taking into account of the uncertainties, Han
Xin-she and Ye Heng-kui established the product sales
forecast model on product sales in a period of time which
provided an important reference to forecast durable goods
production and sales [3]. Leng Ke-ping discussed a simple
sales process in the market from the game theory,
established corresponding mathematical model and
suggested the optimal strategy of the corporation product
sales [4]. Mo Jiang-tao, Pan Hong-juan, Mi Fang-fang and
Zhou Fang-ming studied the advance sales of the seasonal
demand products using a two-stage pricing strategy [5].
On the law of demand, past researches have discussed
the mechanism of price impacting on sales and discussed
corporations’ competitive strategy in the condition of
supply surplus, but lacked research on the influence of
indicators in the sales process based on brand credit
degree and choice cost. Taking the theory of SIS model
for reference, this paper builds repeat purchase brand
sales model based on the brand economics [6], and aims to
introduce brand credit degree and choice cost into the
sales model, and make digital simulation on data models
variables such as brand sales cycle, population proportion,
extreme point of brand purchase, and brand coverage etc.
It provides a theoretical support for corporations applying
brand economics theory to brand building and
decision-making. It can effectively guide the practice of
corporations brand sales.
II.THE DEFINITION OF SALES MODEL
VARIABLES BASED ON THE BRAND
ECONOMICS
Brand category degree is the mental awareness
degree of how consumers specify a certain brand as a
category psychologically, and it can generally be obtained
by testing and analysis [7]. Through the analysis of the
audience and means in brand promotion, we can get the
correlation coefficient of brand and the promotion means,
thus the data of valid daily brand contact rate can be
obtained which determined by brand category degree, the
correlation coefficient between brand and promotion
means, brand investment, which are all proportional to
valid daily brand contact rate. The valid daily brand
contact rate represents the degree of the promotion
effectiveness.
We first define the valid daily brand contact rate λ
which embodied brand credit degree is the function of Bc,
such as,
λ = λ(Bc)
(1)
According to the definition of brand economics,
Bc=b*s is brand credit degree, brand category degree
b∈ [0,1], brand strategy s∈ [1 0], when b=1 and s=1, thus
Bc=1. In order to simplify the analysis, we set s=1, thus
Bc∈ [0,1][7]. Based on the above assumptions, we can
obtain λ by the following equation,
m11    mk1  b1 
  c1    ci               
m1i    mki  bk 
(2)
Where ci is brand promotion investment proportional
of the category i of the brand, mki is correlation
coefficient between brand category i and promotion
means k, and bk is brand category degree when the brand
uses the promotion means k.
Equation (2) can be explained economically as
follows: assuming that the brand needs k kinds of
promotion means, valid daily brand contact rate is
multiplied by the investment proportion of the brand in all
promotion means, correlation coefficients of the brand
and promotion means as well as brand category degree.
Valid daily brand contact rate is not only a function of
brand investment amount but also a function of the
correlation coefficient between brand and promotion
means.
Equation (2) also provides a method to measure the
effectiveness of brand promotion. Generally, when we put
the limited business promotion investment expenses into
the maximum correlation coefficient between the brand
and promotion means, its valid daily brand contact rate is
maximum too. The correlation coefficient of brand and
promotion means can be obtained by investigation and
testing, we will focus on the λ value influenced by brand
category degree in the following analysis.
We secondly define valid daily brand purchase rate
embodied choice cost μ, is the function of Cc, such as,
μ = μ(Cc)
(3)
According to the definition of brand economics, Cc is
choice cost, and Cc=f(Bc), Cc is inversely proportional to
Bc[7]. In order to simplify the analysis, we set s=1, thus
Bc∈ [0,1], μ=μ(f(Bc)), and μ is inversely proportional to
Bc. Equation (3) can be explained economically as
follows, the smaller choice cost of the brand is, the higher
daily brand purchase rate of the brand is.
To establish the repeat purchase brand sales model,
we define variables as follows: 1, i is the purchase
population proportion of a certain brand; 2, s is the
potential purchase population proportion of a certain
brand, and s is determined by brand position, target
market size, population income level and consumption
propensity; 3, λ is valid daily brand contact rate of a
certain brand, or the population proportion contact rate of
a certain brand, and is proportional to promotion
effectiveness and brand category degree. 4, μ is daily
brand purchase rate of a certain brand, or the population
proportion purchase a certain brand, and it is inversely
proportional to choice cost and is concerned with the
product type. 5, б = λ / μ, is the effective consumer
contact number added by brand credit degree and choice
cost during the brand sales.6, t is the time of sales
duration of a certain brand.
III.REPEAT PURCHASE BRAND SALES MODEL
ANALYSIS AND SIMULATION RESULTS
Repeat purchase brand sales model mainly analyzes
the brands in the field of daily consumption [8]. While
brands are repeatedly purchased or products are relatively
unimportant, consumers would not be excited in a lot of
decision-making activities in the brain [9]. The brands will
be purchased by consumers without hesitation and
maintain a stable brand purchase rate.
We define s0(s0>0) as potential purchase population
proportion, and i0(i0>0) as purchasing population
proportion, and s0 + i0 = 1.
We can build the Repeat Purchase Brand Sales
Model,
di
ds
 si  i
 si
dt
, dt
Using equation
(4)
   /  , then we get,
di
1 

