Firm A is about to embark on a risky development project that offers a .2 chance of a $4 million profit and a .8 chance of a $0 profit. Unexpectedly, firm B proposes a joint venture. In return for its expertise, firm B will receive 25 percent of any profit. With firm B aboard, the chance of success is expected to rise to .25. After much deliberation, firm A decides to turn down the joint venture and continue on its own. Two years pass, and firm A has overcome most of the development hurdles. The estimated chances of success are now .8. Now firm C offers to pay firm A $3 million for all rights (and profits) concerning the development project. Deciding to take the sure $3 million, firm A now sells out. Show that whatever firm A's attitude toward risk, the pair of decisions just outlined is contradictory. (Hint: There are only three outcomes across the two decisions: $4 million, $0, and $3 million, with the associated utilities 100, 0, and u, respectively.) Show that no value of u is consistent with firm A's pair of choices.