4.Jenny is an expected utility maximiser. When offered lottery l,, she accepts it.1 1(100, 60;52(a) Suppose Jenny were asked to choose between l, and l,, where:2 1l2 = (100, 60;3신.Which lottery will Jenny prefer, and why?(b) Consider another lottery l,, where:1 1l3 = (120, 40;-2'2When asked to choose between l, and l3 Jenny prefers l3. What does thisimply about Jenny's attitude to risk? How are l, and l, related? Illustrate thetwo lotteries in a diagram with wealth on the x-axis and utility on the y-axis.

Expected Payoff= Probability of Payoff* Payoff

Jenny is an expected utility maximiser. When offered lottery l, she accepts it. 1 1, 4 = (100, 60; 5.2' (a) Suppose Jenny were asked to choose between l, and l,, where: 2 1 2 = (100,60;3'· Which lottery will Jenny prefer, and why? (b) Consider another lottery l3, where: 1 1 lz = (120,40; %3D When asked to choose between 4 and l3 Jenny prefers l3. What does this imply about Jenny's attitude to risk? How are l4 and l3 related? Illustrate the two lotteries in a diagram with wealth on the x-axis and utility on the y-axis.

Jenny is an expected utility maximiser. When offered lottery l, she accepts it. 1 1, 4 = (100, 60; 5.2' (a) Suppose Jenny were asked to choose between l, and l,, where: 2 1 2 = (100,60;3'· Which lottery will Jenny prefer, and why? (b) Consider another lottery l3, where: 1 1 lz = (120,40; %3D When asked to choose between 4 and l3 Jenny prefers l3. What does this imply about Jenny's attitude to risk? How are l4 and l3 related? Illustrate the two lotteries in a diagram with wealth on the x-axis and utility on the y-axis.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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. Explain the interpretation of a utility function and why such a function should be increasing. is said that the utility function of a decision maker is given by Ua(x) = 2ax – x², r € R for some a > 0.For which lotteries with random outcomes X is the above function a utility function? Explain your answer and give an example of a lottery or specify a distibution of the random variable X for which the function mentioned in relation 2 is not a utility function. 3. Consider a decision maker with initial wealth 0 and this decision maker needs to play a lottery L having a random outcome X bounded above by a > 0. This means P(X 0 be given and L a lotery with random outcome X having cumulative distribution function if r a and assume that the utility function of the decision maker having initial wealth w = 0 is given by the function uq listed in relation 2. Compute the expected utility of this lottery and the certainty equivalence of this lottery.
Find the attached file.
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. If you examine the decision tree in Figure 9.12 (orany other decision trees from PrecisionTree), you willsee two numbers (in blue font) to the right of each endnode. The bottom number is the combined monetaryvalue from following the corresponding path throughthe tree. The top number is the probability that thispath will be followed, given that the best strategy isused. With this in mind, explain (1) how the positiveprobabilities following the end nodes are calculated,(2) why some of the probabilities following the endnodes are 0, and (3) why the sum of the probabilitiesfollowing the end nodes is necessarily 1.
2. Consider the following two player game in normal form: Player 2 R 0, 5 2, 3 2, 3 Player 1 M 2, 3 0, 5 3, 2 B 5,0 3, 2 2, 3 (a) Show that for Player 1, strategy T is strictly dominated by a mixed strategy in which actions M and B are played with positive probability. (b) Find a mixed strategy Nash equilibrium of this game. 352
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