 i i  (1  )
dt
 

(5)
The solution of (5) is,
1
 
  (1 )t 
1


e


 ,  1

  1     1
i (t )  
1

1
 t  i  ,  1
0 

(
6)
As t→∞,
 1
1  ,  1
i ( )   
0,  1
(7)
Drawn from the above model, for repeat purchase
brand, we have:
Proposition I: When б> 1 and λ> μ, the valid daily
brand contact rate is higher than the daily brand purchase
rate, regardless of the initial i0 is large or small, as time
passes i (∞) converges to a stable value (1-1/б), by the
definition of б, we know that λ and μ determine the size
of the i(∞), i(∞) is proportional to μ and i(∞) is inversely
proportional to λ. The larger λ and the smaller μ is , the
larger б is, so is the larger i(∞). Thus the corporation has
infinite life cycle, and can continue operating forever. At
the same time μ determines the duration of each stage of
the brand life cycle. The smaller μ is, the longer time i(t)
convergence to the stable value needs. Thus increasing
the brand category degree and lowering the choice cost
are available to consumers to purchase a certain brand
without hesitation. Ultimately increasing μ can effectively
improve the stability of brand production and sales as
soon as possible.
Using the software matlab[10] to simulate the model,
we get the simulation as Fig.1.. The fig.1. shows i(∞)
respectively maintaining the same convergence (1-1/8) =
0.875 on 50th and 80th days when б=8, λ=0.8, μ=0.1, i0
respectively is 0.8 and 0.09. Fig.2. shows i(∞)
respectively maintaining the same convergence
(1-1/4)=0.75 on 100th and 180th days when б=4, λ=0.8,
μ=0.05, i0 is 0.8 and 0.09 respectively. Through the
simulation, we get the empirical formula, when i(t)
reaches a stable value, t*Bc=100t0(the unit is day), where
t0 is a constant determined by product type. The larger Bc
and the smaller Cc are, the smaller t is, then corporations
can significantly shorten the brand promotion period and
cut costs for promotion, meanwhile the production scale
can keep stable at a reasonable level as soon as possible.
When б gets smaller and gradually closes to a value 1,
i(∞) becomes smaller, then a brand with low brand
category degree will converge to a low brand purchase
population proportion. Corporations will fall into "muddy
middle zone[11]" or the brand will die out of the market
owing to the condition that the product scale fail to
expand, then we get proposition II.
Proposition II: When б  1, then λ  μ, and the brand
purchase population proportion i(t) will decrease with the
time t prolonged until it is 0, which means the brand
could not be sustainable and has a life cycle.
From λ=λ(Bc), μ=μ(Cc), with the other conditions
remain unchanged, brand credit degree Bc and choice cost
Cc influence б through λ and μ respectively, then i(t) has
different changing curve, the smaller Bc and Cc are, the
smaller б is, thus the faster i(t) decreases. When б=0, λ=0,
i (t )  i0e  t
.
Fig.2. Simulation graph when б=4, μ=0.05.
Using the software matlab to simulate the model, we
get the simulation as Fig.3., i(∞) converges to 0 on about
160th day when б=0.8, λ=0.08, μ=0.1, and i0 is 0.8 and
0.09 respectively, which means when brand category
degree is low, regardless of the initial purchase population
proportion is large or small, the brand category will die
out of the market, but the brand duration may varies, as
shown in Fig.4., i(∞) will converge to about 0.07 and 0.02
on 600th day when б=0.8, λ=0.008, μ=0.01, i0 is 0.8 and
0.09 respectively. Although the brand category can also
exists, but will gradually withdraw the market because of
lacking profit margins. When compared Fig.3. and Fig.4.,
we can infer that the lower the daily brand purchase rate
is, the slower the brand dies, which would confuse the
corporation’s decision-makers to mistakenly believe that
the brand can develop sustainably, thereby to increase the
promotion investment. But when brand category degree is
