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Appendix to Chapter 9 Bundling and Tying 393

the $7,000 price is the better option. Similarly, one can check that the studio’s

optimal price for film Y is $6,000 per screen per week. At these prices, the films

will be sold to both chains and will produce $13 million in total revenue.

What if the studio were to sell the films as a package at a bundled price?

The last column of Table 9A.1 shows the combined value each chain puts on

the film package. Clearly, the studio’s optimal bundled price is PB$18,000.

At this price, both chains purchase the bundle, and the studio earns $18 mil-

lion per week. Bundling has increased the studio’s revenue by $5 million, or

some 38 percent. What is the source of this additional profit? The answer lies

in the fact that each chain’s values for the films are negativelycorrelated. That

is, the chain with the higher value for one film has the lower value for the other.

Since higher and lower values are offsetting, the chains have very similar total

values for the bundled package. By bundling films, the studio can set a price

($18,000) that extracts nearly all of each chain’s total value (or consumer sur-

plus) for the films, without pricing either chain out of the market.

Notice that bundling holds no advantage over separate pricing if the

chains’ values for film Y are reversed. In this scenario, chain 1 puts higher val-

ues ($13,000 and $11,000) on both films. Each chain’s values are positivelycor-

related; that is, high values go with high values, low values with low values.

Check for yourself that the studio’s optimal bundled price is PB7,000 

6,000 $13,000. In other words, the bundled price is simply the sum of the sep-

arate film prices. Sold separately or as a bundle, the films deliver exactly the

same revenue.

Bundling can be profitable even when the goods’ values are uncorrelated.

Consider once again the studio’s pricing problem, but now let each chain have

TABLE 9A.1

Selling Films: Separate

Sales versus Bundling

Depending on the

circumstances, a firm

can increase its

revenue via bundling.

(a)

Values ($000)

Film X Film Y Bundle

Theater Chains Chain 1 13 6 19

Chain 2 71118

(b)

Values ($000)

Film X Film Y Bundle

Theater Chains Chain 1 13 6 19

Chain 2 71118

Chain 3 15 2 17

Marginal cost 5510

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