Lucky Pierre is a risk-averse prospector in Ballarat who has struck it rich. He has $W worth of gold – his only wealth – safely hidden away on his mining claim. He wants to get his gold away from the...

Lucky Pierre is a risk-averse prospector in Ballarat who has struck it rich. He has $W worth of gold – his only wealth – safely hidden away on his mining claim. He wants to get his gold away from the claim to the bank in Melbourne. His friend, Mr Cobb, will transport the gold for him free of charge. With probability p, all the gold transported on a given trip will be stolen, and with probability (1 – p), none of the gold will be stolen. Two options are available to Pierre: to attempt to transport the gold in one trip, or to attempt to transport the gold in two trips (one-half of the gold in each trip). The probability that the gold being transported on one trip will be stolen is independent of the probability that the gold being transported on the other trip will be stolen. a For each option (one or two trips), explain what are the sets of possible outcomes? What is the probability of each outcome occurring? What is Lucky Pierre’s wealth in each outcome? b Show that Lucky’s expected utility is larger if half the gold is transferred in each of two trips than if all the gold is transferred in a single trip.