Chemistry Reference
In-Depth Information
R
k
.Q
k
/
z
k
q
A
c
k
3
L
k
R
k
.Q
k
/
p
A
c
k
Q
k
P
i ¤k
L
i
Fig. 1.8
Example 1.4; the best response function (
thick line
)ofatypicalfirmk with a linear cost
function and quadratic price function
implying that at the interior equilibrium
A
Q
2
c
k
D
x
k
:
2 Q
Summation over all N firms yields
P
lD1
c
l
2 Q
NA
N Q
2
Q
D
;
and therefore
NA
P
l
D
1
c
l
N
C
2
Q
2
D
:
The individual quantities in equilibrium are then obtained as
A
!
(1.14)
NA
P
l
D
1
c
l
N
C
2
1
2
q
.NA
P
lD1
c
l
/=.N
C
2/
x
k
D
c
k
2A
C
P
lD1
c
l
.N
C
2/c
k
D
2
q
.N
C
2/.NA
P
lD1
c
l
/
:
For positivity of all equilibrium quantities, additional conditions are required,
namely that
c
k
<
2A
C
P
l
¤
k
c
l
N
C
1
for all k:
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