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Question about Economies of scope

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1. (9-4) According to a statistical study, the following relationship exists between an electric light and the power plant's fuel costs (C) and its eight-hour output as a percent of capacity (Q):
C = 16.68 + 0.125Q + 0.00439Q2

a) When Q increases from 50 to 51, what is the increase in the cost of fuel for this electric plant?
b) Of what use might the result in part a be to the plant's manager?
c) Derive the marginal (fuel) cost curve for this plant, and indicate how it might be used by the plant's manager.

HINTS:
C = 16.68 + 0.125Q + 0.00439Q2
a. At Q=50, C =
At Q=51, C =
Therefore the change in cost = C(at Q=51) - C(at Q=50) =
b. Refer to text.
c. C = 16.68 + 0.125Q + 0.00439Q2
Marginal cost, MC = dC/dQ =
At Q=50, MC =
At Q=51, MC=
Compare these to your answer in a.

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