1. a. Emi Nakamura's preferences over gambles in which the probability of events 1 and 2 are both 1/2 can be represented by the von Neuman-Morgenstern utility function. 5 + .52, where y is her consumption if event 1 happens and y2 is her consumption if event 2 happens. Emi is offered a gamble that allows her a consumption of $25 if event 1 happens and $9 if event 2 happens. How much income would Emi have to make with certainty to be just as well off as with the lottery? b. John's utility function is U(c) = ln(c). He purchases a risky asset that pays $404 with probability 0.6 and $1097 with probability 0.4. What is the risk premium associated with this asset?