574 Chapter 13 The Value of Informationa. Firm B must decide now whether to undertake the R&D investment.
What course of action maximizes its expected profit? (Use a decision
tree to justify your answer.)
b. Suppose instead that firm B can postpone its R&D decision for six
months, by which time it will have learned the court’s ruling on its
patent. What is its expected profit if it waits? Depending on the court
outcome, what actions should it take?
c. Suppose instead that firm B can build a 75 percent speed, prototype
chip before committing to the full-scale R&D investment. The
prototype chip will either run cool (C) or hot (H). The firm’s
scientists believe that the prototype will certainly run cool if the R&D
effort is to succeed: Pr(CƒS) 1.0. If the R&D effort is doomed to fail,
the scientists believe that the prototype chip will run hot with
probability 2/5: Pr(HƒF) .4. Find Pr(SƒC) and Pr(SƒH).
d. Should the firm build the prototype chip at a cost of $2 million? Use a
decision tree to justify your answer. (Assume that the firm cannotwait
for the patent outcome.)
*10. A government agency suspects that one of the firms it has hired under
a cost-plus contract is padding its bills to the government. If padding is
going on and if the agency can prove its case in court, it estimates it
could save $2 million in disallowed costs. However, the cost of bringing
a large-scale legal action against the firm is considerable, about
$500,000. The agency’s auditors believe that there is a 20 percent
chance that padding is going on. Its lawyers reckon that there is a 75
percent chance of proving and winning the legal case (if padding is
indeed taking place).
a. Assuming the agency is risk neutral, use a decision tree to determine
its best course of action.
b. Suppose the agency can conduct a preliminary investigation (conduct
audits and interview dozens of employees) before deciding whether to
bring a case. From the investigation, the agency can expect one of two
results: a “clean” outcome (C) or a “questionable bill of health” (Q).
If cost padding really is going on, there is a 75 percent chance that the
investigation will signal Q. If there really is no cost padding, then the
chance of C is 80 percent. (There is a 20 percent chance that would-
be whistle-blowers, such as disgruntled employees, will allege
questionable practices even when no padding is going on.) If an
investigation results in outcome Q, what is the chance that cost
padding is going on?
c. Use a decision tree to determine the expected value to the agency of
conducting an investigation.*Starred problems are more challenging.c13TheValueofInformation.qxd 9/26/11 11:02 AM Page 574