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:
+ .0033Q + .0000029Q^2 – .000046QZ – .026Z + .00018Z^2
where variable cost measured in pence per kilowatt-hour. (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 average 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).