Question

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

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: (Source: Johnston, “Chapter 4,” in Statistical Cost Analysis)

AVCAVC = 1.241.24 + 0.0033Q0.0033Q + 0.0000029Q20.0000029Q2 - 0.000046QZ0.000046QZ - 0.026Z0.026Z + 0.00018Z20.00018Z2

where AVCAVC = average variable cost (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.)

QQ = output; measured in millions of kWh per year

ZZ = plant size; measured in thousands of kilowatts

What is the long-run total variable cost function for electricity generation?

0.0033+20.0000029Q−0.000046Z0.0033+20.0000029Q−0.000046Z

0.0033Q+20.0000029Q2−0.000046QZ0.0033Q+20.0000029Q2−0.000046QZ

1.24Q+0.0033+0.0000029Q−0.000046Z−0.026ZQ+0.00018Z2Q1.24Q+0.0033+0.0000029Q−0.000046Z−0.026ZQ+0.00018Z2Q

1.24Q+0.0033Q2+0.0000029Q3−0.000046Q2Z−0.026ZQ+0.00018Z2Q1.24Q+0.0033Q2+0.0000029Q3−0.000046Q2Z−0.026ZQ+0.00018Z2Q

What is the long-run marginal cost function for electricity generation?

1.24+0.0066Q+0.0000087Q2−0.000092QZ−0.026Z+0.00018Z21.24+0.0066Q+0.0000087Q2−0.000092QZ−0.026Z+0.00018Z2

1.24Q+0.0033Q2+0.0000029Q3+0.000046Q2Z+0.026ZQ+0.00018Z2Q1.24Q+0.0033Q2+0.0000029Q3+0.000046Q2Z+0.026ZQ+0.00018Z2Q

0.0033Q+20.0000029Q2+0.000046QZ0.0033Q+20.0000029Q2+0.000046QZ

1.24Q+0.0033+0.0000029Q+0.000046Z+0.026ZQ+0.00018Z2Q1.24Q+0.0033+0.0000029Q+0.000046Z+0.026ZQ+0.00018Z2Q

Holding plant size constant at 150,000 kilowatts, what is the short-run average variable cost function for electricity generation? (Note: Z is measured in thousands of kilowatts)

1.39−0.0036Q+0.0000029Q21.39−0.0036Q+0.0000029Q2

1.39+0.0066Q+0.0000029Q21.39+0.0066Q+0.0000029Q2

1.39−0.0072Q+0.0000029Q21.39−0.0072Q+0.0000029Q2

1.24+0.0033Q+0.0000029Q21.24+0.0033Q+0.0000029Q2

Holding plant size constant at 150,000 kilowatts, what is the short-run marginal cost function for electricity generation? (Note: Z is measured in thousands of kilowatts)

1.39+0.0066Q+0.0000029Q21.39+0.0066Q+0.0000029Q2

1.39−0.0072Q+0.0000087Q21.39−0.0072Q+0.0000087Q2

1.24+0.0033Q+0.0000029Q21.24+0.0033Q+0.0000029Q2

1.39−0.0036Q+0.0000029Q21.39−0.0036Q+0.0000029Q2

For a plant size equal to 150,000 kilowatts, what is the output level that minimizes short-run average variable costs? selector 1   
  • 1,241.38
  • 2,482.76
  • 620.69
  • 2,275.86
million kWh per year At the output level thus obtained, the short-run average variable cost is selector 1   
  • 4.41
  • 0.27
  • -6.43
  • -1.96
pence per kWh and the short-run marginal cost is selector 2   
  • 4.41
  • 0.27
  • -4.20
  • -13.13
pence per kWh.
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