572 Chapter 13 The Value of Information- Consider the following simplified version of the television game show
Let’s Make a Deal. There is a grand prize behind one of three curtains; the
other two curtains are empty. As a contestant, you get to choose a curtain
at random. Let’s say you choose curtain 3. Before revealing what’s
behind the curtain, the game show host always offers to show you what
one of the other curtains contains. She shows you that curtain 2 is empty;
in fact, she always shows you an empty curtain. (You know that’s how the
game works; so do the audience and everybody else.) Now you must
decide: Do you stick with your original choice, curtain 3, or switch to
curtain 1? Which action gives you the better chance of finding the grand
prize? - Opening a multimillion dollar musical on Broadway is the ultimate
financial gamble. Hits such as The Phantom of the Operacan earn millions
in profit. Disasters too numerous to name have meant millions in losses.
In the 2011 season, the producers of the musical Spider Man, Turn off the
Darkwith state-of-the-art special effects and music and lyrics by Bono and
The Edge faced high hopes and an important decision: whether to
mount the usual series of out-of-town previews or to open directly on
Broadway. A direct opening would save considerable costs (estimates for
the Broadway run alone were spiraling above $60 million) but would give
up the valuable opportunity to revise and craft the show based on
audience reactions in tryouts.
a. A direct Broadway opening is projected to have three possible
outcomes: a “Hit” (implying net profit of $30 million), a “Solid
Show” ($10 million in profit), or a “Bomb” ($50 million in losses).
The producers’ best probability estimates of these outcomes are .3,
.5, and .2, respectively. What is the expected profit of a direct
Broadway opening?
b. Alternatively, the producers could test the production in a series of
out-of-town previews at an added cost of $7 million. By carefully
taking the pulse of the audience, the producers can expect one of
three findings. If the show is “Well-Received” (probability .35), then
only mild tweaking will be needed and estimated Broadways profits
from an extended run will be $24 million. If the show has definite
“Kinks” (probability .45), then besides being less appealing to
audiences, the show will require fixing and reworking, reducing the
estimated Broadway profit to $12 million. Finally, if the production
turns out to have “Major Problems” in front of the preview
audiences (probability .2), then the producers should cut their
losses and not open on Broadway at all (so they are only $7 million
in the red).
What is the expected overall profit from previewing the show out
of town? Is this more profitable than opening on Broadway directly?
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