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 + .0000029Q2 − .000046QZ − .026Z + .00018Z2
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 obtained in Part (d).