Download How Information Sharing Impact Pricing Power in Longitudinal Monopoly Market

How Information Sharing Impact Pricing Power in Longitudinal
Monopoly Market
Li Zhiwen, Luo Dingti
Management Science & Engineering Research Institute
Hunan University of Technology, Zhuzhou, China 412008
Abstract Aiming at a two-echelon supply chain that consists of one manufacturer and one retailer in a
longitudinal monopoly market, where the retailer owns posterior information of demand, the paper
studies the effects of information shared with manufacturer by the retailer on both parties’ pricing
powers. We show that when the retailer forecasts the market scale may expand, information sharing
increases its pricing power, but the profit of the manufacturer decreases; however, when the retailer
forecasts the market scale may shrink, the change of the retailer’s pricing power between ante- and
post-information sharing depends on the relative precision of the forecast information, but it is certain
that after information sharing the higher its precision of forecast information, the greater its pricing
power and the more it benefits from the strategy of sharing information.
Key words supply chain, posterior information, pricing power, information sharing
1 Introduction
The so-called enterprise power is the ability of one firm (the source) to influence the intentions and
actions of another firm (the target)[1]. And the decision-making power is the force influence of one
decision-maker compared with that of another decision-maker. Usually, the higher a decision-maker’s
force status and prestige, the greater its power. Generally, the decision-making power includes
internal-firm decision-making power (such as the firm’s management decision-making power surplus
value owning power ) and external-firm decision-making power (such as the arrangement of
decision-making power among the member firms in a supply chain). However, presently, many
literatures have discussed the effects of internal-firm management decision-making power on the firm’s
performance [2]~[3], but few studies the effects of the arrangement of inter-firm decision-making power
on the firm’s performance, Rajian [4] and Munson [5] study the reasons why a certain firm has power in a
supply chain. Rajian [4] demonstrates that the information is the source of power, Munson [5] considers
that the information is the main determinant factor in the game of member firm’s power in a supply
chain, he also proves that when a member firm owns information, its power increases, alternatively, if
the information is shared (or leaked), the receiving party is empowered.
The wholesale price between the upstream and the downstream firms in a supply chain determines
directly the distribution of both parties’ profits. Usually, in the practical trade, both parties will bargain
on the wholesale price within an adjustable scope. Du Yifei [6] derives the scope of wholesale price by
comparing the distribution of both parties’ profits and the equilibrium price in the static game with those
in the dynamic game when the upstream and the downstream firms own the pricing power respectively.
Luo Dingti [7] quantifies the pricing power on the wholesale price between the upstream and the
downstream firms in a supply chain, shows that the pricing power determines the wholesale price, then
explores the impact of the longitudinal transference of the pricing power on the operational benefit of
the whole supply chain, finally, points out that each party’s pricing power determines its profit, and it is
impossible for the supply chain to achieve its optimal profit due to the double marginalization problem.
Facing the changeful market, the change of demand certainly causes the change of the wholesale price
in a supply chain. Chen Jinliang [8] analyses the supply chain coordination in demand forecast update
condition with symmetric information, proves that the total benefit of the system will be maximum as
long as the supplier provides goods to retailer with a price lower than its cost, and the double
marginalization problem will disappear. Yang Bo [9] analyses the information sharing mechanism in a
supply chain where the manufacture sets the wholesale price, the wholesale price and quantity
simultaneously according to its prior information, proves that the precision of market demand forecast
will influence greatly the behavior of information sharing between the upstream and the downstream
、
、
348
firms.
This paper tries to quantify the pricing power of the upstream and the downstream firms in a
supply chain, then analyses the effects of demand information shared with manufacture by the retailer
having the posterior information of demand on the arrangement of both parties’ pricing power and both
parties’ profits.
