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:16 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 out- put level obtained in Part (d).