9. information with joint probability frame Return to the risky versus safe choice originally chronicled in Table 9.1. Let initial wealth be zero and α = .5. Before deciding Ralph will observe an information source that will report a signal of g or

b. The joint probability of dollar gain (100 or 400) and signal (g or

b) under the risky choice is displayed below. For example, the joint probability of 100 and g is .2α. The riskless choice, of course, continues to offer a dollar gain of 240. Further assume Ralph’s initial wealth is zero.
100 400 signal g .2α 1 − α
signal b .8α 0

(a) Determine Ralph’s optimal use of this information for each of the utility specifications in Table 9.9. Also determine the resulting certainty equivalent for each such specification

(b) Write a short paragraph detailing how your analysis differs, or does not differ, from our work in Tables 9.8 and 9.9.