2 Model Assumption
We assume that the supply chain consists of one manufacture, one retailer and one product., and
the upstream and the downstream firms are independent monopolies. Further, ordering flexibility exists
between the manufacture and the retailer. Specifically, the meaning of each notation in the model is as
follows
q
------- market demand of the product
p
------- the retail price of the product
CM
------ the marginal producing and transporting cost of the manufacture
CR
------- the marginal sale cost of the retailer
w
------- the wholesale price between the manufacture and the retailer
πM
------- the profit function of the manufacture
πR
------- the profit function of the retailer
'
α (α ) ------- factor of the retailer’s pricing power before (after) information sharing
β (β ' )
------- factor of the manufacture’s pricing power before (after) information sharing
Clearly, α + β = 1 and α ' + β ' = 1 hold.
Suppose that the market demand is monotonic linear q = a − bp, a = a 0 + ε , ε ∈ N (0, v) , where a 0
is the aggregate potential market demand scale, ε is the influence of market demand uncertainty,
normally distributing with zero mean and variance v . Furthermore, a 0 and ε are common knowledge
for both parties. And θ , which is from a , is retailer’s posterior information of demand, which can be
interpreted as the potential demand scale after the retailer’s spot check with the pattern
θ = a + e, e ∈ N (0, s ), where s is the variance of retailer’s posterior information [9]. Hence, the prior
information of demand function is
q = E (a) − bp = a 0 − bp .
(1)
After the retailer acquires the posterior information, we have the following expression according to
Bayes conditional probability
s
v
θ
E (a | θ ) =
a0 +
s+v
s+v
We assume that t = s /( s + v) , which denotes the relative precision of retailer’s market demand forecast
information. Obviously, t increases with s , which is the variance of retailer’s posterior information.
The lower t , the lower s and the higher retailer’s precision of forecast. Therefore, after the retailer
acquires the posterior information θ , the demand function is
(2)
q = E (a | θ ) − bp = ta 0 + (1 − t )θ − bp
3 Pricing Model without Posterior Information
In practical trade the arrangement of pricing power on the wholesale price exists between the
manufacture and the retailer. Firstly, we consider two special states
1) The manufacture owns the absolute pricing power, so the game problem here is
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Max E (π M ) = (w − C M )q
1
w
s.t. Max E (π R ) = ( p − w − C R )q
1
q
2)
Substitute expression (1) into the expression above, the solution of the game problem is
1
w*1 =
(a 0 − bC R + bC M )
2b
The retailer owns the absolute pricing power, so the game problem here is
1
MaxE (π R ) = ( p − w − C R )q
w, q
s.t.MaxE (π M ) = ( w − C M )q ≥ 0
1
Substitute expression (1) into the expression above, the solution of the game problem is w * 2 = C M
However, in the practical trade, usually, the pricing powers of the manufacture and the retailer are
usually comparative, neither of them has absolute power, so the wholesale price basically depends on
both parties’ pricing powers [7]. Before information-sharing the pricing power of the manufacture and the
retailer respectively is α , β , hence, the initial wholesale price contract is
w = αw * 2 + β w * 1 = αC M +
*
Here
1
β (a 0 − bC R + bC M )
2b
(3)
1+ α
(a 0 − bC M − bC R ) , from which we find
4
a 0 − bC M − bC R > 0
q0 =
(4)
4 Pricing Model and Profits with Posterior Information
4.1 The Retailer Does not Share the Information
The retailer acquires the posterior information by spot check. Suppose that the retailer has
flexibility in ordering quantity, and it does not share the information with the manufacture, so the
wholesale price contract is not changed, still as expression (3).
