Question: 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:¹?

AVC=124 + .0033Q + .0000029Q² - .000046QZ - .026Z + .00018Z²

Where AVC= average variable cost (ie 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 of electricity generation

b. Determine the long run marginal function of 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.

a. Determine the short run average variable cost and marginal cost at the out put level obtained above.