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Robert Barber

TUTORIAL 4MONDAYJUNE 2 20144PM5PMQUESTION 45Textp 173Mr Fogg is planning an aroundtheworld trip The utility from the trip is a function of how much he spends on it Y given by UYlog Y Mr Fogg has 10000 to spend on the trip If he spends all of it his utility will beU10000log 100004 In this problem we are using logarithms to the base 10 for ease of computation a If there is a 25 percent probability that Mr Fogg will lose 1000 of his cash on the trip what is the trips expected utility b Suppose that Mr Fogg can buy insurance against losing the 1000 say by purchasing travelers cheques at an actuarially fair premium of 250 Show that his utility is higher if he purchases this insurance than if he faces the chance of losing the 1000 without insurance c What is the maximum amount that Mr Fogg would be willing to pay to insure his 1000 d Suppose that people who buy insurance tend to become more careless with their cash than those who do not and assume that the probability of their losing 1000 is 30 percent What will be the actuarially fair insurance premium Will Mr Fogg buy insurance in this situation This is another example of the moral hazard problem in insurance theory QUESTION 48Textp 173 Sophia is a contestant on a game show and has selected the prize that lies behind door number 3 The shows host tells her that there is a 50 percent chance that there is a 15000 diamond ring behind the door and a 50 percent chance that there is a goat behind the door which is worth nothing to Sophia who is allergic to goats Before the door is opened someone in the audience shouts I will give you the option of selling me what is behind the door for 8000 if you will pay me 4500 for this option a If Sophia cares only about the expected dollar values of various outcomes will she buy this option b Explain why Sophias degree of risk aversion might affect her willingness to buy this option
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