9) A risk-neutral individual with current wealth w has already decided investing all his wealth in a project that has two possible net wealth outcomes wn and we (with probabilities pr and pę, respectively) where wn > w > we > 0, Pr Pe E (0,1), and pr + Pe = 1. Before he invests, he realises that there is a source of information that tells the individual which outcome will be realised with truth, what is the value of this information for the individual? a ) p, (ω-ω,) b) (Pr – Pe)w, c) PhWn + Pewp – w, d) Pn(w – wn).
Q: Consider the constant relative risk aversion utility of wealth function from Chapter 3 for an…
A: In economics, utility refers to the amount of satisfaction that a consumer receives from the…
Q: (b) An investor's utility function is given by: U(w) = In(w 2 ) where w is the investor's level of…
A: U = ln(w2)
Q: Consider the two options in the following table, both of which have random outcomes: a. Determine…
A: a. Expected Value of option 1 (EV1) Expected Value of option 2 (EV2)
Q: Questions 18 through 20 refer to the following information: Shawn's consumption is subject to risk.…
A: Expected utility (EU) is a very useful concept used in game theory, finance and economics. It is…
Q: Farmer Brown faces a 25% chance of there being a year with prolonged drought, with zero yields and…
A: Probability of drought = 25% Probability of normal year = 75% Inital Wealth = 25,000
Q: (c) Construct risk-neutral probabilitiès för and verify the risk-neutral value for the call option…
A: I have used formula which is given in the following step for finding answers.
Q: A risk averse investor with utility function: u(w) = (w)1/2 where w represents wealth, He has $200…
A: P1: $50 in the risky asset, $150 in the risk-free asset (Total wealth $200)
Q: Prospect Y = ($8, 0.25 : $14, 0.75) If Will's utility of wealth function is given by u (x) = x025,…
A: When a person has guaranteed return out of a deal then the person is said to have certainty…
Q: Question 1) Dave is an expected utility maximizer and his von Neumann-Morgenstern utility function…
A: Let us simplify the utility function - U(W) = 0.8(w)1/3 Initial Wealth = 27000
Q: Consider the problem of an entrepreneur/borrower with no money and a project requiring L=200 to be…
A: As per the question , Entrepreneur can work hard or shirk . Returns are same in both conditions but…
Q: 1. Consider the following utility functions, u(w) and v(w), which are functions of wealth w and the…
A: We are going to find the CARA and CRRA to answer this question.
Q: Assume that the probability of having an accident in a year is 0.08. Suppose that your yearly income…
A: Expected Utility refers to an economic term summarizing the utility that an organization or…
Q: 5. You are a risk-averse decision maker with a utility function U(I) = vI, where I denotes your…
A: Risk premium is defined as the maximum amount that an individual investor desires to pay to…
Q: You are given the following payoff table: State of Nature Altemative Sz 36 49 A2 144 0. A3 81 Prior…
A: Expected Utility can be calculated by multiplying probability with the utility.
