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Cost Analysis and Optimal Decisions 261

In the preceding example, a typical accounting allocation would assign the

$2.4 million in fixed costs to the products in proportion to output: $1.6 million

to the first product and $.8 million to the second. (The first product consti-

tutes two-thirds of total output.) Thus, the first product’s accounting profit

would be 

1 (10 9)(1.2) 1.6 $.4 million. Based on this measure, the

product appears to be unprofitable. What if the firm discontinues its produc-

tion? The firm will no longer earn any contribution from the first good. But

there will be no decline in the $2.4 million fixed cost; now the entire fixed cost

will be assigned to the second item. Left producing a single good, the firm will

be unable to earn a profit (its losswill amount to 2.4 1.5 $.9 million) and

will be forced to shut down. Here, allocating fixed costs leads to a disastrous

series of decisions. As we noted earlier, the firm’s optimal course of action is to

produce both products. To repeat, assigning fixed costs to products is unnec-

essary (and potentially misleading). Instead, the only relevant long-run issue is

whether the firm’s total contribution covers these fixed costs in the aggregate.

Allocating Costs

Revisited

In the example that opens this chapter, the managers of a sports shoe company were engaged in a

debate over what strategy would lead to the greatest profit. Should production of the boys’ shoes

be increased? Cut back? Discontinued? The correct answers to these questions depend on a care-

ful analysis of relevant costs. To clarify the situation, management has gathered cost information

about different sales quantities. The firm’s production managers have supplied the data on direct

(i.e., variable) costs. Recall that production of women’s and boys’ running shoes share $90,000 in

fixed costs. The firm’s accountants allocate this cost to the two lines in proportion to numbers of

pairs. The output of women’s shoes is 8,000 pairs.

Pairs Allocated Average

of Shoes Price Revenue Direct Cost Cost Total Cost

1,600 $40 $64,000 $66,400 $15,000 $50.88

2,400 36 86,400 74,400 20,769 39.65

3,200 32 102,400 85,600 25,714 34.79

3,600 30 108,000 92,400 27,931 33.43

4,000 28 112,000 100,000 30,000 32.50

Thus, if the volume of boys’ shoes is 4,000 pairs, the product’s output is one-third of the

total; hence, its allocation is (1/3)($90,000) $30,000. Allocations for other outputs are

computed in the same way. Average total cost is the sum of direct and allocated costs

divided by total output.

The firm currently is charging a price of $36 per pair and selling 2,400 pairs per week.

How would management evaluate the current profitability of this strategy, and how might

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