Identifying the Consumer

Awareness of Product’s

advertisement by means of

Nerlove and Arrow model:

A first order differential

equation

ABSTRACT

Many differential equations and functions are

widely used today not only in the field of applied

sciences such as Engineering but it may also be

helpful in Economic sciences such as in Business

and Marketing fields. And since Industrial

Engineering is a course that deals on the numerical

and quantitative data about technical and applied

skills such as improving systematic processes

through the use of statistical analysis, interpersonal

communication, designing, planning, quality

control, operations management, computer

simulation, and problem solving that may be

applicable in the world of trade and industry, We

take into consideration that we can apply higher

mathematics on the business or marketing aspect

in a company.

This research study aims mainly to

promote the application of a simple

advertising model proposed on 1962

which is called the Nerlove and Arrow (N-

A model).This will help us to determine

the number of people aware in a certain

product. In addition, this will also serves

as an advantage to a company because it

will help them to regulate and control their

marketing strategy whether it is efficient

enough or not to get the attention of their

customers.

This study will not only help us but also

other people to become their basis on their

future researchers about dynamic models

regarding to advertising aspects. This will

also help dealers or salespersons on how to

attain their goals on sales or the marketing

demand without wasting their money on a

wrong forecast to their advertisements.

As a whole, this research will help the

company to determine what strategic

techniques they will use in order to attain

their goal of reaching a specific target

audience.

INTRODUCTION

Advertising is a tool of a company to

communicate and persuade an audience to

purchase their products, goods or services.

They usually use numerous forms of paid

Medias in Television and radio commercials,

print ads on newspapers or magazines, giving

flyers or leaflets and billboards. Ads are placed

where publicists believe they will reach the

largest and most relevant audience; based on

journalism ethics they usually sited those ads

on the front page of a newspaper or magazines

because it is the commonly seen page of the

broadsheet. Based on a reliable source, a

commercial industry uses advertising to drive

the consumption of their product and may place

ads to raise awareness or encourage a change

This research will help the

company to carefully regulate and control

their marketing techniques to attain the

company’s product satisfaction that will

help them to minimize cost in providing

advertisements and commercial ads. In

addition, the company will lessen its

burden about the competition in other

products in such a way that if one brand

will increase its advertisements we can

also conclude that the sales will also

increase.

As a whole, this study helps to assess

the effectiveness and efficiency of their

advertising campaign in order to achieve

the company’s goal and product’s

gratification through the help of a simple

linear differential equation in first order. On

the latter part of this study, we will show

different examples of real life problems for

further learning.

EXPERIMENTAL DETAILS,

COMPUTATION

PROCEDURES AND

THEORETICAL ANALYSIS

The marketing strategy and techniques

of a company must be based on a

quantitative and numerical statistics and

data to provide them an efficient and

competent answer mainly concerning on

the awareness of a group of people to a

given advertisement of a certain product.

Based on the Nerlove and Arrow

model or the (N-A model), we create a

simple model regarding on the variables

that may be include in the computation of

the consumer advertisement awareness.

We represent:

x (t) – refers to the publicizing activity of

the ads which is mainly denotes to the

amount of money the company spend for

the advertisement of their product.

Y (t) - represents awareness of the target

consumers of the company who would

became aware to their products after

having their advertisements.

We can relate this x(t) publicizing activity

of the ads and the Y (t) awareness of the

consumers to the model proposed by

Nerlove and Arrow on 1962.

The original equation created by Nerlove

and Arrow are as follow:

Equation 1 : Nerlove and Arrow Model

Based on a liable source, the

equations shows a(t) is the current

advertising expense and a(t) and

g(t) are the time. Equation 1

states that the net investment in

goodwill is the difference between

the current advertising expense

and the reduction of standard of

goodwill.

And for further study, we create a simple

model through the help of N-A model which

is given by a simple Differential Equation:

Equation 2: Proposed Equation based on

Nerlove and Arrow Model

Where k is a constant corresponding to

declining rate and b is the constant

which describes the advertising

efficiency and effectiveness.

The given equation contains two terms

in the right side.

The first term xq(t) provides the linear

growth of awareness of consumers as

a result of advertising.

The second term −kY reflects the

opposite process, i.e. forgetting about

the product.

As you can notice, the equation we proposed merely

based on the model of Nerlove and Arrow is a good

example of Linear Differential Equation of First Order.

So first, we should rewrite this equation in the

standard form:

The integrating factor is the exponential function:

Therefore the general solution of the given differential

equation is given by

The constant of

integration C can be found as

usual from the initial condition A

(t0)= A0.

In the examples below we

consider how awareness of

customers A(t) varies at different

advertising modes.

EXAMPLE NO. 1

(WHERE COEFFICIENTS

K AND B ARE GIVEN)

EX 1

Management of Swiss

Fragrances Inc. decided to advertise

the Watson’s Stretch mark minimizers

which is their newly released product

and is permanently during the year. The

advertising budget is P12, 000. The

coefficients k and b are k = 1/4, b = 25.

