Regal Electrogas

In: Business and Management

Submitted By EBRUm
Words 273
Pages 2
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.
AVC = 1.24 + .0033Q + .0000029Q2 − .000046QZ − .026Z + .00018Z2
TC = AVC*Q = 1.24Q + .0033Q2 + .0000029Q3 − .000046Q2Z − .026ZQ + .00018QZ2
b. Determine the long-run marginal cost function for electricity generation.
Differentiate TC to get
MC = 1.24 + .0066Q + .0000087Q2 − .000092QZ − .026Z + .00018Z2
c. Holding plant size constant at 150,000 kilowatts, determine the short-run average variable cost and marginal cost functions for electricity generation.
Put Z= 150 to get
AVC = 1.24 + .0033Q + .0000029Q2 − .000046QZ − .026Z + .00018Z2
=1.24 + .0033Q + .0000029Q2 − .000046Q*150 − .026*150 + .00018*150*150
=1.24 + .0033Q + .0000029Q2 – 0.069Q – 3.9 + .4.05
= 1.39 - 0.0657Q + .0000029Q2
TC= AvC*Q = 1.39Q - 0.0657Q2 + .0000029Q3
MC= 1.39 - 0.1314Q+ .0000087Q2
d. For a plant size equal to 150,000 kilowatts, determine the output level that minimizes short-run average variable costs.
We need to minimise AVC = = 1.39 - 0.0657Q + .0000029Q2
So dAVC/ d Q= 0
- 0.0657 + .0000058Q = 0
Q= 11327.586

e. Determine the short-run average variable cost and marginal cost at the output level obtained in Part (d) put Q=11327.586 in the eq
AVC = 1.39 - 0.0657Q + 0000029Q2
=1.39 -744.0253 + 327.11006 *.0657*11324.586…...

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