Question

A company has a linear total cost function and has determined that over the next three months it can produce 12,000 units at a total cost of $224,000. This same manufacturer can produce 18,000 units at a total cost of $296,000. The selling price per unit is $13.25. i. Determine the revenue, cost and profit functions using q for number of units. ii. What is the fixed cost ? iii. What is the marginal cost ? iv. Find the break-even quantity. v. What is the break-even dollar volume of sale ? vi. What will profit be if the company shuts down operation? vii. If, because of a strike, the company will be able to produce only 10,000 units, should it shut down for the next three months ? why or why not ?

Answer 1

i. The revenue, cost and profit functions using q for number of units are:

TR = 13.25q,

$\frac{TC - 224,000} {296,000 - 224,000} = \frac{q - 12,000} {18,000 - 12,000},$

$\frac{TC - 224,000} {12} = \frac{q - 12,000} {1},$

$TC - 224,000 = 12q - 144,000,$

TC = 12q + 80,000.

TP = TR - TC = 1.25q - 80,000.

ii. The fixed cost is:

FC = 80,000.

iii. The marginal cost is:

MC = TC'(q) = 12.

iv. The break-even quantity is:

$BEQ = 80,000/(13.25 - 12) = 64,000.$

v. The break-even dollar volume of sale is:

TR = 13.25×64,000 = 848,000.

vi. The company shuts down operation at P < AVC or P < 12.

vii. If, because of a strike, the company will be able to produce only 10,000 units, then:

TP = 1.25×10,000 - 80,000 = -67,500.

But it should not shut down for the next three months, because it can cover its variable costs.