Construct and solve the differential

equation describing the number of

people A (t) aware of this product.

Solution

The equation of dynamics of A (t) is written in

equation in the standard form:

dA/dt=xq(t)-kY

We assume that the time t is measured in

months. By the condition of the problem,

the advertising costs are constant during

the year, so every month they are equal to:

Substituting the known data leads to the

following differential equation:

The integrating factor for this equation has

the form:

The general solution is written as

We determine the constant of

integration C from the initial condition A(t =

0) = 0. Hence, C = −100,000. Then the

particular solution is expressed by the

formula:

Thus in case of permanent advertising, the

number of potential buyers aware of the

product grows non-linearly approaching the

maximum value of:

Answer

There are 100,000 people

aware to the newly

advertised Watson’s Stretch

mark minimizers.

EXAMPLE NO. 2 !!!

A newly opened J.C Metal

Corporation in introduced through an

advertising operation to a population of

500,000 potential customers.The new

corporation is assumed to be proportional

to the number of people who are not yet

aware of it.

Where t is the time (in months), and where

y is the number of people (in thousands)

who have heard of the new

corporation.Half of the population has

heard of the new corporation by the end of

1 year.How many will have heard of it by

the end of 2 years?

EXAMPLE No. 3

Ka Joe Metal

Corporation is introduced

through an advertising of their

product of the rate of k=0.07

and 30,000 people be aware at

the end of 9 months.What

would be the number of

potential customer?

RESULTS AND

DISCUSSIONS!!!!

According to the experimental

details, computation procedures and

theoretical analysis shown on the latter

part of this research, the results we obtain

from the real life problems presented are

helpful in determining the number of

people who are aware to their product by

means of advertisements either in

television, magazines, billboards, radio or

newspapers. Through the help of linear

differential equation on first order the

company will able to determine whether

the promotion of their new product hit it off

to the market.

We should always keep in

our minds that in order to come

up with the total number of

population or people who are

aware to the newly advertised

product wherein coefficients k and

b are given, we should use this

formula:

But if there is a specific number

of population given on the

problem, we can use this

formula in able to determine

the people who became aware

to the newly advertised

product of a company.

Through this research

study, we can help various

implications that are very

important for our daily lives.

Below are some examples of

relevance of this study.

Managerial decisions

We can help managers and businessminded people to estimate their product ads toacquire their target consumers. Managers willable to consider the different techniques andmethods on various managerial insights andconcepts regarding on the product to beadvertised. The proposed model, will help themto form ideas and resolutions whether forexample they will stop the advertisement oftheir product mainly because it doesn’t becamepopular the people, or they should maintaintheir advertisement because their product hasbeen recognized by the population, they mightalso estimate the cost they will use in givingads to their product or it might help them todetermine the sales of their product after orbefore the advertising activity.

Future Researches

This study will also help the future

researchers as one of their basis or

reference to their study. This will also help

them to broaden their knowledge

aboutenhancing the marketing strategies

and techniques in order to increase the

consumer familiarity in the services or

products they offer. We will also able to

help them to determine how awareness

advertising widenthe company’s goals,

objective and intention for the benefit of

the company itself which is merely based

on the target consumer market and the

company image you wish to portray.

CONCLUSION

AND SUMMARY!!!!

This marketing trend is the extent

to which consumers recognize the brands

of the products offered in the company

which can correctly associate these brands

with particular product offerings. Growing

brand awareness is a primary aim in the

introductory stage of the product life cycle,

when your company is attempting to enter

the local marketplace and acquire

consumer awareness. Improving consumer

awareness through advertising keeps your

small business in the minds of consumers,

which can lead to increased interchange at

your place of business.

As a whole, We therefore

conclude that Differential equations

have much importance in the field

ofindustrial engineering playing a

role of solving problems, cascade

future data and etc, together with the

mathematical principles and

quantitative solutions and

computations. Differential equation

is quite important in the field. Using

concept of formulation, solving

problems got easier.

REFERENCES:

◦ http://cd1.edb.hkedcity.net/cd/maths/en/curr_syll/

AS_AppMaths%20Syl_e/Unit_02.pdf

◦ http://gsm.ucdavis.edu/sites/main/files/file-

attachments/howdoesawareness.pdf

◦ http://www.utdallas.edu/~sethi/OCT%20Book%20

Revisions/ch7r05h.pdf

◦ http://www.jstor.org/discover/10.2307/2551549?ui

d=3738824&uid=2&uid=4&sid=21104707699387

◦ http://faculty.wwu.edu/curgus/Courses/321_20114

0/DEs_Po_Bo_Ar_2.pdf

◦ http://peitz.vwl.uni-

mannheim.de/fileadmin/user_upload/peitz/lehre/B

arroso2008.pdf

◦ http://marketingscience.info/assets/documents/2

30/20006.pdf

Gracias paraescuchar!