Problem Set 6 Solution 1 Calculate Pratt s risk aversion for the following functions a b at at c at 2 A wealthy individual has hired you to analyze an investment project The project consists on building a luxurious hotel for a total cost of 500 million The project is going to be a total success with probability 30 a mild success with probability 60 and a total failure with probability of 10 The hotel will run for a hundred years If a total success the hotel is going to produce 60 million a year if a mild success 50 million a year and only 30 million a year if it be the total wealth in present value of this individual in fails The interest rate is 10 Let millions The total wealth of this individual before hotel is 600 million Discount Factor Present Value of Success Present Value of Mild Success Present Value of Failure Net Present Value of Success 600 500 659 95 759 95 Net Present Value of Mild Success 600 500 549 96 649 96 Net Present Value of Failure 600 500 329 98 429 98 a If the utility function of this individual is should he build the hotel Utility of NOT building the Hotel axuxe 10x 2 10 axaxaeraae 2 lnuxx 15x 221 21 15 15xrxxxr 5 uxx 7x 43204 54 7 7xrxxxr x1110 100160659 951 100150549 961 100130329 981 uxx 600 600u Problem Set 6 Solution Utility of building the Hotel 30 759 60 649 10 429 661 He should build the Hotel If the utility function of this individual is b should he build the hotel Utility of NOT building the Hotel Utility of building the Hotel 30 ln 759 60 ln 649 10 ln 429 6 48 He should build the Hotel 3 Consider the following game L R U 1 1 1 1 D 1 1 1 1 a b Is there a dominant strategy No no player has a dominant strategy Is there a never best response strategy No there is no never a best response strategy c Find all pure strategy Nash Equilibria L U and R D d Find all mixed strategy Nash Equilibria Player 1 plays L with 50 chance and R with 50 chance Player 2 plays U with 50 chance and D with 50 chance lnuxx 600 ln6006 39u 1 1 1 12ppppppp
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