Jonny plans to invest $8,000 in one of the following instruments:

• Bonds of X Ltd., yielding 14% (a1)
• US treasury Bonds, yielding 11% (a2)

Based on his knowledge of current economic conditions and the outlook for the industry of X Ltd., Jonny assesses the prior probability that X Ltd. will go bankrupt as 0.1.

If this happens, Jonny will lose both principal and interest and receive no money at the end of the year. If X Ltd. does not go bankrupt, Jonny plans to sell the bonds, plus interest, at the end of one year.

Jonny assesses the probability that the US Savings Bonds will fail to pay off as zero. Jonny also plans to sell these, plus interest, one year later.

Jonny is risk-averse and decides to choose the investment that yields the highest expected utility. Assume that Jonny's utility for an amount of $x is given by square root of X, where x is the gross payoff.

Required

1. Based on his prior probabilities, which investment should Jonny choose?
2. Rather than choosing on the basis of his prior probabilities, assume that Jonny decides to analyze the current financial statements of X Ltd. These financial statements can look "good" (G) or "bad" (B). After his analysis, Jonny realizes that the statements look good. On this basis Jonny asses the probability that the financial statements would look good given that the firm was actually heading for bankruptcy is 0.2 = Prob(G | B) where B denotes the state of heading for bankruptcy. Similarly, Jonny knows that Prob (G | NB) = 0.70 where NB denotes the state of not heading for bankruptcy. Which investment should Jonny now take? Explain why.