Page 31 - Azerbaijan State University of Economics

THE JOURNAL OF ECONOMIC SCIENCES: THEORY AND PRACTICE, V.80, # 1, 2023, pp. 21-34

Theorem 3
The monopolist agrees on launching one sale agent at city center and several sale
agents at margin instead of just one sale agent at city center, if:

2
2 ( ) + ( − 2 ) − ( + − 1)
≥ 2
+ − 1

Proof: We already know that if there is a sale agent at city center, then, according to
equation (3) the monopolist profit equals to:

M

2
π = ( − ) p = − ( ) − F − γ
M

Now this issue will be studied that if the monopolist wants to have a sale agent at city
center and several (K) sale agents at city margins, here, as far as the consumers are
located at the same steers as K sale agents are located and there are n consumers in
1
D
each street which in case of purchase have the surplus of p + − B and the rest s-K
2
streets without sale agents whose consumers will have a surplus of − in case of

purchase (purchase from central sale agent), therefore, the profit of sale agents will be
equal to:

D
D
M

M

D
Π = ∑ K π + π = [ ̂ ( − p ) + − ̂ ( − p )] − (K + 1)F =
i=1

C
i

(K + 1)γ (12)

where, indicates the profit of sale agents located at city center, (K + 1)γ is total

profit of all sale agents including those located at city center and K sale agents located
at streets (γ is the profit unit of each sale agent). By solving and simplification of the
above equation:

2

2 − (2 − )( ) − − s B + ( +1) + ( +1)
M
p = 2 (13)

2 − (2 − ) − −
2

Therefore, the monopolist's profit in this state equals to:

M

2

π = (2 − )( ) − 2 + + s B − ( + 1) − ( +
2
1) (14)

The comparison of equations 3 and 14 shows that the monopolist agrees with
launching one sale agent at city center and several sale agents at margins instead of
just one sale agent at city center, when the following equation is established:

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