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# WeekofFeb09 - the government decides to insure Bob in the following way no matter what outcome occurs Bob will receive the expected value of the

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W3211 Spring 2009 Professor Vogel Recitation for the Week of February 09, 2009 w , is U ( w ) = w 1 = 2 \$16 . He is given the option to either keep his \$16 or to invest his \$16 in a new ±rm called Spri. If he invests in Spri, there are three possible outcomes. With probability 1 = 4 he receives \$36 , with probability 1 = 4 he receives \$16 , and with probability 1 = 2 he receives \$ x 2 (for x & 0 ). (a) What is the expected value of this investment if x = 1 ? (b) If x = 1 (c) If x = 1 , will Bob agree to make the investment? (d) What is the value of x at which Bob is indi/erent between investing in Spri or not investing in Spri? (e) Suppose that x = 3 . What is the certainty equivalent of this investment for Bob? (f) Suppose that the government prefers that Bob not have to bear any risk. So
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Unformatted text preview: the government decides to insure Bob in the following way: no matter what outcome occurs, Bob will receive the expected value of the investment. The government doesn&t charge Bob for this insurance. What is the expected cost to the government of this insurance contract with Bob? (g) Suppose x = 0 . Moreover, Bob is now able to invest any fraction r , with ± r ± 1 , of his \$9 in Spri. If he invests \$9 r in Spri, then with probability 1 = 4 he receives \$36 r , with probability 1 = 4 he receives \$16 r , and with probability 1 = 2 he receives \$ x 2 r = 0 . Without solving explicitly for r , what is the equation that determines the value of r > at which Bob will be indi/erent between making the investment or not?...
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## This note was uploaded on 12/21/2009 for the course ECON 1211 taught by Professor Govel during the Spring '08 term at Columbia.

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