Chapter 9

: Applications of Cost Theory

**329**

3. A study of the costs of electricit

y

generation for a sample of 56 British firms in

1946-1947

.yielded the following long-run cost function.

"

AVe

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

2

where

* Ave *=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.

b. Determine the long-run marginal cost function for electricit

y

generation.

c

.

Holding plant size constant at 150,000 kilowatts, determine the short-run

average variable cost and marginal cost functions for

electricity generati

on.

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).

4"1

Assuming that all other factors remain unchanged, determine how a firm's breakeven

point is affected by each of the following:

a. The firm finds it necessary to reduce the price per unit because of increased

foreign competition.

b. The firm's direct labor costs are increased as the result of a new labor

contract.

c

.

The Occupational Safety and Health Administration (OSHA) requires the

firm to install new ventilating equipment in its plant. (Assume that this

•

action has no effect on worker productivity.)

5/

~

001-Aire Corporation manufactures a line of room air conditioners. Its breakeven

sales level is 33,000 units

.

Sales are approximately normally distributed.

Expected sales next year are 40

,000 units with a standard deviation of 4,000 units

.

•

a. Determine the probability that Cool-Aire will incur an operating loss

.

b

. Determine the probability that Cool-

Aire will operate above its break-even

point

.

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