Problem Set 6 Econ 300 Fall 2013 Due Date: December 10th Please return your answers in legible handwriting. Do don’t forget to write your NAME and University ID. Please show your work, you will be awarded partial credit for coherent attempts, but no credit will be granted for unjustified correct answers. 1. Calculate Pratt’s risk aversion for the following functions: a. ()axu x e at 10x b. 2( ) lnu x x at 15x c. 5()u x x at 7x 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 fails. The interest rate is 10%. Let x be the total wealth in present value of this individual (in millions). The total wealth of this individual (before hotel) is $600 million. a. If the utility function of this individual is ()u x x, should he build the hotel? b. If the utility function of this individual is ( ) lnu x x, should he build the hotel? 3. Consider the following game: U D L (1,1) (-1,-1) R (-1,-1) (1,1) a. Is there a dominant strategy? b. Is there a never best response strategy? c. Find all pure strategy Nash Equilibria d. Find all mixed strategy Nash
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