Firm B is considering whether to pursue an R&D effort to develop a powerful new microchip. One concern with the 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                                              -$40 million Successful R&D/Exclusive production rights                                                                        $50 million Successful R&D/Shared production rights                                                                        $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(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(Hƒ F) = .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 cannot wait for the patent outcome.)