9781118041581

(Nancy Kaufman) #1
572 Chapter 13 The Value of Information


  1. 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?

  2. 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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