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A study of the costs of electricity generation for a sample of 56 British firms

ID: 1176285 • Letter: A

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:

AVC = 1.24 + .003Q + .0000029Q^2 - .000046QZ - .026Z + .00018Z^2

Where AVC = average 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 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).

Explanation / Answer

a long run total variable cost function is-

1.24Q + .003Q^2 + .0000029Q^3 - .000046(Q^2*Z) - .026QZ + .00018Q*Z^2


b 1.24 + .006Q + .0000087Q^2 - .000092(Q*Z) - .026Z + .00018Z^2


c SAVC= 1.24 + .003Q + .0000029Q^2 - 69Q - 3900 + 40500000

SMC=1.24 + .006Q + .0000087Q^2 - 138Q - 3900 + 40500000


d 22158.27


e AVC=$38981485.76

MC=$37442664.53