BE Fianl note

Suppose Jessica has two choices: receive $12000 and 30 utils or take a gamble that has a 55% chance of a $20000 and 45 utils, and a 45% chance of a $0 payoff and zero utility. Assuming Jessica is a utility maximizer, what will she likely choose? a) Jessica will not take the gamble b) Jessica will take the gamble c) It cannot be determined d) Jessica is indifferent

1b

Utility functions incorporate a decision maker’s attitude towards risk. Let’s assume that the following utilities were assessed for Danica Wary. x u(x) -$2,000 0 -$500 62 $0 75 $400 80 $5,000 100   Would a risk neutral decision maker be willing to take the following deal: 30% chance of winning $5,000, 40% chance of winning $400 and a 30% chance of losing $2,000? Using the utilities given in the table above, determine whether Danica would be willing to take the deal described in part a? Is Danica risk averse or is she a risk taker? What is her risk premium for this deal?

A Bank has foreclosed on a home mortgage and is selling the house at auction. There are two bidders for the house, Zeke and Heidi. The bank does not know the willingness to pay of these three bidders for the house, but on the basis of its previous experience, the bank believes that each of these bidders has a probability of 1/3 of valuing it at $800,000, a probability of 1/3 of valuing at $600,000, and a probability of 1/3 of valuing it at $300,000. The bank believes that these probabilities are independent among buyers. If the bank sells the house by means of a second- bidder, sealed-bid auction, what will be the bank’s expected revenue from the sale? The answer is 455, 556. Please show the steps in details thank you!

To go from Location 1 to Location 2, you can either take a car or take transit. Your utility function is: U= -1Xminutes -5Xdollars +0.13Xcar (i.e. 0.13 is the car constant) Car= 15 minutes and $8 Transit= 40 minutes and $4 What is your probability of taking transit given the conditions above? What is your probability of taking transit if the number of buses on the route were doubled, meaning the headways are halved? Remember to include units.

Suppose your classmate Yakov offers you a wager: He will choose a playing card at random from a deck and pay you $1,000 if it is red, but you have to pay him $1,000 if it is black. Assume your wealth is currently $3,000. The graph shown below plots your utility as a function of wealth. Use the graph to answer the questions that follow. UTILITY (Units of utility) 100 90 8 8 70 288 50 40 30 20 10 0 WEALTH (Thousands of dollars)

Consider the two Nash equilibria found above. Is any one of them a Perfect Bayesian Equilibrium (PBE)? Explain. In particular, consider each NE and argue why they are or are not part of a PBE. [Note: A complete description of PBE must specify beliefs as a part of description of the equilibrium.]

Here is my question!

You are attempting to establish the utility that your boss assigns to a payoff of $1,100. You have established that the utility for a payoff of $0 is zero and the utility for a payoff of $10,000 is one. Your boss has just told you that they would be indifferent between a payoff of $1,100 and a lottery which has a payoff of $10,000 where the probability of losing is 0.4. What is your boss' utility for $1,100? (Round your answer to 1 decimal place.) Utility of $1,100

Suppose that there is a risky bet that promises a 50-50 chance of winning or losing $1000 for someone with a starting income of $59000. The certainty equivalence of this risky bet refers to the certain income that provides the same utility as does this risky bet (in expectation). Calculate the certainty equivalence of this risky bet respectively for the following utility functions: a. U (D)= √I 1 b. U (D)=-I c. U (I) = In(1) Round all answers to 3 decimal places.

a) Consider a set of monetary outcomes X = {x1,... , Xk} where the outcomes are arranged in increasing order x, g(x;) for all i = 1,... K, j=i j=i with at least one of the inequalities being strict. Explain the intuition of first-order stochas- tic dominance. Show that, for expected utility preferences with vNM utility u that is strictly increasing in money, if p first-order stochastically dominates q then p > q.

Suppose Jimi has reference dependent preferences over guitars and money as in Tversky and Kahneman (1991). His utility functions are given below. Gains Gains 400 -2 -2 2 Guitars 2$ Losses Losses i-600 -2 What is the least amount of money Jimi is willing to accept to sell one of his guitars? (just enter a dollar amount, i.e., "10o0", not "$1000"

Show all steps, please and thank you.

a) Consider a set of monetary outcomes X {x1,... , xK} where the outcomes are arranged in increasing order x E q(x;) Σα) for all i = 1 . Κ , for all i = 1, ... K, %3D j=i j=i with at least one of the inequalities being strict. Explain the intuition of first-order stochas- tic dominance. Show that, for expected utility preferences with vNM utility u that is strictly increasing in money, if p first-order stochastically dominates q then p > q. b) Consider the following decision problems: Decision 1: Choose between A. A sure gain of £240. B. A 25% chance to gain £1000, and a 75% chance to gain nothing. Decision 2: Choose between C. A sure loss of £750. D. A 75% chance to lose £1000, and a 25% chance to lose nothing. The lotteries in each decision are independent. When people are offered both decisions, and it is explained they will receive both of their choices, it has been found that most people choose A and D, so receive A + D. Discuss why such preferences might occur. Compare this pair…

1) Expected Utility formulation was initially proposed as a solution to the St. Petersburg paradox (or, its predecessor). However, does it really solve all such paradoxes? More specific, consider an individual whose "little Bernoulli" utility functions is, a la Cremer, given by u(x) = x^. Construct a lottery similar to St. Petersburg lottery in that your lottlery, too, gives a finite prize with probability one, but not only the expected value, but also the expected utility of your lottery (calculated using the u(.) above) is not finite. Discuss how that violates EU as a solution for the St. Petersburg paradox.

Consider two individuals, Dani and Tom. Dani's utility function is given by U(c)=In(c), where c is the amount of consumption in a given period. Tom's utility is U(c)=c^2 a) In two separate graphs, draw Dani and Tom's utility function (U in y-axis, c in x-axis). b) Both Dani and Tom can purchase a lottery that pays 5 with 75% probability, and 15 with 25% probability. Calculate and mark on the graphs the utility evaluated at the expected level of consumption for the lottery. Then calculate and mark on the graphs the expected utility for Dani and Tom. c) How do utilities at the expected level of consumption compare to the expected utility? What explains the difference between Dani and Tom? What implication does this difference have for their risk preferences?

How would this exercise be solved step by step?

What would be the solution?

Behavioral evidence suggests that the likelihood of both fifirms choosing high prices can be increased if their executives can (A) engage in informal communications and signal their intention to keep high prices; (B) play mixed strategies; (C) use the K-level thinking; (D) none of the above.