ubariho Julius’ utility function is U(W)=ln(W). His current wealth is $5,000. He is now given a...
ubariho Julius’ utility function is U(W)=ln(W). His current wealth is $5,000. He
is now given a chance to buy a futures contract on Nickel that gives him 75% chance of
winning $5,000, and 25% chance of losing $4,000. What is his, Julius’ certainty equivalent
for holding the futures contract?
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ubariho Julius’ utility function is U(W)=ln(W). His current
wealth is $5,000. He
is now given a...
Suppose Peter Brown’s utility for total wealth (A) can be represented by the utility function U(A)=ln(A)....
Suppose Peter Brown’s utility for total wealth (A) can be represented by the utility function U(A)=ln(A). He currently has $1,000 in cash. A business deal of interest to him yields a reward of $100 with probability 0.5 and $0 with probability 0.5. If he owns this business deal in addition to the $1,000 and considers selling the deal, what is the smallest amount for which he would sell it (i.e., the amount of the deal such that he is indifferent...
An investor's utility function is ?(?) = ln ?, where w denotes net wealth. He has...
An investor's utility function is ?(?) = ln ?, where w denotes net wealth. He has $100 for investment. There are two assets, a “safe” one and a “risky” one. The safe asset yields 10% return with certainty. The risky asset yields 19% return with probability 0.5, and 2% return with probability 0.5. a.) How much money should the investor invest in each asset? 2. b.) Now suppose instead of 2% it is changed to 1%, while all other information...
Joe's wealth is $100 and he maximizes his expected utility. Joe’s utility as a function of...
Joe's wealth is $100 and he maximizes his expected utility. Joe’s utility as a function of his wealth is U(W) = W1/2. Joe might oversleep his economics exam. He figures there is only a 1 in 10 5 chance that he will, but if he does, it will cost him $100 in fees to the University to take an exam later. Joe's neighbor, Mary, never oversleeps. She offers to wake Joe one hour before the test, but he must pay...
b. My utility is U(w) with initial wealth W. There is a 50% chance I gain...
b. My utility is U(w) with initial wealth W. There is a 50% chance I gain $x (so my wealth becomes W +x), and a 50% chance I lose $x so my wealth falls to W-x. Let c be my certainty equivalent for this gamble. Explain how the sign of the derivative dc/dx depends on my attitude towards risk.
Gamma’s utility function over wealth levels w is given by u(w) = √ w. His initial...
Gamma’s utility function over wealth levels w is given by u(w) = √ w. His initial wealth is $400. With probability π, Gamma will get into an accident that will result in a loss of $300. With probability (1 − π), Gamma does not have an accident, and hence suffers no loss. 1. Argue (mathematically) that Gamma is risk averse. 2. What is the expected value of Gamma’s loss? 3. ABC Inc. sells auto insurance. It charges a premium of...
Terry’s utility of wealth is given by: u(w) = ln(w). Suppose Terry has $1 million in...
Terry’s utility of wealth is given by: u(w) = ln(w). Suppose Terry has $1 million in his bank account and a beach house worth $2 million. With probability 1/3, his beach house will get destroyed by a hurricane. (a) Is Terry risk-averse, risk-neutral, or risk-loving? Verify your answer using calculus. (b) Determine the actuarially fair premium for an insurance plan that will compensate him $2 million if his beach house gets destroyed by a hurricane. (c) Write out the two...
2, A consumer has utility function for wealth U(W)-W, wealth W-$1,000, and faces a 50% chance...
2, A consumer has utility function for wealth U(W)-W, wealth W-$1,000, and faces a 50% chance of facing a loss of $875. The consumer's expected utility is (a) 7.5 (b) 8.0 (c) 8.5 (d) 9.0
My von Neumann Morgenstern utility function is U (W) = 32 + (9/5)w1/2 for wealth w....
My von Neumann Morgenstern utility function is U (W) = 32 + (9/5)w1/2 for wealth w. I face a gamble that pays 1 with probability %, and 4 with probability %. Calculate my certainty equivalent for this gamble: CE=_ . Calculate my risk premium p for this gamble p=
2. Risk Premium a. Suppose the utility function is given by the equation ?(?) = ln(?...
2. Risk Premium a. Suppose the utility function is given by the equation ?(?) = ln(? + 1). Graph utility at the points $0, $80, $100. b. Suppose there is a lottery where you win $100 with 20% chance, $80 with 30% chance, and $0 with 50% chance. What is the expected winnings (in dollars)? What is the expected utility (in utils)? Add this point to the graph. c. What is the utility at the expected dollar winnings (i.e., what...
Sam's utility of wealth function is U(w) =15w. Sam owns and operates a farm. He is...
Sam's utility of wealth function is U(w) =15w. Sam owns and operates a farm. He is concerned that a flood may wipe out his crops. If there is no flood, Sam's wealth is $360,000. The probability of a flood is 1/15. If a flood does occur, Sam's wealth will fall to $160,000. a. Calculate Sam's expected utility. (please just enter the number, round to integer) b. Calculate the Sam's risk premium. (please just enter the number, round to integer)
b. My utility is U(w) with initial wealth W. There is a 50% chance I gain $x (so my wealth becomes W +x), and a 50% chance I lose $x so my wealth falls to W-x. Let c be my certainty equivalent for this gamble. Explain how the sign of the derivative dc/dx depends on my attitude towards risk.
2, A consumer has utility function for wealth U(W)-W, wealth W-$1,000, and faces a 50% chance of facing a loss of $875. The consumer's expected utility is (a) 7.5 (b) 8.0 (c) 8.5 (d) 9.0
My von Neumann Morgenstern utility function is U (W) = 32 + (9/5)w1/2 for wealth w. I face a gamble that pays 1 with probability %, and 4 with probability %. Calculate my certainty equivalent for this gamble: CE=_ . Calculate my risk premium p for this gamble p=
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