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- Prospect Y = ($6, 0.25 ; $15, 0.75) If Will's utility of wealth function is given by u(x)=x0.25, what is the value of CE(Y) for Will? (In other words, what is Will's certainty equivalent for prospect Y?) (The certainty equivalent represents the maximum amount a person would be willing to pay to acquire a risky prospect, and equivalently, the lowest price for which they would be willing to sell a risky prospect if they already owned it) (Note: The answer may not be a whole number; please round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)(Ch 7) Suppose a standard normal random variable has an 80 percent chance falling in an interval (–z, z). The value of z is approximately ____ (use Appendix C-1). a. 1.45 b. 1.35 c. 1.96 d. 1.28Millicent’s utility function is U(w) = W0.5 , where W is her wealth. She owns a “pure water” producing firm that will be worth GH100 or 0 Ghana cedis next year with equal probability. a. Suppose her firm is the only asset she has. What is the lowest price at which she will agree to sell her pure water? (Hint: price=amount that will give her the same expected utility) b. Assume that she has GH200 safely stored under her mattress, find the new lowest price at which she will agree to sell her “pure water” producing firm c. From your answers in parts (a) and (b), what is the relationship between her wealth and her degree of risk aversion?
- Y = 1million + 56.43*X + error By how much does the expected value of Y change if X increases by 2 units? (Round your answer to two decimal places: ex: 123.45) Y = 50 + 3X + error By how much does the expected value of Y change if X decreases by 10 units?At a company, 20 employees are making contributions for a retirement gift. Each of the 20 employees is choosing how many dollars to contribute from the interval [0,20]. The manager of these 20 employees announces that she will contribute dd dollars for every dollar that an employee contributes. The payoff to employee ii who makes contribution of xixi dollars is bi(1+d)xi−xi, where bi>0.bi(1+d)xi−xi, where bi>0. Assume that d=4d=4, bi=0.25bi=0.25 for i=1,2,…,10i=1,2,…,10, andbi=0.5bi=0.5 for i=11,12,…,20i=11,12,…,20 What is the best contribution level of any employee ii for i=1,2,…,10i=1,2,…,10. At a company, 20 employees are making contributions for a retirement gift. Each of the 20 employees is choosing how many dollars to contribute from the interval [0,20]. The manager of these 20 employees announces that she will contribute dd dollars for every dollar that an employee contributes. The payoff to employee ii who makes contribution of xixi dollars is bi(1+d)xi−xi,…FINITE REPETITION Alice and Bob are playing a repeated game in which a certain stage game is played twice in succession. All behaviour in the first period is observed by both players before the second period commences. In the stage game, Alice has 3 pure strategies and Bob has 2 pure strategies. How many pure strategies does Bob have in the repeated game? (If necessary, use a calculator to compute this number.) 2 6 2187 3 36 64 7 729 128 216 Please do fast ASAP fast
- We consider the following decision problem, with 4 decisions di,i∈{1,…,4}, and four possible outcomes ωi,i∈{1,…,4}, with the following table of profits: ω1 ω2 ω3 ω4 d1 30 30 0 30 d2 20 20 20 20 d3 0 50 10 40 d4 15 30 10 25 Which decision should be chosen for rewards depending on four different possible outcomes, according to the maximin rule, maximax rule, and optimism-pessimism rule with α<1/3?Let P(A) = 0.2, P(B) = 0.6 and P(A or B) = 0.5. Are events A and B mutually exclusive? Why or why not?Prospect Y = ($4, 0.25 ; $16, 0.75) If Will's utility of wealth function is given by u(x)=x0.25, what is the value of U(EV(Y)) for Will? (In other words, how much utility would Will get were he to receive the expected value of Y?) (Note: The answer may not be a whole number; please round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)
- Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)Suppose that there is a 20 percent change that George's coffee shop will make $9000 in profits in January and a 40 percent chance it will make 1000 profits and a 40 percent chance that it will make -$1000 in profits (i.e., it will lose $1000). Calculate the coffee shop's expected profits2 Prove rigourously, "Constant relative risk aversion (CRRA) implies decreasing absolute risk aversion (DARA), but the converse is not necessarily true."