Eco 550

Chapter 9

3. 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:16

AVC = 1.24 + .0033Q + .0000029Q2 - .000046QZ - .026Z + .00018Z2

Where AVC = 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.).

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

VC = AVC(Q)

VC = 1.24Q + .0033Q2 + .0000029Q3 .000046Q2Z .026QZ + .00018QZ2

B. Determine the long-run marginal cost function for electricity generation.

MC = 1.24 + .0066Q + .0000087Q2 .000092QZ .026Z + .00018Z2

C. Holding plant size equal to 150,000 kilowatts, determine the output level that minimizes short-run average variable cost and marginal cost functions for electricity generation.

Z = 150(thousand) kilowatts

SRAVC = 1.24 + .0033Q + .0000029Q2 .000046Q(150) .026(150) + .00018(150)2

SRAVC = 1.39 .0036Q + .0000029Q2

SRMC = 1.24 + .0066Q + .0000087Q2 .000092Q(150) .026(150) + .00018(150)2

SRMC = 1.39 .0072Q + .0000087Q2

D. For a plant size equal to 150,000 kilowatts, determine the output level that minimizes short-run average variable costs.

d(SRAVC)/dQ = 0 (condition for minimum SRAVC) = .0036 + .0000058Q = 0

Q* = 620.7 (million) kilowatt-hours/year

E. Determine the short-run average variable cost and marginal cost at the output level obtained in Part (d).

SRAVC = 1.39 .0036(620.7) + .0000029(620.7)2 = .27 pence

SRMC = 1.39 .0072(620.7) + .0000087(620.7)2 = .27 pence

They appear to be equal....