BNQ12.1 Case: Consider a Lottery with 3 Possible Outcomes: ▪ $125 will be received with Probability 0.2 $100 will be received with Probability 0.3 $50 will be received with Probability 0.5 ■ ▪ Question: What is the Expected Value of the Lottery?
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- 5. An individual has a utility function given by (W) - √W, and initial wealth of $100. If he plays a costless lottery in which he can win or lose $10 at the flip of a coin, compute his expected utility. What is the expected gain? Will such a person be categorized as risk neutral?2. Alex plays football for a local club in Kumasi. If he does not suffer any injury b y the end of the season, he will get a professional contract with Kotoko, which is worth $10,000. If he is injured though, he will get a contract as a fitness coa ch worth $100. The probability of the injury is 10%. Describe the lottery What is the expected value of this lottery? What is the expected utility of this lottery if u(x) = √X Assume he could buy insurance at price P that could pay $9,900 in case of inj ury. What is the highest value of P that makes it worthwhile for Alex to purcha se insurance? What is the certainty equivalence for this lottery?Hello can any one help with this Economics question: A contractor spends Dollar 3,000 to prepare for a bid on a construction project which, after deducting manufacturing expenses and the cost of bidding, will yield a profit of dollar 25,000 if the bid is won. If the chance of winning the bid is ten per cent, compute his expected profit and state the likely decision on whether to bid or not to bid?
- Info : Janet’s attitude to risk (risk averse, risk neutral, or risk loving) is independent of her wealth. She has initial wealth ww and is offered the opportunity to buy a lottery ticket. If she buys it, her final wealth will be either w+4 or w−2, each equally likely. She is indifferent between buying the ticket and not buying it. Janet offers her friend Sam (who has identical preferences and initial wealth) the following proposition: They buy the ticket together, and share the cost and proceeds equally. Should Sam accept the offer?3. Suppose that Jon Snow's utility function is given by U(I)=501 where I represents annual income in thousands of dollars. a. Is Jon risk loving, risk neutral, or risk averse? Explain b. Suppose that Jon is currently earning an income of $1000 and can earn that income next year with certainty. He is offered a chance to take a new night watch job that offers a 0.25 probability of earning $2000 and a 0.75 probability of earning $500. Should he take the new night watch job?Extra info: Janet’s attitude to risk (risk averse, risk neutral, or risk loving) is independent of her wealth. She has initial wealth w and is offered the opportunity to buy a lottery ticket. If she buys it, her final wealth will be either w+4 or w−2, each equally likely. She is indifferent between buying the ticket and not buying it. Janet offers her friend Sam (who has identical preferences and initial wealth) the following proposition: They buy the ticket together, and share the cost and proceeds equally. Consider the setup from Question 1 and 2. Sam has another idea: They buy two tickets (that have independent outcomes) and share the costs and proceeds equally. Is this better than buying no tickets? a. Yes, Sam's solution is preferable to buying no ticket. b. Yes, Sam's solution is inferior to buying no ticket. c. Both Janet and Sam would be indifferent between pooling their risk and buying no ticket. d. There is not enough information to answer this question.…
- Suppose you visit with a financial adviser, and you are considering investing some of your wealth in one of three investment portfolios stocks, bonds, or commodities. Your financial adviser provides you with the following table, which gives the probabilities of possible returns from each investment To maximize your expected return, you should choose: Stocks Bonds Probability Return Probability Return 0.15 20% 0.15 16.7% 06 10% T 04 7.5% 0.25 8% 0.45 3.3% OA bonds OB stocks OC. commodities OD. All of the portfolios have the same expected return. If you are risk-averse and had to choose between the stock or the bond investments, you would choose OA the stock portfolio because there is less uncertainty over the outcome OB. the bond portfolio because there is less uncertainty over the outcome. OC. the stock portfolio because of greater expected return. OD. the bond portfolio because of greater expected return. Commodities Probability Return 02 20% 0.2 15% 0.2 8% 02 02 5% 0%2. Ronald has $18,000. But he is forced to bet it on the flip of a fair coin. If he wins he has $36,000. If he loses he has nothing. Ronald's expected utility function is 0.5x0.5 + 0.5y0.5, where x is his wealth if heads comes up and y is his wealth if tails comes up. What safe income would make him exactly as well off as this bet?6- Suppose Firm B is selling 1 -year insurance contracts for houses. Suppose Firm B's customers are divided into three categories with different probabilities of needing a payment. First category will ask for a payment of 500000 with probability 0.10, the second category will ask for a payment of 250000 with probability 0.15 and the third category will ask for a payment of 100000 with probability 0.2 a. Calculate Firm B's expected payment for the year. Suppose Firm B has 120 customers in the first category, 230 in the second category and 405 in the third category. b. Calculate individual premium if Firm B charges the same amount to all its customers. 1 c. Calculate individual premium if Firm B utilizes the risk groups and charges the same amount of premium within groups d. Which group/groups are more likely to buy the insurance with group pricing compared to the case with uniform pricing?
- $10000, faces a 1. Calculate the expected utility of a person who has wealth W potential loss of C $5000 with probability π and has a utility index u(x) over money: = (i) π = 0.01 and u(x) = x²; (ii) π = 0.01 and u(x) = √√√√x; (iii) π = = 0.1 and u(x) = −2-x/10000. (iv) π = : 0.1 and u(x) = ln(x) with the natural base (v) π = = 0.1 and u(x) = log₁0 (x) with the base 10 =Question 12 Rhianedd has a utility function of the formu u(W)=√W. She has initial wealth of £140. She also has a lottery ticket that will pay £70 with probability 0.1 and zero otherwise. What is the certainty equivalent of the lottery for Rhianedd? Round your answer to 2 decimal places. Add your answer3. The day prior to the release of yearly profits, a stock has price equal to 1. An investor is deciding whether to buy the stock or not. The investor has a wealth equal to 10. Yearly profits can be high with probability 0.4 or low with probability 0.6. If profits are high, the price will double on the following day; if profits are low, the price will halve on the following day. If the investor does not buy the stock, her wealth remains unchanged. If the inverstors buys the stock, she will sell the stock on the following day (regardless of whether the profits are high or low) and she will accrue the relative profit or loss. In other words, she cannot hold the stock for more than one day. The investor does not discount the future and she abides von-Neumann and Morgenstern axioms. Her vNM utility index over money is u (x) = r with 3 E (0,2). • Write down the two possible gambles faced by the investor. • Does the investor buy the stock or not? Explain. • Compute the Arrow-Pratt measure of…
