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 +.0000029Q^2 - .000046QZ - .026Z + .00018Z^2

Where AVC=average variable cost(i.e., working costs of generation), measured in pence per kilowatt-hour(kWh). (A pence was a British monetary unit equal, at that time, to 2 cents U.S.)

Q= output, measured in millions of kWh per year

Z= plant size, measured in thousands of kilowatts

A. Determine the long-run variable cost function for electricity generation.

B. Determine the long-run marginal cost function for electricity generation.

C. Holding plant size constant at 150,000 kilowatts, determine the short-run average variable cost and marginal cost functions for electricity generation.

D. For a plant size equal to 150,000 kilowatts, determine the output level that minimizes short-run average variable costs.

E. Determine the short-run average variable cost and marginal cost at the output level in Part (d).