Firm B is considering whether to pursue an R&D effort to develop a powerful new microchip. One concern with the chip's design is that the chip might generate too much heat operating at high speeds. Indeed, there is the risk that the heat problem will doom the R&D effort. Firm B's scientists believe that there is a .5 chance that the R&D effort will succeed (S) and a 5 chance it will fail (F). If the effort succeeds, there is a second. risk. Firm B has filed several patents concerning the design of the chip. If these patents are upheld in court, it will have the exclusive right to produce the chip. However, a competitor, firm Z, has been pursuing a similar chip design and has filed its own patents. If the courts decide in favor of firm Z, both firms will be free to produce similar chips and will share the market. Firm B's legal department estimates a .6 chance that its patents will be upheld giving it exclusive production rights. The following table lists firm B's possible profit outcomes. Failed R&D Investment: Successful R&D/Exclusive Production Rights: Successful R&D/Shared Production Rights: -$40 million $50 million $ 5 million

a. 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(CIS) 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(H/F) 4.

Find Pr(SC) and Pr(S|H).

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 cannot wait 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.