Sidewalk Sam’s brother Morgan von Neumanstern is an expected utility maximizer. His von Neumann-Morgenstern utility function for wealth is u(c) = lnc. Sam’s brother also sells sunglasses on another beach in Atlantic City and makes exactly the same income as Sam does. He can make exactly the same deal with the casino as Sam can.
(a) If Morgan believes that there is a 50% chance of rain and a 50% chance of sun every day, what would his expected utility of consuming (cs, cr) be?
(b) How does Morgan’s utility function compare to Sam’s? Is one a monotonic transformation of the other?
(c) What will Morgan’s optimal pattern of consumption be? Answer: Morgan will consume _______ on the sunny days and ____ on the rainy days. How does this compare to Sam’s consumption? ________.