14. useful and useless information Ralph faces a choice problem in which the dollar outcome is uncertain.

Ralph thinks of the uncertainty as reflecting natural and economywide events. For simplicity, four such events or states are possible, denoted in usual fashion. The four states are equally likely, and Ralph is risk neutral. The outcome structure is displayed below, where you will notice the possible choices are denoted a1, a2 and a3.

state s1 state s2 state s3 state s4 a1 225 225 225 100 a2 900 900 100 100 a3 625 625 625 100

(a) Determine Ralph’s best choice.

(b) Now suppose Ralph can purchase information before making a choice. The information source will tell whether the actual state is s1 or s2 versus s3 or s4. You should think of this as telling Ralph whether the state will be "low" or "high" in terms of the indexing system. Put differently, the information will tell Ralph whether the outcome is confined to the two left-hand or the two right-hand columns of the outcome table. How much would Ralph pay for this information (i.e., at what price is he indifferent between buying and not buying the information)?

(c) Consider the case where the information costs 500. Ralph will not pay such a price. The information is not needed. What does Ralph substitute for the lack of information?

(d) Suppose the information structure will reveal whether s4 is true, that is, whether life is in the left three columns or the right-most column of the outcome table. How much would Ralph pay for this information?