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A study of costs of electricity generation for a sample of 56 British firms in 1946-1947 yielded the following long-run cost function: 16AVC = 1.24 + .0033Q + .0000029Q2 - .000046QZ - .026Z + .00018Z2Where AVC = average variable costs of generation (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 yearZ = plant size, measured in thousands of kilowattsa. 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).
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