Q: A firm has a portfolio composed of stock A and B with normally distributed returns. Stock A has an…
A: Given data, Stock-A, Annual Expected return= 15% Annual volatility = 20% Position firm in stock A…
Q: Mrs Gomez has a portfolio with an expected return of 7%. The portfolio is evenly invested in a stock…
A: The expected return is the profit or loss that an investor anticipates on an investment that has…
Q: Consider a certain butterfly spread on IBM: this is a portfolio that is long one call at $250, long…
A: A call option is an agreement among a purchaser and a dealer to acquire a specific stock at a…
Q: Let us assume that you have two possible mutually exclusive projects available and you need to…
A: We have been given two projects with the following possible pr Project A Ri pi 50 0.4 20 0.5…
Q: 1. George maximizes expected utility and he has a von-Neumann-Morgenstern utility function u (c) =…
A: Utility = c1/2 Initial Wealth = $1000 success rate = 9% If successful then payoff = $100,000 Payoff…
Q: Q.No.4. If you are supposed to a 40/60 chance of gaining or losing Rs.400 and insurance that removes…
A: Certainty equivalence is the certain amount of money in which person become indifferent between…
Q: Risky Prospect K is defined as: K- ($8, 0.30 : $13 ,0.70) If my utility of wealth function is given…
A: The utility is calculated as the difference between the marginal utility of the first unit and the…
Q: urgent ! 1,1 3,0 0,3 2,2 (a) Can strategy profile (B,D) be played at the first stage if the game is…
A: We have 2×2 game in which row player has two actions A ans B and column player has action C and D
Q: Using the Utility Function in Portfolio Management, where the utility function is the constant…
A: The certainty equivalent is a return that is assured and somebody would prefer to receive now over…
Q: Suppose Real Option Inc. has a product that generates the following cash flow. At t=1, the demand…
A: We are going to use Present value of cash flow methodology to answer this question. Note: As per the…
Q: Your uncle offers you a "sure-fire" investment opportunity. All you have to do is invest $2000 and…
A: The time value of money is a concept of simple interest and compound interest which states that the…
Q: 4. Suppose an investment project has an NPV of $75 million if it becomes successful and an NPV of…
A: The net present value, also known as net present worth, is applied to a series of cash flows that…
Q: Assume you can invest in 2 projects whose payoff depend on the state of the economy. The profits…
A: We have two states of recession and no recession with probability 0.5 and 0.5 each.
Q: Consider an investor with initial wealth Yo: who maximizes his expected utility from final wealth,…
A: Utility function : u(y) = log(y) There are two risky securities to invest in 1 & 2. With returns…
Q: 10. Which one of the following measures may be used to measure the risk of an investment on its own?…
A: Investment is an essential part of creating wealth as well as attain higher economic growth and…
Q: A charter school operator gets utility out of the number of students she enrolls, where U =…
A: The utility is Given as U = Students0.7 Probability of enroll 100 students = 0.75 Probability of…
Q: Prove rigourously, "Constant relative risk aversion (CRRA) implies decreasing absolute risk aversion…
A: Answer in step 2.
Q: Prospect Y = ($6, 0.25 ; $19, 0.75) If Will's utility of wealth function is given by u (x) = x0:25,…
A: The utility function tells how the utility received by the individual changes as the individual…
Q: Suppose that a one-year project that requires an initial investment of $5 million has a 65% chance…
A: Given: Project initial investment is = $5 million The project has a 65% chance of generating = $12…
Q: 2.- Recall the model of an investor whose investment income is taxed at rate t. The investor has §w…
A: Contingent simply refers to the random plan/event. Hence, contingent consumption means consumption…
Q: 6) For the payoff table below, the decision maker will use P(s1) = .15, P(s2) = .5, and P(s3) = .35.…
A: The probability of different alternatives s1, s2 and s3 are P(s1)=0.15, P(s2 )=0.50 P(s3)=0.35.
