A consumer who has $1000 is represented by the expected utility function u(x) = √x. A...
Question 2 [25 marks] Consider Edgar who has preferences over money represented by utility function (y) = (y2/3. He has an initial income y = $150. Edgar has the possibility of entering a lottery (at zero cost) in which he may win $66 with probability 1/3 and lose $25 with probability 2/3. c) (5 marks] Calculate Edgar's certainty equivalent (CE), and provide an interpretation for it, in the context of this lottery.
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’.
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...
Consider the utility function u(x) = ax + b e^cx where a, b, c are positive scalars. (a) Compute the coefficient of absolute risk aversion. (b) Describe the risk attitude represented by u(x) and how it changes as x increases. (c) Write down the equations to determine the certainty equivalent and the risk premium of a gamble X for an individual with initial wealth w > 0. (d) What is the sign of the risk premium? How does the risk...
A person with the following utility function, u(x) = ln(x) faces a world where with probability 0.1 will suffer of identity theft which will reduce their wealth from $250000 to $100000. This means that we can write: E{u(.)] = 0.91n(x) +0.1ln(y) where x would be the wealth under no identity theft and y the wealth under identity theft. This means that the marginal utilities are: MU 0.9, MUy = 0.1 Using this information answer the following questions 1) What is...
A person with the following utility function, u(x) In(x) faces a world where with probability 0.1 will suffer of identity theft which will reduce their wealth from $250000 to $100000. This means that we can write: Eu(.0.91n(x)+0.1n(y) where would be the wealth under no identity theft and y the wealth under identity theft This means that the marginal utilities are: MU0.9 MUy = 0.1 Using this information answer the following questions 1) What is this persons attitude towards risk? explain...
Lottery - Let $1,000 be your current wealth. There are 100 people and each buys a lottery ticket at $5. The administrative cost of the lottery ticket per person is $5. If you win the lottery, you will get $500. There is only one person who can win the lottery. a. Define the gamble b. Calculate the expected value of the gamble c. Is this gamble favorable, fair, or unfavorable? d. Now, suppose your utility function is U = W5/2....
bling Chuck has risk-loving preferences, Uc(w) W2, and sometimes plays scratch-off tickets. Geraldine, Jack's sister, is risk averse with a utility function, UG(W)-W2. The chance for winning a prize is 1/10 and the price of the scratch-off ticket is $5. Each of them has an initial wealth of 100. What is the smallest prize that will cause Chuck to buy a ticket? What would be the expected payout of this $5 gamble? What is the smallest prize that will cause...
Problem 4: Risk premium. Casey is considering buying a lottery ticket. The lottery pays $100 with probability and $0 with probability a) What is the "fair" price of the lottery ticket? In other words, what price of the lottery ticket provides the lottery owner an expected profit of zero? b) Suppose that a lottery ticket costs $15. If Casey is willing to buy the lottery ticket, what can we say about Casey's risk premium for this lottery? c) Suppose that...
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...