final_Fall2010

# final_Fall2010 - Econ 51 Final Exam December 6 2010...

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Econ 51: Final Exam December 6, 2010 Instructions: This is a closed book, closed-notes exam. You are allowed to use a hand-held calculator (i.e. no laptop). You have 180 minutes. Please answer all 4 questions. Please use a separate blue book for each question. Please write on each blue book the number of the question, your name, and the name of your TA. Always remember: think before you do the math . intelligently. As always, throughout log means the natural logarithm. Good luck! 1. Uncertainty and externalities (28 points) Rob and Tom are risk averse, with (identical) vNM utilities u ( x ) = log( x ) over next year’s income. They both expect to earn an income of 1,000 dollars, but with probability 10% may become disabled and have no income. They are each o±ered an actuarially fair disability insurance. Each unit of disability insurance pays a dollar in the event of disability. a. (2 points) What is the price of the insurance? Recall that it is actuarially fair. b. (6 points) How many units of insurance does each of them demand? c. (4 points) As it turns out, Rob and Tom are engaged and plan to get married. Once they are married, they will consolidate their bank accounts and act as if they are a single decision-maker . Their utility function of the household remains the same u ( x ) = log( x ), but is now a function of the (consolidated) account balance. Their disability risks are independent, so there is a probability of 1% (0 : 1 squared) that they both become disabled, and probability 81% (0 : 9 squared) that neither is disabled. How many units of insurance would they demand? d. (6 points) Suppose now that the price of insurance is higher, and is 0

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final_Fall2010 - Econ 51 Final Exam December 6 2010...

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