low, even if promotion investment increased, the result is
still futile and even may be counterproductive to
accelerate the death of the brand category.
Fig.1. Simulation graph when б=8, μ=0.1.
Fig.3. Simulation graph when б=0.8, μ=0.1.
Chinese toothpastes have suffered much for a long
time after foreign brands entered the Chinese market - the
correct promotion strategy and heavy investment of
foreign brands have already made them sidelined in the
competition, together with the fact that they have a weak
single interest point which impressed consumers that
toothpastes are just cleaning supplies. In this reshuffle
process, brand category degree and brand credit degree of
Chinese toothpastes are low, thus Chinese toothpastes are
vulnerable in the competition and even some brands died
out.
Fig.4. Simulation graph when б=0.8, μ=0.01.
Proposition I and proposition II illustrate what a key
role brand category degree and choice cost play in brand
sales model. Brand category degree can be gotten through
testing and analysis generally. Valid daily brand contact
rate can be gotten from analyzing the promotion
investment and the correlation coefficient between brand
and promotion means. At the same time daily brand
purchase rate can be observed in actual sales process.
Combined both rates, we can calculate the brand effective
contact number, which can be great help for the certain
brand to predict the change rule of i(t) and t, and can
guide corporations’ sales and production in the selling
process.
IV. REPEAT PURCHASE BRAND CASE STUDIES
A. Chinese toothpaste market
Brand credit degree equals to the product of the
brand category degree and brand strategy. If brand
category degree is high and brand strategy is correct, the
brand market share will maintain in a high level in
long-term. We will research on the brand in Chinese
toothpaste market for example. According to the survey
data of ZhongJing-XianLue Investment Advisory Center,
research on the Chinese toothpastes market shows that
Crest's shares more than 20% in the Chinese toothpaste
market in the first half of 2010, indicating that the
implementation of Procter & Gamble Crest "no cavities"
brand promotion maintains its high brand credit degree
and high brand repeat purchase rate. For repeat purchase
brand, market share is the stable everyday brand purchase
rate, so i(∞)=(1-1/б)=20%, we can calculate б=1.25,
λ=1.25μ, which indicates that Crest toothpaste has high
brand category degree by a large marketing promotion
investment, making the valid daily brand contact rate
higher than daily brand purchase rate to ensure its
popularity in the market.
According to the basic principles of brand economics,
Chinese toothpastes have to establish a mutually
exclusive category with the foreign brands, in order to
increase brand credit degree and reduce choice cost,
namely to implement category confrontation strategy[7].
In recent years, the Chinese herbal medicine efficacy
toothpastes
gradually
rise,
for
example
YUNNANBAIYAO toothpaste[12] got market share
around 9% to 10% in China in the first half of 2010. This
means that its brand credit degree has been significantly
elevated; the core reason for this is that these Chinese
toothpaste brands used the unique Chinese herbal formula
for oral health care, which is of great significance to
stabilize its brand repeat purchase rate by establishing a
single interest point.
B. Coca-Cola and Qinchi wine
Other examples are new-formula Coca-Cola and
Qinchi (a wine brand in China). Due to the wrong product
positioning, brands or categories above lasted only a very
short time. The core reason is that they both have low
brand category degree or product quality, leading to brand
credit plummeting. In April 1985, Coca-Cola announced
it would use the new formula instead of the old one,
because the Company believed that “the bold decision
was the best decision the Company has made[13]”.
