Consider the bilateral trade problem of Section 3.4. Assume that the seller's type

is commonly known to be zero and that the buyer's type is drawn from the set

[0, 1]. Consider the following fixed price mechanism: The buyer reports her type.

If the reported type is above 0.5, then the object is transferred from the seller to

the buyer, and the buyer pays to the seller 0.5 dollars. Otherwise, the seller keeps

the object and no payments are made. Now consider the alternative mechanism

in which the seller can choose either price 0.4 or price 0.5. The buyer reports

her type. If her type is above the price that the seller chose, then the object is

transferred from the seller to the buyer, and the buyer pays to the seller the price

that the seller chose. Otherwise, the seller keeps the object and no payments are

made. Prove that this mechanism has a Bayesian equilibrium on the space of all

finite types that ex post Pareto dominates the truthful equilibrium of the fixed

price mechanism.

(c) In the setting of problem (c) in Chapter 9, find a mechanism and a Bayesian

equilibrium of that mechanism that interim Pareto-dominate on all finite type

spaces the mechanism that chooses alternative a regardless of agents' types. Do

the mechanism and Bayesian equilibrium that you find ex post Pareto-dominate

the constant mechanism?

If the respondent agreed with the statement and reported a

high degree of confidence in the response, then susceptibility to cer-

tainty overconfidence is likely. If the respondent disagreed with the

statement, and did so with 50 to 100 percent confidence, then sus-

ceptibility to certainty overconfidence is less likely. If respondents

agree but with low degrees of confidence, then they are unlikely

to be susceptible to certainty overconfidence. Confidence in one's

knowledge can be assessed, in general, with questions of the follow-

ing kind:

Which Australian city has more inhabitants?Sydney or Mel-

bourne?

How confident are you that your answer is correct? Choose one: 50

percent, 60 percent, 70 percent, 80 percent, 90 percent, 100

percent.

If you answer 50 percent, then you are guessing. If you answer 100

percent, then you are absolutely sure of your answer.

Two decades of research into this topic have demonstrated that in all

cases wherein subjects have reported 100 percent certainty when answering

a question like the Australia one, the relative frequency of correct answers

has been about 80 percent. Where subjects have reported, on average, that

they feel 90 percent certain of their answers, the relative frequency of correct

answers has averaged 75 percent. Subjects reporting 80 percent confidence

in their answers have been correct about 65 percent of the time, and so on.

Question 8:

Respondents describing themselves as sophisticated or

highly sophisticated investors are likelier than others to exhibit

certainty overconfidence. If the respondent chose "somewhat so-

phisticated" or "unsophisticated," susceptibility is less likely.

2) (20 points) Lynn has a utility function UNI\") = W\1. Suppose we are interested in the mean scores on an exam. A random sample of 36 scores is taken and gives a sample mean (sample mean score) of 68 (x= 68). In this example we have the unusual knowledge that the population standard deviation is 3 points. Do not count on knowing the population parameters outside of textbook examples. Find a confidence interval estimate for the population mean exam score (the mean score on all exams). Find a 90% confidence interval for the true (population) mean of statistics exam scores.1. Suppose that Natasha's utility function is given by u(1) = 1^0.5, where I represents annual income in thousands of dollars. a. Is Natasha risk loving, risk neutral, or risk averse? Explain, b. suppose that Narasha is currently earning an Income of $10,000 (1 == 10) and can earn that income next year with certainty. She is offered a chance ,to take a new job that offers a .5 probability of earrung $16,000 and a .5 probability of earning $5000. Should she take the new job? c. In (b), would Natasha be willing to buy insurance to protect against the variable income associated with the new job? If so, how much would she bt willing to pay for that insurance? (Hint: What is the risk premium?) 2. Draw a utility function over income u()) tha describes a man who is a risk lover when his mcoall is low but a risk averter when his income is high. Can you explain why such a utility function might reasonably describe a person's preferences?2. Omer has utility for consumption such that U(C) = C/3. He faces a 50% chance that his consumption will be 125 and a 50% chance it will be 27. (a) What is his expected utility from this uncertain outcome? (b) What is the utility of his expected consumption? (c) What would be the AFI premium? (d) What is the slope of the budget line for the AFI insurance offer? (e) What is the premium for an unfair policy that yields expected consumption that is equal to his Certainty Equivalent