4. Suppose a subjective learning DM has prior belief that assigns equal weight, 1/3, to thethree states, wi, w2, and w3, of the world (i.e., good, bad, and ugly weather). Supposethe DM expects to receive information about the true state. In particular, let be theDM's subjective information structure which puts equal weight on each posterior belief,p = (2/3, 1/6, 1/6) and q = (1/6,2/3, 1/6) and r = (1/6, 1/6,2/3), but zero weight onany other posterior belief. Let f = (12,6,0) and g = (0,12,6) and h = (6,0,12) bethree acts available to the DM and suppose the DM receives payoff from each outcomea by the function u(a) = a. Answer the following questions.(a) Show that the DM strictly prefers (f, g} over 1/2{g} + 1/2{h}(b) Show that the DM strictly prefers (f, g} over {f, 1/2g + 1/2h}(c) Show that the DM strictly prefers {f, g, h} over {f, 1/2g+ 1/2h, h}

From the calculations, the DM is strictly preferring in part (a) but is indifferent in parts (b) and…

Answered: 4. Suppose a subjective learning DM has…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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(Derive the coefficients of absolute and relative risk aversion of the following functions, and point out th conditions to make each function increase and concave: (а) и (х) —х- (b/2)x2 (b) µ (x) = (B/(B –- 1))x!-1/B (c) µ (x) = (1/ (B – 1)) [A +Bx]'¬1/B
Static Bayesian Games] We consider a games with 2 players. Player 1 has only asingle type; however, Player 2 can have two types I and D, each with probability 50%. Bothplayers have two actions available to them. The game has the following payoffs (P1 is the rowplayer, P2 the column player):
Suppose an individual faces uncertainty over the following set of monetary outcomes A = {-10, 4, 8, 13, 22} Suppose the individual abides to the vNM axioms. a) How can you represent her preference relation over gambles over A? b) Is this representation unique? c) Is it the only one satisfying the expected utiltiyproperty? d) Suppose u(-10) = 0, u(22) = 1. Also assume that u(4) = 0.5, u(8) = 0.55 and u(13) =0.65. Can you build a gamble that is indifferent to the degenerate gamble that gives 4 with certainty? What is the utility of the following gambles p = (0.1, 0.2, 0.5, 0.2, 0), q = (0.2, 0.2, 0.2, 0.2, 0.2), r =(0.3, 0, 0.2, 0.1, 0.4). How does the individualrank these three gambles?
[Adverse Selection] Each of the two players receives an envelope, in which there is anamount of money that is equally distributed from $0, $1, $2, ..., $100. The amounts in twoenvelopes are independent. After receiving the envelope, each individual can check exactlyhow much money is put in his/her own envelope. Then each player has the option to exchangehis/her envelope for the other individual's prize. The decisions are made simultaneously. Ifboth individuals agree to exchange, then the envelopes are exchanged; otherwise, if at leastone player chooses not to exchange, each individual keeps his/her own envelope and receivesits attached sum of money.a. Model this game as a static Bayesian game (write the normal formrepresentation) and find the Bayesian Nash equilibrium.b. Consider a new game where the probability distribution of money in eachenvelope is changed. The amount is equal to $100 with probability 90%, and is equalto each number in $0, $1, $2, ... ,$99 with probability 0.1%.…
5 players must simultaneously choose a number from the interval [0, 9]. Let xi denote the number chosen by player i; x = (x1, . . . , x5) all the selected numbers; x−i = x\xi all the selected numbers except the one chosen by player i. If player i chooses the number xi ∈ [0, 9], while the others choose numbers x−i, then the utility of player i is given by ui(xi, x−i) = 4(9 − xi) + 2Σ5 j=1 xj. Find the Nash equilibrium of the game and the corresponding utilities. Would all players be better off if they signed a binding contract before the game, obligating them to choose the number 9?
those determinations. Respond to the following questions in a minimum of 175 words: . Consider a situation that you might need to use your understanding of probability to make an informed decision. • What sorts of information would you collect? • How might you use what you have learned about probability to determine a course of action? What are the possible benefits and limitations of this approach? Due Monday Reply to at least 2 of your classmates. Be constructive and professional in your responses. Copyright 2020 by University of Phoenix. All rights reserved. New Group 1 17 Responses 33 Replies
Soft selling occurs when a buyer is skeptical of the usefulness of a product and the seller offers to set a price that depends on realized value. For example, suppose a sales representative is trying to sell a company a new accounting system that will, with certainty, reduce costs by 10%. However, the customer has heard this claim before and believes there is only a 30% chance of actually realizing that cost reduction and a 70% chance of realizing no cost reduction. Assume the customer has an initial total cost of $300. According to the customer's beliefs, the expected value of the accounting system, or the expected reduction in cost, is . Suppose the sales representative initially offers the accounting system to the customer for a price of $19.50. The information asymmetry stems from the fact that the has more information about the efficacy of the accounting system than does the . At this price, the customer purchase the accounting system, since the expected…
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.
Can Question 10 be answered?
Consider a worker who works for at most two periods (say, when young and when old) at a particular firm. Each period, the worker can choose between exerting high effort and exerting low effort. The worker's cost of exerting high effort are Cy when young and Co when old. The worker's cost of exerting low effort are zero. The effort of the worker is difficult to observe by the firm. With probability T, the firm observes the worker's effort at the end of a period. With the remaining probability, the firm does not observe the worker's effort. The firm can only fire the worker when it observed that the worker has shirked. In that case, the firm is also allowed to withhold the worker's wage for the period in which the worker was caught shirking. When exerting high effort, the worker's productivity is q, when young and q, when old. When exerting low effort, the worker's productivity is zero. The worker's value of alternative job opportunities is when young and v, when old. For simplicity, the…
Soft selling occurs when a buyer is skeptical of the usefulness of a product and the seller offers to set a price that depends on realized value. For example, suppose a sales representative is trying to sell a company a new accounting system that will, with certainty, reduce costs by 10%. However, the customer has heard this claim before and believes there is only a 20% chance of actually realizing that cost reduction and a 80% chance of realizing no cost reduction. Assume the customer has an initial total cost of $200. According to the customer's beliefs, the expected value of the accounting system, or the expected reduction in cost, is $____ . Suppose the sales representative initially offers the accounting system to the customer for a price of $12.00. The information asymmetry stems from the fact that the ______(sales rep or buyer) has less information about the efficacy of the accounting system than does the ______(sales rep or buyer) . At this price, the…
4.

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