However, in July 1985, Coca-Cola Company announced
to reuse the previous Coca-Cola formula because of the
pressure. Only after 82 days, the new Coca-Cola quit
from the market because of the wrong product positioning.
Even Qinchi was the advertising pillar Wang in CCTV,
unfortunately, its market situation was rapidly
deteriorated because of bad product quality[14].
C. Porsche and Apple
Porsche is the world famous car brand, the
production of Porsche 911 has been by far the world's
best-selling since 1963 when the car was produced. It
updated constantly averaging about 1.5 years on
technology and shape, launched about 30 kinds of car
models for consumers to choose totally. Porsche has a
very high brand category degree in the field of luxury
sports car, thereby enhanced its brand credit degree, thus
it need constantly introduce new products to meet market
needs and to ensure sustainable development of
corporations. The new product release time is
proportional to the valid daily brand contact rate and
inversely proportional to daily brand purchase rate. The
smaller λ and the larger μ are, the shorter intervals of new
product releases is. Luxury brand should arrange the
production and stocking to prevent temporary supply
shortage and surplus of products based on the extreme
point of purchase population proportion.
Apple Inc. takes a completely different category
confrontation strategy from the "Wintel" compatibility
architecture and continues to invest into innovative
research and product development, thus makes Mac, iPad,
iPod, iphone and other products maintain a high brand
category degree. Apple Inc. establishs unique market
position and wins high recognition of the market. Because
of its high brand category degree and the correct
marketing strategy, Apple brand credit degree increases
and accumulates rapidly. The queuing up to purchase and
short supply of the recent products (iphone4s) is a good
proof.
Corporaions need to innovate or introduce new
products to maintain its brand credit degree in the brand
sales cycle in order to improve their brand coverage. If
the brands lack sustained R&D strength and ability to
innovate, they will disappear without new category
release after a short honeymoon-like time relying on
powerful promotion. Different corporations can analyze
the problems of their own brand in order to improve the
final brand coverage by increasing brand promotion when
brand category degree is a certain value, and increasing
the valid daily brand contact rate. It also shows the
importance of the rule “Have a promotion theme every
year, Have promotion activities every month.” in
corporation marketing promotion [15].
V. CONCLUSION
The new sales model as proposed in this research
paper on the basis of brand economics is an in-depth
exploration and extension to traditional arrangement of
new product launch and distribution. Through the
research, we get functions of the variables and variation
disciplines of brand sales cycle, brand purchase
population proportion by adding brand credit degree,
choice cost and other indicators to the sales model.
Realistic simulation results obtained by using
software matlab to simulate the repeat purchase brand
model brings us to a firm conclusion that brand can
prolong the brand life cycle, quicken the process of
product stability, boost sales, elevate purchase rate and
enlarge market share as well by increasing brand category
degree and reducing choice cost. In this way, brand
economics theory is further developed in this paper,
which should be significant in brand building and sales
practice because it could provide a theoretical support to
guild corporations to establish their core brand business
strategy to obtain higher profits and raise market share
through increasing brand awareness and using correct
brand strategy.
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