9781118041581

Relevant Costs 235

Question 1, the only marginal cost associated with the best seller is the explicit

$12 cost paid to the publisher. The manager maximizes profit by setting MR

equal to MC. Since MR  24 2Q, we have 24 2Q 12. The result is

Q 6 hundred books and P $18. This outcome is listed in Table 6.1a.

By comparison, what are the optimal order quantity and price when shelf

space is limited, as in Question 2? The key point is that ordering an extra best

seller will involve not only an out-of-pocket cost ($12) but also an opportunity

cost ($4). The opportunity cost is the $4 profit the shelf space would earn on

an already stocked book—profit that would be forgone. In short, the total cost

of ordering the book is 12  4 $16. Setting MR equal to $16, we find that

Q 4 hundred and P $20. Given limited shelf space, the manager orders

fewer best sellers than in Question 1. Table 6.1b compares the profitability of

ordering 400 versus 600 books. The cost column lists the store’s payment to

the publisher ($12 per best seller). Forgone profit is measured at $4 per book.

We confirm that ordering 400 books is the more profitable option, taking

into account the forgone profit on sales of other books. Indeed, the logic of

marginal analysis confirms that this order quantity is optimal, that is, better

than any other order size.

Finally, Question 3 asks how the manager should plan sales and pricing of

the 400 best sellers already received if demand falls to P  18 2Q. The key

here is to recognize that the original $12 purchase price is irrelevant; it is a

sunk cost. However, opportunity costs are relevant. The opportunity cost of

keeping the best seller for sale has two elements: the $4 profit that another

book would earn (as in Question 2) plus the $6 refund that would come if the

copy were returned. Therefore, the total opportunity cost is 6  4 $10.

TABLE 6.1

An Optimal Book Order

The optimal number of

books to order and sell

depends on demand,

sales costs, and oppor-

tunity costs.

Sales Forgone Final

Price Revenue Cost Profit Net Profit

(a)Qs 600 $18 $10,800 $7,200 $ 0 $3,600

(b)Qs 400 20 8,000 4,800 1,600 1,600

[Qs600] 18 10,800 7,200 2,400 1,200

(c)Qs 200 14 2,800 4,800 800 1,600

Qr 200 6 1,200 0

[Qs400] 10 4,000 4,800 1,600 2,400

[Qr0] 6 0 0

[Qs0] — 0 4,800 0 2,400

[Qr400] 6 2,400 0

c06CostAnalysis.qxd 9/29/11 1:46 PM Page 235