A study of the costs of electricity generation for a sample of 56 British firms in 1946-1947 yielded the following long-run cost functions: AVC= 1.24 + .0033Q +.0000029Q2- .000046QZ-.026Z +.00018Z2 where AVC = average variable cost (i.e. working costs of generation), measured in pence per kilowatz (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 kilowatz
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 kilowatz, determine the short- run average variable cost and marginal cost functions for electricity generation
d. For a plant size equal to 150,000 kilowatz, 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.