[Steps Shown] 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:

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 + .0033Q + .0000029 Q ² - 0.000046QZ - .026Z + .00018Z 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

Determine the long-run variable cost function for electricity generation.
Determine the long-run marginal cost function for electricity generation.
Holding plant size constant at 150,000 kilowatts, determine the short-run average variable cost and marginal cost functions for electricity generation.
For a plant size equal to 150,000 kilowatts, determine the output level
that minimizes short-run average variable costs.
Determine the short-run average variable cost and marginal cost at the out-

put level obtained in Part (d).

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[Steps Shown] 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:

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