Question: A study of the costs of electricity generation for a sample of 56 . British firms in 1946-1947 yielded the following long-run cost function:

\(AVC=1.24+.0033 Q+.0000029 Q^{2}-.000046 Q Z-.026 Z+.00018 Z^{2}\)

where \(AVC=\) average variable cost (that is, working costs of generation), measured in pence per kilowatt-hour. (A pence was a British monetary unit, being equal to-at that time-two U.S. cents.)

\(Q=\) output, measured in millions of kilowatt-hours per year

\(Z=\) plant size, measured in thousands of kilowatts

1. Determine the long-run variable cost function for electricity generation.
2. Determine the long-run marginal cost function for electricity generation.
3. Holding plant size constant at 150,000 kilowatts, determine the shortrun average variable cost and marginal cost functions for electricity generation.
4. For a plant size equal to 150,000 kilowatts, determine the output level that minimizes short-run average variable costs.
5. Determine the short-run average variable cost and marginal cost at the output level obtained in Part (d).

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