Suppose that the outcome space contains three outcomes {1,2,3). Consider the following four lotteries: A (0.3, 0.7,0) B = (0,0.8,0.2) (0,0.5, 0.5) C = D = (0.6, z, y) Assume that a decision maker is indifferent between A and B, and is indifferent between C and D. Suppose the decision maker's preferences over lotteries satisfy the Independence Axiom, find out 1.y. (Hint: You can use graph to get intuition.)
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- There are two shows on Netflix that Jeff can watch, Show 1 and Show 2. x₁ measures the number of episodes watched of Show 1 and x₂ measures the number of episodes watched of Show 2. Jeff's preferences can be represented by u(x₁, x₂) = x² + ax². Jeff has 11 hours available for watching Netflix today. Each episode of Show 1 lasts 30 minutes, while each episode of Show 2 lasts one hour. For all question parts, round to three decimal places if necessary. For parts (a) - (f), let a = 1. Draw Jeff's indifference curves for the utility levels u = 4, 9, 16. Draw a straight line between the bundles (x₁, x₂) = (4, 0) and (x₁, x2) = (0, 4). Now, use your picture to determine whether the following two statements are true or false. Answer "1" for true. Answer "0" for false. a) Statement 1: Jeff's preferences are strongly monotone. 1 b) Statement 2: Jeff's preferences are strictly convex. 0 c) Find the bundle at which one of Jeff's indifference curves is tangent to the budget line. (x₁, x^2) = ( d)…There are two shows on Netflix that Jeff can watch, Show 1 and Show 2. x₁ measures the number of episodes watched of Show 1 and x2 measures the number of episodes watched of Show 2. Jeff's preferences can be represented by u(x₁, x₂) = x² + ax². Jeff has 5 hours available for watching Netflix today. Each episode of Show 1 lasts 30 minutes, while each episode of Show 2 lasts one hour. For all question parts, round to three decimal places if necessary.Two players play the following game for infinite times. For the player to continue to cooperate what would be the ranges of their discount factor, δ_1 and δ_2, respectively? cooperate betray cooperate (10,20) (-25,30) betray (15, -22) (-12, -18)
- which of the two is Pareto optimal V= In x1 + 2 In x2 u= 2 In x1+ In x2 (1,2) (2,1) (2,1) (1,2) (1.5, 1.5) (1.5, 1.5) (3,0) (0,3)A driver's wealth $100,000 includes a car of $20,000. To install a car alarm costs the driver $1,750. The probability that the car is stolen is 0.2 when the car does not have an alarm and 0.1 when the car does have an alarm. Assume the driver's von Neumann- Morgenstern utility function is U(W) = In(W). Suppose the driver is deciding between the following three options: (a) purchase no car insurance, do not install car alarm; (b) purchase fair insurance to replace the car, do not install car alarm; and (c) purchase no car insurance, install car alarm. Of these three options, the driver prefers: A. option (a). B. option (b). C.option (c). D.options (a) and (b). E. options (a) and (c). F. options (b) and (c). G.all options equally. H.none of these options.Jiffy-Pol Consultants is paid $1,000,000 for each percentage of the vote that Senator Sleaze receives in the upcoming election. Sleaze’s share of the vote is determined by the number of slanderous campaign ads run by Jiffy-Pol according to the function S = 100N/(N + 1), where N is the number of ads. If each ad costs $4,900 approximately how many ads should Jiffy-Pol buy in order to maximize its profits? A) 2,853. B) 1428. C)98 D) 477.
- A driver's wealth $100,000 includes a car of $20,000. To install a car alarm costs the driver $1,750. The probability that the car is stolen is 0.2 when the car does not have an alarm and 0.1 when the car does have an alarm. Assume the driver's von Neumann-Morgenstern utility function is U(W) = ln(W). Suppose the driver is deciding between the following three options: (a) purchase no car insurance, do not install car alarm; (b) purchase fair insurance to replace the car, do not install car alarm; and (c) purchase no car insurance, install car alarm. Of these three options, the driver prefers: A. option (a). B. option (b). C. option (c). D. options (a) and (b). E. options (a) and (c). F. options (b) and (c). G. all options equally. H. none of these options.Finn is in charge of decorations for an upcoming festival, and he is planning to decorate withclovers (C) and flags (F). Suppose his preferences over decorations can be represented by theutility function U(C, F) = C^(3/4)F^(1/4) For this problem, assume C and F are infinitely divisible so you don’t need to worry aboutrestricting to whole-number answers.(a) Write Finn’s budget constraint as a function of the prices PC, PF , and his budget I.(b) Write Finn’s constrained optimization problem in Lagrangian form and derive the threefirst order conditions.(c) Use two of the first order conditions to show that Finn’s marginal rate of substitution(MRS) equals the marginal rate of transformation (MRT) at the optimum. (Note: Youdo not need to solve the constrained optimization any more than this.)A consumer buys (x1, X2 , X3 ) at price vector (P,, P2 , P3). We make three observations of his behavior: At (P,P,,P;) = (1,1,2), the consumer chooses (x,,x,,x3) = (5,19,9) At (P, P,,P,) = (1,1,1), the consumer chooses (x,,x,, x3 ) = (12,12,12) At (P, P,,P,) = (1, 2,1) , the consumer chooses (x,,x,,x; ) = (27,11,1) %3D %3D Does the consumer's behavior satisfy WARP? What about SARP?
- Cost-Benefit Analysis Suppose you can take one of two summer jobs. In the first job as a flight attendant, with a salary of $5,000, you estimate the probability you will die is 1 in 40,000. Alternatively, you could drive a truck transporting hazardous materials, which pays $12,000 and for which the probability of death is 1 in 10,000. Suppose that you're indifferent between the two jobs except for the pay and the chance of death. If you choose the job as a flight attendant, what does this say about the value you place on your life?An investor is confronted with three investment opportunities as indicated in the following table: Investment A probability 1/2 1/4 1/4 Investment B Investment C probability 1/4 1/2 1/4 probability 1/2 3/8 1/8 return return return -$15 -$10 $0 $20 $10 $10 $35 $20 $20 Please answer Questions 10-13 based on this information. Consider Investment C above and an agent with a utility function U(x) = 1 – e-*. Assume that the initial wealth is 0. Based on the Principle of Expected Utility, how much is this agent willing to pay to receive the expected return of this investment without bearing the risk? O 6.25 0.5Suppose that you are the owner of a bakery. The customers who buy the cakes you bake have different tastes x for the chocolate content, with x ranging from 0 to 1. The total number of customers is N = 100 are equally distributed along the [0,1] line. If x is the customer's most preferred chocolate content (location of the customer), and the cakes have chocolate content z, then customer x bears a unit utility cost of $1. Suppose that all customers' reservation price for a slice of a cake is $3. The marginal cost of producing one slice of a cake of any chocolate content is equal to $1. Suppose that you would always like to serve all the customers. a. Your company offers just one type of cake, say regular, with z =1/2 What price will you set for a slice of a cake? b. Suppose that in addition to regular chocolate cake z=1/2 you are also considering offering the high-chocolate variety, that is zHC = 3/4. What price will you set for the slice of your new cake? If running the high-chocolate…