Expected utility question - microeconomics?

Posted on 2014-04-22 10:56:00 in Economics by JAMES

Amy is a risk-averse gold-digger who has struck it rich. She has $W worth of gold - her only wealth - safely stashed away on her claim. She wants to get her gold from her claim to the big city where she hopes to spend it. Her friend will transport the gold for her free of charge. With probability q, all the gold on any trip will be stolen; with probability (1-q), none of it will be stolen. Amy is considering whether to transport all of the gold in a single trip, or to make two separate trips.



a) Assume that the risks of the gold being stolen in separate trips are independent events. Verify that the expected monetary value of Amy's wealth is the same when half of the gold is transferred in each of two trips as when all the gold is transferred in a single trip.



b) Show that her expected utility is larger if half of the gold is transferred in each of two trips than if all of the gold is transferred in a single trip.



c) How do your answers change if the risks of the gold being stolen in each trip are perfectly positively correlated (if gold is stolen in one trip, then it will for sure also be stolen in the other)?

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