lecture 3 short run price competition
TRANSCRIPT
-
8/17/2019 Lecture 3 Short Run Price Competition
1/12
4/14/
. .
1. I2. C 3. S ( )4. B
-
8/17/2019 Lecture 3 Short Run Price Competition
2/12
4/14/
A :
• • •
• R M P ( AA C , 1838, F ): N E
.
• A : – F – F :
-
8/17/2019 Lecture 3 Short Run Price Competition
3/12
4/14/
.
• C ( ):C ( ) = , =1, 2, 2, 1 ≥ 0 ...(1)
(Q) = Q , , > 0, > , Q = 1 + 2 ...(2)
(A ) ∈ A = 0, ∞ , =1, 2.
P :Π ( 1, 2) = ( 1 + 2) C ( )
, ,
, 1 , 2 C N :
F :( ) 2 = 2 ; 1 1,
Π 1 ( 1 , 2 ) = ( 1 + 2 ) 1 C1 ( 1)= (1 + 2 ) 1 1 1
( ) 1 = 1 ; 2 2,
Π 2 ( 1 , 2) = ( 1 + 2) 2 C2 ( 2)= (1 + 2) 2 2 2
S :
= ( 1 + 2 ), , 1 , 2≥
0
, C , C
-
8/17/2019 Lecture 3 Short Run Price Competition
4/12
4/14/
C C :
F 1 :
1
2
R1( 2)
R2( 1)
2
1
F 2 :
1211
211 2),(
0 cbqbqaqqq
−−−=∂
Π∂=
21
211 2
1
2)( q
bca
q Rq −−
==
2212
212 2),(
0 cbqbqaqqq
−−−=∂
Π∂=
12
122 2
1
2)( q
bca
q Rq −−
==
b
ca 2−
bca
21
−
bca
22
−
bca 1−
I : , ,
.
:
C :
N : 2≥ 1 1 ≥ 2
C ( ) :
bcca
q c3
2 211
+−=
bcca
q c3
2 122
+−=
321 ccabQa p cc
++=−=
22
1 )(9
)2(
3
2
3))(( ci
jici
i jc
iicc
i qbb
cca
b
cac
ccaqc p j =
+−=
−
−
++=−=Π
+
bcca
qqQ ccc3
2 2121
−−=+=
C :
-
8/17/2019 Lecture 3 Short Run Price Competition
5/12
4/14/
1
2
R1( 2)
R2( 1)
2
1
S : 1 1*, 1* < 1.......
bca 2−
bca
21
−
bca
22
−
bca 1−
A 1 , 1
2 . A , , 1
( 2).
. .
S :• , N≥ 1
• 2 :
, .
(2) H , .
L (1) , . , .
-
8/17/2019 Lecture 3 Short Run Price Competition
6/12
4/14/
F 1 1 : 111
111 )(max1
cqqqbacqqQ p N
ii
q−
−=−=Π ∑=
FOC : ∑=
−−−=∂
Π∂=
N
i
i cqbbqa
q 21
1
1 20
H , : ∑=
−−
= N
ii N qb
caqqq R
2321 2
1
2),...,,(
S , C: 1 = 2 = = N = = . , :
+
−==
+
−=
1)1( N N
bca
NqQb N
caq ccc
1++
=−= N Nca
bQa p cc 2
2
2
)()1(
)( cci qbb N
ca =+
−=Π
:
(N=2, 3, )
0lim =∞→
c
N q
−
=
+
−
=∞→∞→ b
ca N
N b
caQ
N
c
N 1limlim
e
N
c
N pc
N Nc
N a
p ==
++
+=
∞→∞→ 11limlim
,
I C , ,
.
C . ! (
). H , , N=1.
C .
-
8/17/2019 Lecture 3 Short Run Price Competition
7/12
4/14/
• A : .• , 1 ( )
. .
• I , 2 ( ) 1
. H , .
• :(1) I ?(2) H
C ?
G : .
F : , 1= 2=
2 2 , 1 , 1, . 2 ( C ):
11222
1
2)( q
bca
q Rq −−
==
111
1111211 22))((max
1
cqqq
bca
qbacqqq Rq psq
−
−−
+−=−+=Π
, C :
ccs qqb
caq 111 23
2>=−= ccs qq
bcaq 222 4
34
-
8/17/2019 Lecture 3 Short Run Price Competition
8/12
4/14/
:
cs pcaca
p =+
<+
=3
2
4
3 cs Qb
cab
caQ =
−>
−=
3
)(2
4
)(3
cs
bca
1
2
1 8
)(Π>
−=Π
C .
cs
bca
2
2
2 16)(
Π<
−
=Π
:
• J B C (45 C ),
, , .
• B : N ,
.
-
8/17/2019 Lecture 3 Short Run Price Competition
9/12
4/14/
A :
• 2 . , (
• M Q=D( )
• .
• F .
• .
N N , .
:(1) C .(2) I , .
>
=
<
=
>
=
<
=
12
2122
1222
212
21
2111
2111
211
0
)(21
)(
),(
0
)(21
)(
),(
p pif
p pif p D
p pif p D
p p D
p pif
p pif p D
p pif p D
p p D
:
-
8/17/2019 Lecture 3 Short Run Price Competition
10/12
4/14/
:
F : F B (2006)
N B :
1. .2. C .
L 1 , 2 , 1 , 2 B N :
(1) G 2 = 2 ; 1 Π 1 ( 1 , 2 ) = ( 1 1) 1
(2) G 1 = 1 ; 2 2
Π 2 ( 1 , 2) = ( 2 2) 2
(3) 1 2 D1 D2.
, .
(Π 1 + Π 2) (Π ): 0 ≤ Π 1 + Π 2 ≤ Π
. .
-
8/17/2019 Lecture 3 Short Run Price Competition
11/12
4/14/
. .
. .
-
8/17/2019 Lecture 3 Short Run Price Competition
12/12
4/14/
. .