1. Suppose a company can select among two decisions (d1 and d2) and face three states of nature (s1, s2 and s3) withthe following payoff table:Decision s1 s2 s3d1d2150 200 20050200500The probabilities of s1, s2, and s3 are unknown. Using the optimistic approach, what is the optimal decision and what isthe value of the payoff? Place the optimal decision in the first answer box and the maximum payoff used to arrive at thisdecision in the second.Question 6 options:2. Suppose a company can select among two decisions (d1 and d2) and face threestates of nature (s1, s2 and s3) with the following payoff table:Decision s1 s2 s3d1d2150 200 20050 200 500The probabilities of s1, s2, and s3 are unknown. Using the conservative approach, what is the optimal decision and what isthe value of the payoff? Place the optimal decision in the first answer box and the maximum payoff used to derive thissolution in the second.Question 7 options:83. Suppose a company must consider two decisions (d1 and d2) under two states of nature (s1 and s2). Suppose theexpected value functions for d1 and d2 are given as:EV(d1) p(8) + (1-p)(6)EV(d2) p(15) + (1-p)(3)where p = P(s1) and 1-p = P(s2). In conducting sensitivity analysis, which of the following is correct?Question 8 options:d2 is the optimal decision as long as p > 0.30d2 is the optimal decision as long as p > 0.05d1 is the optimal decision as long as p > 0.30d2 is never the optimal decision

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1. Suppose a company can select among two decisions (d1 and d2) and face three states of nature (s1, s2 and s3) with the following payoff table: ecision s1 s2 s3 150 50 d1 200 200 d2 200 500 he probabilities of s1, s2, and s3 are unknown. Using the optimistic approach, what is the optimal decision and what is he value of the payoff? Place the optimal decision in the first answer box and the maximum payoff used to arrive at this ecision in the second. Question 6 options:

1. Suppose a company can select among two decisions (d1 and d2) and face three states of nature (s1, s2 and s3) with the following payoff table: ecision s1 s2 s3 150 50 d1 200 200 d2 200 500 he probabilities of s1, s2, and s3 are unknown. Using the optimistic approach, what is the optimal decision and what is he value of the payoff? Place the optimal decision in the first answer box and the maximum payoff used to arrive at this ecision in the second. Question 6 options:

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A salesperson is trying to sell cars. The number of cars that she will sell depends on her effort "e" and her luck. Given her effort e, with probability 4e she is able to sell four cars, and with probability (1 - 4e) she is able to sell only one car. Her personal cost of effort is 100e². The dealership pays her a bonus b for each car sold. The salesperson is risk-neutral, and wants to maximize her expected utility, which is her expected income minus her effort cost. a) Given the bonus b, the salesperson's best response function is b) Suppose the dealership pays b = 2. Then the expected number of cars sold will be E(Q)=
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Question10: The game matrix table arranged according to player A is given.by solving the game with the graphic method;2-)Find the probability of playing strategy 1 of B.2-)Find the probability of playing B's strategy 2.3-) Find the expected game value.
3. Consider the game below. С1 C2 C3 R1 1, 1 4, 6 8, 5 1, 2 5, 4 R2 R3 2, 6 2, 7 7, 6 0, 7 3.1. Does the game have any pure strategy NEs? 3.2. Check whether a mixed strategy NE exists in which A is mixing R1 and R2 with positive probabilities, playing R3 with zero probability, while B is mixing C1 and C3 with positive probabilities while playing C2 with zero probability. [Let (p1,P2, P3) be the probabilities with which A plays (R1, R2,R3) and let (q1,92, 93) be the probabilities with which B plays (C1, C2,C3). Make use of the following NE test: m* is a NE if for every player i, u;(mị , m²¿) = u;(Si, m²¡) for every si E S¡|m¡(sji) > 0 and u¡(m¡ ,m²¡) > u¡(s¡,m;) for every si E S¡ |m¡ (s¡) = 0. Hint: Each player must be indifferent between those of her pure strategies that are used (with positive probability) in her mixed strategy, and unused strategies must not yield a payoff that is higher than the payoff a player gets with her NE (mixed) strategy.] %3D
2. Christiaan can go hiking, or he can stay at home. Hiking would be fun if nothing bad happens, but there is a risk if he goes hiking that he will meet a bear (not fun) or get bitten by a snake (very not fun). Christiaan decides that if there is a 5% chance of meeting a bear and a 1% chance of getting bitten by a snake, he would prefer to go hiking rather than stay at home. However, if the chance of meeting a bear is 10% and the chance of a snake bite is 5%, he definitely would rather stay at home. then (a) Consider the utility function: U (stay home) = 25, U (hike no event) = 100, U (hike & snake) -1000, U (hike & bear) = -200. Does this utility function represent Christiaan's pref- erences? Explain. (b) Suppose that the utility function in (a) does represent Christiaan's preferences. Would Christiaan prefer to hike or stay home if the probability of meeting a bear is 6% and the probability of being bitten by a snake is 4%? Show your work.
. 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.
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(ii) A mixed strategy profile (p, q) is one in which p = (p,P2.... P) is the mixed strategy of player 1, and q- (g1, q2,..q4) is the mixed strategy of player 2. Show that if p, >0 in a Nash equilibrium profile (p*, q*), the player 2 must also play i with strictly positive probability q'; > 0. (State clearly any theorem you use to show this. You are not required to justify the theorem.) %3D
1. Mr. Smith can cause an accident, which entails a monetary loss of $1000 to Ms. Adams. The likelihood of the accident depends on the precaution decisions by both individuals. Specifically, each individual can choose either "low" or "high" precaution, with the low precaution requiring no cost and the high precaution requiring the effort cost of $200 to the individual who chooses the high precaution. The following table describes the probability of an accident for each combination of the precaution choices by the two individuals. Adams chooses low precaution Adams chooses high precaution Smith chooses low precaution Smith chooses high precaution 0.8 0.5 0.7 0.1 1) What is the socially efficient outcome? For each of the following tort rules, (i) construct a table describing the individuals' payoffs under different precaution pairs and (ii) find the equilibrium precaution choices by the individuals. 2) a) No liability b) Strict liability (with full compensation) c) Negligence rule (with…