The expected profit function of the retailer is
2
E (π R ) = E[( p − w * − C R )q ] = ( p − w * − C R )(ta 0 + (1 − t )θ − bp)
∂E (π R )
ta + (1 − t )θ + bw * + bC R
= 0 , we have p * = 0
∂p
2b
2
From the first-order condition
Substituting expression (2) into the expression above, we find q * =
ta 0 + (1 − t )θ − bw * − bC R
(5)
2
Therefore, the expected profits of the manufacture and the retailer are
1
2
E (π R ) = ( p − w * − C R )q =
(ta 0 + (1 − t )θ − bw * − bC R ) 2
4b
1
2
E (π M ) = ( w * − C M )q = ( w * − C M )(ta 0 + (1 − t )θ − bw * − bC R )
2
Substituting expression (3) into the expression above, we have
1
1
1
2
E (π R ) =
(ta 0 + (1 − t )θ − (1 − α )a 0 − (1 + α )(bC M + bC R )) 2
4b
2
2
1
2
(1 − α )(a0 − bC R − bCM )(2ta0 + 2(1 − t )θ − (1 + α )(bCM + bCR ) − (1 − α )a0 )
E (π M ) =
8b
4.2 The Retailer Shares the Information
After the retailer acquires the posterior information, it shares it with the manufacture, which causes
the change of both parties’ pricing powers. Hence, the new factors of both parties’ pricing powers
350
respectively are α ' , β ' , they will draw a new contract. Consider the two special states again:
1) The manufacture owns the absolute pricing power, so the game problem here is
3
Max E (π M ) = ( w − C M )q
w
s.t. Max E (π R ) = ( p − w − C R )q
3
q
Substitute expression (2) into the expression above, the result of the game problem is
1
w*1 =
(ta 0 + (1 − t )θ − bC R + bC M )
2b
2) The retailer owns the absolute pricing power, so the game problem here is
3
MaxE (π R ) = ( p − w − C R )q
w, q
s.t.MaxE (π M ) = ( w − C M )q ≥ 0
3
Substitute expression (2) into the expression above, the result of the game problem is w * 2 = C M
Hence, the new wholesale price contract of the trade is
1 '
w *' = α ' w * 2 + β ' w * 1 = α ' C M +
β (ta 0 + (1 − t )θ + bC M − bC R )
(6)
2b
The expected profit function of the retailer is
3
E (π R ) = E[( p − w *' − C R )q] = ( p − w *' − C R )(ta 0 + (1 − t )θ − bp)
∂π R
ta + (1 − t )θ + bw *' + bC R
= 0 , we have p *' = 0
∂p
2b
3
With the first-order condition
Substituting expression (2) into the expression above, we find q *' = (ta 0 + (1 − t )θ − bw *' − bC ) / 2
(7)
Substituting expression (2) into expression (7), we find q = (1 + α )(ta 0 + (1 − t )a 0 − bC M − bC R ) / 4 ,
*'
'
which means ta 0 + (1 − t )a 0 − bC M − bC R > 0
Therefore the profits of the manufacture and the retailer are
1
3
E (π R ) =
(ta 0 + (1 − t )θ − bw *' − bC R ) 2
4b
1
3
E (π M ) = (w − C M )(ta 0 + (1 − t )θ − bw *' − bC R )
2
Since expression (6), we have
1
3
E (π R ) =
(1 + α ' ) 2 (ta 0 + (1 − t )θ − bC M − bC R ) 2
16b
1
2
3
E (π M ) =
(1 − α ' )(ta 0 + (1 − t )θ − bC M − bC R ) 2
8b
（ 8）
5 Effects of Information Sharing On the Pricing Power
Now, we compare the retailer’s profit of ante-information sharing with that of post-information
sharing when the retailer has posterior information
1
2
3
(( a 0 − bC M − bC R )(α − α ' ) + (1 − α ' )(1 − t )(θ − a 0 ))
E (π R ) − E (π R ) =
(9)
16b
(( 2 + α ' − α )(a 0 − bC M − bC R ) + (3 + α ' )(1 − t )(θ − a 0 ))
Similarly, we compare the manufacture’s profit of ante-information sharing with that of
post-information sharing when the retailer has the posterior information
351
1
((a 0 − bC M − bC R )(α − α ' ) + (1 − α ' )(1 − t )(θ − a 0 ))
(10)
8b
((a 0 − bC M − bC R )(α + α ' ) + (1 + α ' )(1 − t )(θ − a 0 ))
Additionally, we compare the wholesale price, quantity and retail price of ante-information sharing with
those of post-information sharing
1
1
(α − α ' )(a 0 − bC M − bC R ) +
(1 − α ' )(1 − t )(θ − a 0 )
(11)
w *' − w * =
2b
2b
q *' − q * = b( w * − w *' ) / 2
(12)
E (π M ) − E (π M ) =
3
2
p *' − p * = ( w *' − w * ) / 2
(13)
In the analysis above, the incentives of the retailer sharing information and the manufacture accepting
