An individual has the following utility function u(w)=2w05 +10 using the expected utility, order the following prospects in terms of preference, from the most to the least preferred. P1 (0.9, 3,500, 500) P2 (0.7, 3700, 400) P3 (0.5, 5000, 350) What is the certainty equivalent level for P3.
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- Tasha is planning to invest in a farming project in 2022, but has a reservation given the different forecast (declined (D),the average (A) and takeoff (T)of the economy. She uses the following to guide her decision making. (i) there is 25% chance she will invest if there is a forecast of declined (ii) there is a 75% chance she will invest if there is a forecast of average growth and (iii) there is a 55% chance of investing if there is a forecast that economy will takeoff. Tashanna believes that for 2022 there is a 20% chance of decline and a 40% chance of average growth and a 40% chance the economy will take off. Based on these probabilities what is the chance that Tattiana will invest in the farming project if the stated forecast hold?Using the normal table or software, find the value of z that makes the following probabilities true. You might find it helpful to draw a picture to check your answers (a) P(Zz) =0.01 (e) P(Z|A bakery would like you to recommend how many loaves of its famous marble rye bread to bake at the beginning of the day. Each loaf costs the bakery $2.00 and can be sold for $7.00. Leftover loaves at the end of each day are donated to charity. Research has shown that the probabilities for demands of 25, 50, and 75 loaves are 30%, 20%, and 50%, respectively. Make a recommendation for the bakery to bake 25, 50, or 75 loaves each morning. Find the expected monetary value when baking 25 loaves. EMV=$(Type an integer or a decimal.) Find the expected monetary value when baking 50 loaves. EMV = $(Type an integer or a decimal.) Find the expected monetary value when baking 75 loaves. EMV = $ (Type an integer or a decimal.) Make a recommendation for the bakery to bake 25, 50, or 75 loaves each morning. The bakery should bake loaves of bread every morning. O 25 50 75 EA manager has to decide whether to prepare a bid or not. It costs P5,000 to prepare the bid. If the bid is submitted, the probability that the contract will be awarded is 50%. If the company is awarded the contract, it may earn an income of P100,000 if it succeeds, or pay a fine of P8,000 if it fails. The probability of success is estimated to be 80%. What is the expected value if the contract is awarded?Q2. (i) Consider a risk averse investor who must decide how much of his initial wealth w to put into a risky asset. The risky asset can have any of the positive or negative rates of return r with probability density function f(r). If ß is the amount of wealth to be put into the risky asset, final wealth under rate of return r will be (w B) + (1+r)ß = w+ ßr. The investor's problem is to choose 3 to maximize the expected utility of wealth. We can write this formally as the following single-variable optimization problem (1) Suppose we have interior optimal 3* falls in (0, w), which is determined by the following first order condition: Ju'(w + ßr)rf(r)dr = 0. (2) Define A(w) as a measure of absolute risk aversion. Please show that if u(.) displays decreasing absolute risk aversion (DARA), i.e. A(w) decreases with w, then the risky asset must be a "normal" good, i.e. 3* increases with w. [Hint: Please read Example 2.6 in Jehle and Reny.] max fu(w + Br)f(r)dr s.t.: 0 ≤ B ≤w. B u" (w) = u'…A 28- year- old man pays $158 for one year life insurance policy with coverage of $110,000. If the probability he will live through the year is 0.9994, what is the expected value for the insurance policy?Annual savings due to an energy efficiency project have a most likely value of $30,000.The high estimate of $40,000 has a probability of 0.2, and the low estimate of $20,000has a probability of 0.30. What is the expected value for the annual savings?Your company must decide whether to introduce a new product. The sales of the product will be either at a high (success) or low (failure) level. The conditional value for this decision is as follows Decision High Low Introduce $4,000,000 -$2,000,000 Do Not Introduce 0 0 Probability 0.3 0.7 You have the option to conduct a market survey to sharpen you market demand estimate. The survey costs $200,000. The survey provides incomplete information about the sales, with three possible outcomes: (1) predicts high sales, (2) predicts low sales, or (3) inconclusive. Such surveys have in the past provided these results Result High Low Predicts High 0.4 0.1 Inconclusive 0.4 0.5 Predicts Low 0.2 0.4 a) Using expected monetary value, what is your decision? b) What is the expected value of perfect information before taking the survey? c) Draw the complete decision tree, including the survey option. d) What is the…1. A person who is 55 year old bought a PHP 2,000,000 life insurance policy at a cost of PHP 1.2 M and has a probability of 0.978 of living to age 56, find the expectation of the policy. 2. nPn-r = ? (Permutations)If the individual’s income is either OA = $30,000 with probability of 0.95 orOB= $5000, what is the expected income of this individual?A property owner is faced with a choice of: A large-scale investment to improve her flats. This could produce a substantial pay-off in terms of increased revenue net of costs but will require an investment of 1.4 million pesos. After extensive market research it is considered that there is a 40% chance that a pay-off of 2.5million will be obtained, but there is a 60% chance that it will be only 800,000 pesos. A smaller scale project to re-decorate her premises. At 500,000 pesos this is less costly but will produce a lower pay-off. Research data suggests a 30% chance of a gain of one million pesos but a 70% chance of being only 500,000 pesos. Continuing the present operation without change. It will cost nothing but neither will it produce any pay-off. Clients will be unhappy and it will become harder to rent the flats out when they become free. What is the best alternative? Use decision tree analysis.Three alternative insulations are being considered for installation on a machine part. After the initial installation, if the insulation fails in any future year, it is replaced by an identical one at a cost lower than the initial cost. The costs and probabilities of failure in any year are given in the table below. Insulation thickness 2 inches 3 inches 6 inches Initial installation cost $900 $1,200 $1,800 Probability of failure in any given year 26.7% 14.4% 6.32% Replacement cost anytime insulation fails in future $600 $800 $1,200 If the analysis period is infinte (i.e, N = infinity), calculate the expected EUAC of the 2-inch insulation. The MARR is 11% per year. OA. $414 O B. $259 O C. $104 O D. $155SEE MORE QUESTIONS