Q: A maximizing investor with preferences u(u, ơ) = 0.2µ – 0.50^2 will allocate a portfolio worth 4000…
A:
Q: You are considering investing in one of two projects, which have the following returns and…
A: Part (a) Mean return of project A = Σ X p(X) Mean of project A = 0.1(-0.2) + 0.25(0.1) +0.3(0.15) +…
Q: There are only two (equally-likely) states of nature in this economy: boom and bust, which are…
A: Equity beta is a measure of a stock’s systematic risk. It is estimated by comparing the sensitivity…
Q: risk-averse consumer with $100,000 in wealth faces 0.1 probability of losing half of his wealth…
A: Here, we calculate the given as follow;
Q: An individual has the following utility function u(w)=2w05 +10 using the expected utility, order the…
A: The expected utility mainly refers to the expected utility which involves the expected or the…
Q: Use the utility function u = E (r,) – 0.5 A ož where A is the risk aversion parameter and A = 3.5.…
A: The law of diminishing marginal utility is the additional satisfaction that a consumer gets by…
Q: Prospect Y = ($6, 0.25 ; $15, 0.75) If Will's utility of wealth function is given by u(x)=x0.25,…
A:
Q: Millicent’s utility function is U(w) = W0.5 , where W is her wealth. She owns a “pure water”…
A: In economics, "risk aversion" is a situation in which an individual prefers lower returns or he is…
Q: Risky Prospect K is defined as: K = ($5, 0.30 ; $11,0.70) If my utility of wealth function is given…
A: Computation of expected utility of the prospect :- Expected utility = (0.30 x 5^0.6) + (0.70 x…
Q: Mrs Gomez has a portfolio with an expected return of 7%. The portfolio is evenly invested in a stock…
A: The expected return is the profit or loss that an investor anticipates on an investment that has…
Q: Suppose that the consumer is asked to contemplate a gamble with a probability of 60% of winning…
A: The expected income is the sum of income multiplied by its corresponding probability. The expected…
Step by step
Solved in 3 steps
- Y5 Alfred is a risk-averse person with $100 in monetary wealth and owns a house worth $300, for total wealth of $400. The probability that his house is destroyed by fire (equivalent to a loss of $300) is pne = 0.5. If he exerts an effort level e = 0.3 to keep his house safe, the probability falls to pe = 0.2. His utility function is: U = w0.5 – e where e is effort level exerted (zero in the case of no effort and 0.3 in the case of effort).a. In the absence of insurance, does Alfred exert effort to lower the probability of fire?HINT: Calculate and compare the expected utility i) with effort, and ii) without effort. If effort is exerted, then the effort cost is paid regardless of whether or not a fire occurs.b. Alfred is considering buying fire insurance. The insurance agent explains that a home owner’s insurance policy would require paying a premium α and would repay the value of the house in the event of fire, minus a deductible “D”. [A deductible is an amount of money that the…A risk-eutral plaintiff in a lawsuit must decide whether to settle a claim or go to trial. The defendants offer $70,000 to settle now. If the plaintiff does not settle, the plaintiff believes that the probability of winning at trial is 40%. If the plaintiff wins, the amount awarded to the plaintiff is X. Will the plaintiff settle if X is $87,500? What if X= $280,000? What is the critical value of X that would make the plaintiff indifferent between settling and going to trial? If the plaintiff were risk averse instead of risk neutral, would this critical value of X be higher or lower? If the amount to be awarded at trial with a win (X) were $87,500, then the plaintiff would settle If the amount to be awarded at trial with a win (X) were $280,000, then the plaintiff would not settle The critical value of X that would make the plaintiff indifferent between settling and going to trial is $. (Enter your response using rounded to two decimal places.)An investor with capital x can invest any amount between0 and x; if y is invested then y is eitherwon or lost, with respectiveprobabilities p and 1− p. If p > 1/2, how much should be invested byan investor having a exponential utility function u(x) = 1 − e −bx ,b > 0.
- A risk-neutral plaintiff in a lawsuit must decide whether to settle a claim or go to trial. The defendants offer $50,000 to settle now. If the plaintiff does not settle, the plaintiff believes that the probability of winning at trial is 50% if the plaintiff wins, the amount awarded to the plaintiff is X Will the plaintif settle if x is $62,500? What if X-$250,000? What is the critical value of X that would make the plaintiff indifferent between setting and going to trial? it the plaintiff were risk averse instead of risk neutral, would this critical value of X be higher or lower? If the amount to be awarded at trial with a win (X) were $62,500, then the plaintiff would settle If the amount to be awarded at trial with a win (X) were $250,000, then the plaintiff would not settle The critical value of X that would make the plaintiff indifferent between settling and going to trial is $ (Enter your response using rounded to wo decimal places)A seller will run a second-price, sealed-bid auction for an object. There are two bidders, a and b, who have independent, private values v; which are either 0 or 1. For both bidders the probabilities of v; = 0 and v; = 1 are each 1/2. Both bidders understand the auction, but bidder b sometimes makes a mistake about his value for the object. %3| Half of the time his value is 1 and he is aware that it is 1; the other half of the time his value is 0 but occasionally he mistakenly believes that his value is 1. Let's suppose that when b's value is 0 he acts as if it is 1 with probability 1/2 and as if it is zero with 2 probability. So in effect bidder b sees value 0 with probability 1/4 and value 1 with probability 4. Bidder a never makes mistakes about his value for the object, but he is aware of the mistakes that bidder b makes. Both bidders bid optimally given their perceptions of the value of the object. Assume that if there is a tie at a bid of x for the highest bid the winner is…4) Consider investors with preferences represented by the utility function U = E(r) – Ao². (a) Draw the indifference curve representing a utility level of 10% for an in- vestor with a risk aversion parameter A = 3 in expected return-standard deviation space. (b) In the same graph, draw the indifference curve representing a utility level of 15% for an investor with a risk aversion parameter A = 3. (c) In the same graph, draw the indifference curve representing a utility level of 10% for an investor with a risk aversion parameter A = 5.