information are
 E (π R 2 ) < E (π R 3 )
(14)

3
2
 E (π M ) > E (π M )
Let A = (1 − t )(a 0 − θ ) /( a 0 − bC M − bC R )
The result of the inequality group (14) is as shown in table 1
Table 1 The Condition of the Retailer Sharing Information and the Manufacture Accepting Information
θ > a0
θ < a0
1
α−A
3A + α − 2
'
) ∩ (0,1)
, α ∈(
,1) ∪ (0,
2
1− A
1− A
2
3
E (π R ) < E (π R )
α' >
1
3A + α − 2
α−A
1− A
When
,1) ∪ (0,
) ∩ (0,1)
< A < 1, α ' ∈(
2
1− A
1− A
A −α
When A > α , α ' ∈ (0,
) ∩ (0,1)
α−A
1− A
3
2
'
E (π M ) > E (π M )
α <
α−A
1− A
'
) ∩ (0,1)
When α > A , α ∈ (0,
1− A
5.1 The retailer forecasts the demand scale may expand
If the market demand increases, the conditions θ > a 0 and A < 0 hold. With expression (4) we
conclude that the retailer’s pricing power must change obviously so that it may have the incentive to
share the posterior information, e.g. α ' > (α − A) /(1 − A) > α , that’s to say, the retailer’s pricing power
strengthens, and the manufacture’s pricing power weakens after information sharing. Therefore, the
retailer will set a new contract on the wholesale price. However, the condition of the manufacture’s
accepting the information is α ' < (α − A) /(1 − A) , theoretically, the manufacture will not approve the
shared information, it will never accept the new wholesale price contract.
Conclusion 1. When the retailer forecasts the demand scale may expand, the condition for the retailer’s
sharing the information with the manufacture is in a condition that its pricing power will be strengthened,
which shows the information is the source of power. In the longitudinal monopoly market, although the
information sharing causes the reduction of the manufacture’s profit, the manufacture will have to
accept the reconfiguraiton of the pricing power. For example, the retailer monopolizes the marketing
channels of this kind of product, forcing the manufacture to be an inferior position without the ability of
bargaining, the manufacture has to accept the so-called “overlord clause”.
We compare the wholesale price, quantity and retail price of ante-information sharing with those of
post-information sharing
With the condition α ' > (α − A) /(1 − A) and expressions (11) (12) (13), we have w *' < w * q *' > q *
α−A
When 0 < A <
，
p <p .
*'
*
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，
Hence, we can draw a conclusion:
Conclusion 2. When the retailer forecasts the demand scale may shrink, retailer’s information sharing
strategy causes the reduction in the wholesale price, increase in quantity and the reduction in retail price.
5.2 The retailer forecasts the demand scale may shrink
If the market demand reduces, the condition θ < a 0 holds. And with expressions (4) (8),
0 < A < 1 holds. We divide the state into four kinds of situation to discuss in the following text.
1) 0 < A < 1 / 2 , A > α
After the retailer shares the information, it is certain that its profit of post-information sharing is
greater than that of ante-information sharing no matter how the pricing power changes. And there must
A −α
) ∩ (0,1) , which makes expression (14) hold and assures the increase of the
be a scope α ' ∈ (0,
1− A
A −α
,1} , but
manufacture’s profit. Therefore, the retailer hopes that its pricing power will be α ' = min{
1− A
the change of the pricing power between ante- and post-information sharing depends on A . Assuming
A −α
, obviously, f (t1 ) is the decreasing function of t 1 . In other words, after the
that f (t 1 ) =
1− A
information is shared, the retailer’s pricing power increases with the decrease of t 1 ; with expressions
，
，
(11) (12) (13), we have w *' < w * q *' > q *
p *' < p * , that is, retailer’s information sharing strategy
causes the reduction in wholesale price and retail price, the increase in quantity.
