Microsoft Word 2007 ichrie conference Proceedings Final-Final 06-06-07. doc

 
2007 Annual International CHRIE Conference & Exposition 
509
The price function selected here is for multiple reasons. First, linear form of demand function is broadly used 
in manufacture supply chain (Carr and Karmarkar 2005; Xiao and Yu 2006), also applied in tourism and hospitality 
literatures (Zheng 1997; Wie 2005). Second, price and demand in most of tourism literatures is exponential 
(logarithmic) relationship (Song and Witt 2006; Garín-Munoz 2006). However, this paper focuses on dynamic TSC. 
Especially we are interested in impact of systemic parameters, if change is slightly, linear function is also 
appropriate to depict exponential function within a small interval. Third, the sensitivity of tourists’ quantity in TSC 
to changes of price is simplified to 1 in the model, like Ingene and Parry (1995). 
Notice that, in demand function package holiday price decreases when tourists increasing in both TSC. This 
presents two types of competition mentioned above. Price decrement caused by tourist’s increment in the same TSC 
presents horizontal competition in the TO sector, while price decrement caused by tourist’s increment in the 
competitive TSC presents lateral
 
competition between two TSCs.
Backwards induction is used here to solve this multi-stage game. Let’s start with the last stage of the game in 
which TOs simultaneously decide quantities of tourists. Given the TP’s price 
p
and HA’s price
2
p
, the profit 
function for 
i
TO
is given by expression: 
1
1
1
2
1
(
)
i
i
i
q p
p p
c
π
=
− −
−
(2) 
Taking first-order condition with respect to quantity, then summing up the equations for all TOs in the TSC, 
the total number of tourist is shown as following: 
1
2
1
(
)
1
N
c
p p
Q
Q
N
α
μ
−
− − −
−
=
+
(3) 
As the number total tourist in TO sector is equal to that in HA sector of the same TSC, we obtain the quantity 
for each HA from (3): 
2
1
1
(
1)
N
Q
p
c
p
Q
N
α
μ
−
+
= − − −
−
(4) 
The profit function for 
j
HA
is
2
2
2
2
(
)
j
j
j
p
c q
π
=
−
. Applying the same logic as for TO, HA have no incentive 
to deviate from the optimal quantity if and only if the following quantity is 
selected
1
2
1
2
(
)
(
1)(
1)
N
c
c
p
Q
q
N
M
α
μ
−
− − − −
=
+
+
. This immediately gives 
1
2
1
(
)
(
1)(
1)
MN
c
c
p
Q
Q
N
M
α
μ
−
− − − −
=
+
+
(5) 
The TP’s profit is
3
(
)
Q p c
π
=
−
. Substituting (3) into this function, we can get optimal ticket price as 
bellow: 
1
2
1
2
c
p
Q
c
p
α
μ
−
− −
−
+
=
(6) 
Combining (4), (5) and (6), the total number of tourists is shown: 
1
2
1
(
)
(
1)(2
1)
NM
c
c
c
Q
Q
N
M
α
μ
−
− − − −
=
+
+
(7) 
When two TSCs lateral
 
competition is under considering, equations are extended from (7) for each TSC: 
1
2
(
)
(
1)(2
1)
A
A
A
A
A
A
B
A
A
A
M N
c
c
c
Q
Q
N
M
α
μ
−
−
−
−
=
+
+
,
1
2
(
)
(
1)(2
1)
B
B
B
B
B
B
A
B
B
B
M N
c
c
c
Q
Q
N
M
α
μ
−
−
−
−
=
+
+
Thus, we can obtain the following proposition: