Chemistry Reference
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to the increase of E.
e
'
k
/ by firm k, then this firm might decide to maximize the
utility function
‰
k
.x
1
;:::;x
N
/
D
E.
e
'
k
/
k
Var.
e
'
k
/
D
x
k
f
k
.Q/
.C
k
.x
k
/
C
k
k
x
k
/:
(5.148)
Notice that this function has the same form as the profit of firm k with believed price
function f
k
and cost function C
k
.x
k
/
C
k
k
x
k
. Therefore all results of Sect. 5.1
can be applied to this case by assuming that the firms do not update their informa-
tion about the distributions of the random variables
k
based on the repeated price
observations during the dynamic process. In reality however at each time period a
new sample element for each random variable
k
becomes available, so each firm is
able to update E.
k
/ and Var.
k
/ by using Bayesian methodology. If we now use
the notation E.
k
.t//
D
e
k
.t/ and Var.
k
.t//
D
k
.t/ for the updated expecta-
tion and standard deviation of
k
at time period t, then at the next period the utility
function of firm k becomes
x
k
. f
k
.x
k
C
Q
k
.t
C
1//
C
e
k
.t//
.C
k
.x
k
/
C
k
.t/
k
x
k
/;
so the best response of firm k as well as the resulting dynamic models with both
discrete and continuous time scales become time variant. The details of Bayesian
updating of the distributions of
k
as well as an examination of the asymptotic
behavior of the corresponding time variant dynamical systems are beyond the scope
of this topic. The interested reader may consult Cyert and DeGroot (1971, 1973,
1987) to find out more about the relevant methodology.
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