Jack is offered to participate in the following lottery: he can receive $87.36 with probability 0.41, or $128.88 with probability 0.59.

(a) Suppose Jack evaluates the lottery using the expected utility of the payoff, and his utility function is linear: U(x)=x . What riskless payoff would Jack view as equivalent to the payoff of the above lottery?

(b) Suppose Jack evaluates the lottery using the expected utility of the payoff, and his utility function is logarithmic : U(x)=ln(x) . What riskless payoff would Jack view as equivalent to the payoff of the above lottery?