Page 32 - Azerbaijan State University of Economics

Salah Salimian, Kiumars Shahbazi, Mahdi M. Beknazar: Locating The Sale Agents In Spoke Model
Through Uniform Distribution Of Consumers

2
2

− ( ) − F − γ ≤ (2 − )( ) − 2 + + −
2
( + 1) − ( + 1)

By solving this inequality in respect of F, the following result will be achieved:

2

2 ( ) + ( −2 ) − ( + −1)
≤ 2 (15)
+ −1

This equation shows that if the recoverable cost related to launching sale agent is
sufficiently low, then, the monopolist will agree with launching one sale agent at city
center and several sale agents at margins instead of just one sale agent at city center.
In this state, concerning the profit function of monopolist, the maximum number sale
agents equals to:

2
− ( ) − −
≤ 1

2
2 − 2 ( ) − + +
2

At the end, it should be noted that the results of three theorems 1, 2 and 3 confirms
the work of Mathewson & Winter (1986) who showed that in a linear city, if the city
1
is big enough, i.e. if 2T < F < 4T , one unit sale agent will be established at city
center and if F < 2T, then the agents will be established at city margin. Moreover, in
a small city (F > 4T), just one sale agent will be launched at city center (Shy, 1995).

CONCLUSION
One of the main effective factors on decision making of individuals and firms is location
which is significantly influential on their profitability and survival. In today's world, it is
observed that market is not fully covered in some areas or the number of firms in an area
is more than required. The issue of sale agent is one of the main issues in this regard. In
this paper, the deficiencies and weaknesses of previous models in simplification of non-
competitive location models, especially on the manner of consumers' distribution, the
number of streets, location of sale agents and the optimal number of sale agents have been
studied and discussed. The results showed that under certain condition, if there is just one
sale agent, then, the optimal location of sale agent firm will be at city center rather than
margins. Moreover, it is shown that if the irrecoverable costs are sufficiently high, the
presence of one sale agent at city center is more profitable than several sale agents at
margins for monopolist. In addition, under certain condition, the monopolist agrees with
launching one sale agent at city center and several sale agents at city margins rather than
just one sale agent at city center.

1 The intended city is called a big city, if F < T and the intended city is called a small city if F > T

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