- Deborah is at the casino and is considering playing Roulette. In Roulette, a ball drops into one of 36 slots on a spinning wheel. 17 of the slots are red, 17 are black, and 2 are green. Each slot is equally likely and occurs with probability 1/36. Deborah bets $1.00 on black. If the ball drops into a black slot she receives $2.00 and if it drops into a red or green slot, she receives nothing. The expected value of Deborah's bet (after subtracting the $1.00 she bet) is $ Given that Deborah makes this bet, she must beDeborah is at the casino and is considering playing Roulette. In Roulette, a ball drops into one of 36 slots on a spinning wheel. 17 of the slots are red, 17 are black, and 2 are green. Each slot is equally likely and occurs with probability 1/36. Deborah bets $1.00 on black. If the ball drops into a black slot she receives $2.00 and if it drops into a red or green slot, she receives nothing. a) The expected value of Deborah’s bet (after subtracting the $1.00 she bet) is $________________ b) Given that Deborah makes this bet, is she risk adverse, risk neutral, or risk loving?A salesperson is trying to sell cars. The number of cars that she will sell depends on her effort "e" and her luck. Given her effort e, with probability 4e she is able to sell four cars, and with probability (1 - 4e) she is able to sell only one car. Her personal cost of effort is 100e². The dealership pays her a bonus b for each car sold. The salesperson is risk-neutral, and wants to maximize her expected utility, which is her expected income minus her effort cost. a) Given the bonus b, the salesperson's best response function is b) Suppose the dealership pays b = 2. Then the expected number of cars sold will be E(Q)=
- A risk-averse agent, Andy, has power utility of consumption with riskaversion coefficient γ = 0.5. While standing in line at the conveniencestore, Andy hears that the odds of winning the jackpot in a new statelottery game are 1 in 250. A lottery ticket costs $1. Assume his income isIt = $100. You can assume that there is only one jackpot prize awarded,and there is no chance it will be shared with another player. The lotterywill be drawn shortly after Andy buys the ticket, so you can ignore therole of discounting for time value. For simplicity, assume that ct+1 = 100even if Andy buys the ticket How large would the jackpot have to be in order for Andy to play thelottery? b) What is the fair (expected) value of the lottery with the jackpot youfound in (a)? What is the dollar amount of the risk premium that Andyrequires to play the lottery? Solve for the optimal number of lottery tickets that Andy would buyif the jackpot value were $10,000 (the ticket price, the odds of winning,and Andy’s…Question 6 Which of the below indifference curve correspond to the highest risk aversion? E(r) .60 .40 .20 .09 .05 0 D and C B and A .10 .20 .30 .40 .5 D C B AFirst Player can invest $1.00 with Second Player (low reliance) or $2.00 (high reliance). Based on the payoffs shown below, what is the probability of performance that makes High Reliance optimal? Write your answer as a two digit integer. E.g., if the answer is 33%, write 33. Second Player Perform Breach Invest & Low Reliance 0.25 1.0 First Player 0.25 -1.0 Invest & High Reliance 0.5 1.0 0.75 -2.0