Suppose you are facing two lotteries p and q, where the lotteries are defined over the...
Suppose you are facing two lotteries p and q, where the lotteries are defined over the set of outcomes X = {$1, $10, $25, $100}. The lotteries are defined as follows: p = (0.1, 0.25, 0.6, 0.05) q = (0.2, 0.4, 0.2, 0.2)
(a) Suppose your utility function over outcomes is u(x) = ln(x).
Calculate the expected utility of lottery p and of lottery q, then explain which lottery will be preferred. (3 points)
(b) Now suppose your utility function over outcomes is u(x) = x 0.25. Calculate the expected utility of each lottery. Would your preference between the two lotteries switch relative to your answer in part (a)? (3 points)
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Suppose you are facing two lotteries p and q, where the
lotteries are defined over the...
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2. An individual has a vNM utility function over money of u(x) -Vx, where x is final wealth. Assu...
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6. A decision maker has a vNM utility function over money of u(x) = x2. This...
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Suppose you are facing a lottery that has a payoff of 10b pounds with probability 0.01 and that of 0 with probability 0.99. You are an expected utility maximiser with a utility function,u(x) = −exp(−ax) where x is the payoff in money terms and a > 0 is a parameter. What is the risk premium for this lottery - describe the risk premium as a function of ‘a’ and ‘b’.
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Suppose the function u(x) = x0.5 , where x is consumption, represents your preference over gambles using an expected uti...
Suppose the function u(x) = x0.5 , where x is
consumption, represents your preference over gambles using an
expected utility function.
You have a probability 0.1 of getting consumption xB (bad state)
and a probability 0.9 of getting xG (good state).
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(b, p), where b is the insurance benefit the company pays you if
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Consider historical data showing that the average annual rate of return on the S&P 500 portfolio...
Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 33% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 3%. Calculate the utility levels of each portfolio for an investor with A-3. Assume the utility function is...
Anne has been given a choice between two lotteries. In lottery A a fair coin is...
Anne has been given a choice between two lotteries. In lottery A
a fair coin is flipped. If it comes up heads, Anne wins $50, if it
comes up tails, she wins $150. In lottery B a fair coin is also
flipped. If it comes up heads, Anne wins nothing, if it comes up
tails, she wins $200.
Problem 4 - Choice under uncertainty (20 points) Anne faces an uncertain World with two possible states, good and bad. In the...
2. Consider two lotteries, A and B. With lottery A, there is a 0.90 chance that you receive a payoff of S0 and a 0.10 chance that you receive a payoff of $400. With lottery B, there is a 0.50 chance that you receive a payoff of S30 and a 0.50 chance that you receive a payoff of $50, a) Verify that these two lotteries have the same expected value but that lottery A has a bigger variance than lottery...
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Suppose the function u(x) = x0.5 , where x is
consumption, represents your preference over gambles using an
expected utility function.
You have a probability 0.1 of getting consumption xB (bad state)
and a probability 0.9 of getting xG (good state).
An insurance company allows you to choose an insurance contract
(b, p), where b is the insurance benefit the company pays you if
the bad state occurs and p is the insurance premium you pay the
company regardless of...
Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 33% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 3%. Calculate the utility levels of each portfolio for an investor with A-3. Assume the utility function is...
Anne has been given a choice between two lotteries. In lottery A
a fair coin is flipped. If it comes up heads, Anne wins $50, if it
comes up tails, she wins $150. In lottery B a fair coin is also
flipped. If it comes up heads, Anne wins nothing, if it comes up
tails, she wins $200.
Problem 4 - Choice under uncertainty (20 points) Anne faces an uncertain World with two possible states, good and bad. In the...
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