A study of costs of electricity generation for a sample of 56 British firms in 1
ID: 1178011 • Letter: A
Question
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 + .00018Z2
Where 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 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
VC = AVC*Q = 1.24Q + .0033Q2 + .0000029Q3 - .000046Q2Z - .026QZ + .00018QZ2
MC = dVC/dQ = 1.24 + .0066Q + .0000087Q2 - .000092QZ - .026Z + .00018Z2
Z=150
AVC = 1.24 + .0033Q + .0000029Q2 - .000046QZ - .026Z + .00018Z2
= 1.24 + .0033Q + .0000029Q2 - .0069Q - 3.9 + 4.05
= 1.39 + .0033Q + .0000029Q2 - .0069Q
= 1.39 - .0036Q + .0000029Q2
MC = 1.24 + .0066Q + .0000087Q2 - .000092QZ - .026Z + .00018Z2
= 1.24 + .0066Q + .0000087Q2 - .0138Q - .3.9 + 4.05
= 1.39 + .0066Q + .0000087Q2 - .0138Q
= 1.39 - .0072Q + .0000087Q2
for AVC minimization, dAVC/dQ = 0
.0033 + .0000058Q - .0069 = 0
.0000058Q = .0036
Q = 620.69
AVC = .2727586
MC = .272798
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