2) 0 < A < 1 / 2 , α > A
3A + α − 2
After the retailer shares the information, there might be a scope α ' ∈ (0,
) ∩ (0,1) , which
1− A
causes expression (14) hold and assures the increase of both parties’ profits. Therefore, the retailer hopes
3A + α − 2
,1} . Similarly, the change of the pricing power
that its pricing power will be α ' = min{
1− A
between ante- and post-information sharing depends on A . Let f (t 2 ) = (3 A + α − 2) /(1 − A) , obviously,
f (t 2 ) is the decreasing function of t 2 . Hence, after the information is shared, the retailer’s pricing
power increases with the decrease of t 2 ; with expressions (11) (12) (13), we have w *' > w *
，q
*'
< q*
，
p > p , that is, the retailer’s information sharing strategy causes the increase in wholesale price and
retail price, the decrease in quantity.
3) 1 / 2 < A < 1 , A > α
After the retailer shares the information, there might be a scope
3A + α − 2
A −α
,1) ∩ (0,
) ∩ (0,1) , which causes expression (14) hold and assures the increase of
α ' ∈(
1− A
1− A
A −α
both parties’ profits. Therefore, the retailer hopes that its pricing power will be α ' = min{
,1} .
1− A
Similarly, the change of the pricing power between ante- and post-information sharing depends on A .
A −α
, obviously, f (t 3 ) is the decreasing function of t 3 . Hence, after the
Assuming that f (t 3 ) =
1− A
information is shared, the retailer’s pricing power increases with the decrease of t 3 ; with expressions
*'
*
，
，
(11) (12) (13), we have w *' < w * q *' > q * p *' < p * , that is, the retailer’s information sharing strategy
causes the reduction in wholesale price and retail price, the increase in quantity.
4) 1 / 2 < A < 1 , α > A
α−A
After the retailer shares the information, there must be a scope α ' ∈ (0,
) ∩ (0,1) , which
1− A
353
makes expression (14) hold and assures the increase of both parties’ profits. Therefore, the retailer hopes
α−A
,1} . Compared with the price power of ante-information
that its pricing power will be α ' = min{
1− A
sharing, the retailer’s pricing power of post-information sharing reduces, and the manufacture’s pricing
α−A
power increases. Assuming that f (t 4 ) =
, similarly, f (t 4 ) is the decreasing function of t 4 .
1− A
Hence, after the information is shared, the retailer’s pricing power increases with the decrease of t 4 ;
，
，
with expressions (11) (12) (13), we have w *' > w * q *' < q * p *' > p * , that is, the retailer’s information
sharing strategy causes the increase in wholesale price and retail price, and decrease in quantity.
From what has been discussed above, we can draw the following conclusion:
Conclusion 3. When the retailer forecasts the demand scale may shrink, the change of the pricing power
between ante- and post-information sharing depends on the relative precision of retailer’s demand
forecast information. However, after information sharing, the retailer’s pricing power increases with the
decrease of the relative precision of its demand forecast information. The lower the relative precision of
retailer’s demand forecast information and the higher the precision of its demand forecast information,
the greater its pricing power and the more its profit, which also shows that the information is the source
of power.
6 Conclusion
This paper, under the condition of longitudinal monopoly market, by means of quantitative analysis,
studies the pricing powers of the manufacture and the retailer in a two-echelon supply chain. Under the
condition where the downstream acquires the posterior information of market demand, we discuss the
incentives of the retailer’s sharing information and the manufacture’s accepting information in two
situations, and prove that the information is the source of power. From analyzing, we conclude that
when the retailer forecasts the demand scale may expand, the strategy of sharing information causes its
pricing power to increase and the manufacture’s profit to decrease, in this case the retailer seizes the
overall benefit from market expanding; when the retailer forecasts the demand scale may shrink, the
change of the pricing power between ante- and post-information sharing depends on the relative
precision of its demand forecast information. However, after information sharing, the retailer’s pricing
power increases with the decrease of the relative precision of its demand forecast information. That’s to
say, the higher the precision of retailer’s forecast information, the greater its pricing power and the more
it benefits from the strategy of sharing information.
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