394 Appendix to Chapter 9 Bundling and Tyinguncorrelated values. In particular, suppose that each of the 1,000 theaters that
make up the two chains values film X at $13,000 or $7,000, with each value
equally likely. In turn, each theater values film Y at $11,000 or $6,000, again
with each value equally likely. (Like coin tosses, a theater’s value for one film
is independent of its value for the other.) Thus, the same numbers in Table
9A.1a apply, but with new interpretations. As before, the studio’s optimal sep-
arate film prices are PX$7,000 and PY$6,000, inducing all theaters to pur-
chase both films. Now consider the demand for the films as a bundle. From
the values in Table 9A.1, the possible bundled values are $13,000 (25 percent
of theaters), $18,000, (25 percent), $19,000 (25 percent), and $24,000 (25 per-
cent). If the studio sets PB$13,000, all theaters purchase the film. However,
the studio can do better by raising its price to PB$18,000, inducing 75 per-
cent of the theaters to purchase the bundle. To check this, note that only the
“$13,000” theaters refuse to buy. The studio’s revenue is (18,000)(750)
$13,500,000. In short, even with independent demands, bundling has a rev-
enue advantage over separate sales. (Check for yourself that raising the bun-
dled price above $18,000 is counterproductive.)MIXED BUNDLING Thus far, our discussion has centered on the potential
advantages of so-called pure bundling vis-à-vis separate sales. Of course, firms
frequently offer customers both options: to purchase the bundle or to buy
only one of the goods at a separate price. This policy is termed mixed
bundling.
Table 9A.1b demonstrates the advantage of mixed bundling. Following our
original interpretation, chains 1 and 2 have negatively correlated values for the
films (the same values as before). We have modified the example in two ways.
First, we have added a third buyer, chain 3, which places a very low value on film
Y. (Think of chain 3’s theaters as being spread throughout retirement com-
munities. Film X is Everyone Loves Grammaand film Y is Horror on Prom Night.)
Second, we have introduced a cost associated with producing and selling the
film. (The $5,000 cost in the example reflects the studio’s cost of creating extra
prints of the film for distribution to theaters.)^2
Now consider the studio’s possible pricing strategies. Its most profitable
pure-bundling strategy is to set PB$17,000 and to sell to all three chains
(1,500 theaters), giving it total profit: (17,000 10,000)(1,500)
$10,500,000. (Check for yourself that setting PB$18,000 and selling only
to chains 1 and 2 is less profitable.) Alternatively, the studio can pursue
mixed bundling: pricing the bundle at PB$18,000 and pricing the sepa-
rate films at PX$15,000 and PY$12,000. Given these prices, chains 1 and
2 purchase the bundle, while chain 3 purchases only film X. Therefore, the(^2) In Table 9A.1a, we ignored marginal costs for the purpose of keeping things simple. It is easy to
check (after computing profits rather than revenues) that pure bundling becomes even more
advantageous if marginal costs are present.
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