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 economy-wide events. For simplicity, four such events or states are possible. Denote them Sl' S2' S3' and S4. The events or states are equally likely.

Ralph is risk neutral and must seleet from a menu of three possible choices.

The outcome structure is displayed below.

one two three Sl ~

225 225 900 625 900 625 100 625 100 100 Thus if choice two is taken, Ralph faces 50-50 odds on an outcome of 900 or an outcome of 100.

a] Determine Ralph's best choice.

b] Now suppose Ralph can purchase information before making a choice. The information Süurce will teil whether the actual state is Sl or ~ versus S3 or S4. You should think of this as telli ng Ralph whether the state will be "low" or "high" in terms of the indexing system. Put differentiy, the information will teIl Ralph whether the outcome is confined to the two left-hand Of the two right-hand columns

"In an expected utility setting, the utility function can be multiplied by an arbitrary positive constant, as weil as be increased by an arbitrary constant. U(W) and u + BU(w) teil the same story, as long as B >. O.

of the outcome table. How mueh would he pay for this information?16 Summarize your analysis in a table pattemed after Table 4.2.
e] Consider the ease where the information eosts 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 strueture will reveal whether S4 is true, that is, whether life is in the left three columns or the right-most eolumn of the outcome table. How mueh would Ralph pay for this information?

AppendixLO1