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
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