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The aim of this paper is to formulate the mathematical relationship between firms potential ability and their applied efforts to attract the body of unattached customers. A method is devised in this paper by which management techniques imposed by a particular firm can evaluate its market share. This paper demonstrates the relationship between the applied marketing effort of management and the potential ability of the firm in determining its market share. This paper also investigates the effect of a number of simultaneous marketing impulses on the movement of the body of unattached customers and hence on the size of the market share.

The study of competition among the few has opened two important
(related) fields of research: nonprice competition and customer loyalty in
local and global markets. These have been the results of work of many researchers
specialized in the field of marketing management. This work includes research
by Brunner [

When only two or three firms dominate the market (a situation which is
very common in many markets for manufactured consumer goods), consumer loyalty is particularly important for a firm that aims at gaining the loyalty of a certain segment of the market. This segment will not (in the short-run and in the absence of cut throat
competition) move to another competitor. We have, therefore, loyal customers
who are attached to a particular brand [

Only some part of the firms potential marketing ability may be in
motion. The firm may still be able to inject some new brands or embark on an
intensified advertising campaign or improve the quality of its product [

The position of the body of unattached customers is determined by the magnitudes of a number of independent variables.

Let

These three variables can be expressed in a specified number
of independent variables

Equations (

Now, the body of unattached customers

It follows that

An increase in production speed with a reduction in relative sales prices will reduce the percentage of unattached customers.

Integrating from

The left-hand side represents the
effect

In an effort to maintain its market share, the firm’s effective marketing efforts match the competitors’ efforts.

Now, let

Noting that

If we now differentiate (

Therefore,

Noting that

Then,

From (

In virtue of (

Therefore,

Hence, from (

Similarly,

Equations (

The sum of the virtual moments of the components of changes
in sales to unattached customers would be equal to

Let

Now,

By referring to (

Therefore,

There will also be similar expression for

Therefore,

Similarly, it can be shown that

From (

Let

If

Therefore,

This paper has devised a method by which a particular firm can evaluate its potential capacity in determining its market share.

The relationship between the applied marketing effort and the potential ability of the firm determining its market share has also been demonstrated.

The paper also investigated the effect of a number of simultaneous marketing impulses on the movement of body of unattached customers and hence the size of the market shares.