appropriate to take such cost interdependencies into account in
pricing on and off peak electricity. The former would be reduced
and the latter increased relative to their respective marginal
costs. Under such conditions the range in which the appropriate on
peak price falls would be between the ceiling of the actual on peak
costs and the costs on peak if there were no other services
provided by the firm. It must be emphasized, however, that such
deviations from strict marginal cost pricing are due to cost
interdependencies and should not be implemented, as it is sometimes
averred, for reasons of fairness or equity in the treatment of on
and off peak uses.
RELAXING
THE DEMAND INDEPENDENCE ASSUMPTION
It is
important to analyze the effect of relaxing the assumption of
independence across demands for two reasons. First, the expectation
of peak and off peak price differentials is that this will cause a
substitution of the latter for the former. Second, in a positive
(i.e., profit maximizing) decision maker's world the incentive to
price discriminate in various markets would, a priori, appear to be
different from a normative (i.e., welfare maximization) world.
In order to
keep the mathematics simple it will be assumed that there are two
markets, which may be distinguished based upon time of day or
customer category differences. The quantity demanded in each
depends upon its own price and the price in the other market. Costs
are assumed to be independent. Therefore,
P1 =
f(Q1, P2) (B.30)
P2 =
g(Q2, P1)
If these
alternative specifications of the willingness to pay or demand
functions are substituted in the welfare functions used above, (12)
or (22), the necessary conditions for welfare maximization can be
derived by maximizing W**; note the equality between social
and private costs continues to be presumed:
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