An individual with a current wealth of w and utility function u(x) = 1 - e^-x/R

Question

An individual with a current wealth of w and utility function u(x) = 1 - e^-x/R for some R > 0 has to choose between two investment alternatives: one safe and one risky. The safe alternative returns x > 0 for sure whereas the risky one returns x + 10 with probability 0.8 and nothing with probability 0.2. The individual can also buy perfect information on the return of the risky alternative before making the investment decision. The information costs c > 0. For which values of c will the individual who maximizes expected utility choose to buy the perfect information? How does your answer change as (i) w increases, (ii) R increases, and (iii) x increases? Interpret these changes by relating them to the changes in the risk attitude of the individual.

Explanation / Answer

Expected returns from risky investment = (x+10)0.8 + 0(0.2) = 0.8x + 8

It would buy information iff:

0.8x + 8 + c >=x

c>= 0.2x - 8

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