David is an expected-utility maximizer that likes to drive fast (and reckless at times), so his probability of an accident is 2/3. David's preferences over wealth are u(w) = √w. Suppose that David's initial wealth is $100. If David has an accident, he incurs a $51 loss. How much is the risk premium David willing to pay to be as well off in case of accident or not?

. Bob le Flambeur is offered a raffle ticket. With probability p, the raffle ticket wins, and pays 5 dollars. With probability 1-p, the ticket loses and pays nothing. One ticket costs 1 dollar. (a) If Bob has von Neumann-Morgenstern utility u(x)=³ over change in wealth z, what is the certainty equivalent for Bob of buying one ticket (as a function of p)? What is the risk premium? Solution: If Bob buys a raffle ticket, then with probability p he gains 4 dollars (5 dollars minus the price of the ticket), and with probability 1-p he loses 1 dollar. His expected utility is therefore 64p-(1-p) = 65p-1. The certainty equivalent is therefore CE(p) = 365p-1. The expected value of the lottery is 4p- (1 − p) = 5p - 1, giving a risk premium of R(p)=5p-1-65p - I. (b) Now suppose that, instead of the utility function above, Bob is risk-neutral. An un- scrupulous raffle saleswoman makes Bob the following offer. For 50 cents, she will tell him whether the ticket for sale will win or lose before Bob…

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Consider a person with the following utility function over wealth: u(w) = ew, where e is the exponential function (approximately equal to 2.7183) and w = wealth in hundreds of thousands of dollars.  Suppose that this person has a 40% chance of wealth of $100,000 and a 60% chance of wealth of $2,000,000 as summarized by P(0.40, $100,000, $2,000,000). a. What is the expected value of wealth? b. Construct a graph of this utility function . c. Is this person risk averse, risk neutral, or a risk seeker? d. What is this person’s certainty equivalent for the prospect?

Question 2 A person has a wealth of $20,000 but faces an accident that results in a loss of S12,000 with probability, p. Suppose that Bermoulli utility is given by u(x) = -1/x. 1. Determine the maximum amount of money the person is willing to pay for complete coverage (as a function of p). 2. Now suppose that an insurance company offers an insurance contract with a deductible of $2,000. Again, determine the maximum amount of money a person is willing to pay for this insurance contract.

You take a position with a large real estate development company as your first job after graduation.  Your first big assignment is to sell an office building – you have been informed the company’s cost into the building (and the bottom line price it is willing to accept) is $400,000.  You have identified a likely buyer and you assess that his top price is either $500,000 with a probability of .3, $600,000 with a probability of .5, or $1,000,000 with a probability of .2.  You have to commit to a posted price – what price will maximize your profitability?

An investor has a power utility function with a coefficient of relative risk aversion of 3. Compare the utility that the investor would receive from a certain income of £2 with that generated by a lottery having equally likely outcomes of £1 and £3. Calculate the certain level of income which, for an investor with preferences as above, would generate identical expected utility to the lottery described. How much of the original certain income of £2 the investor would be willing to pay to avoid the lottery? Detail the calculations and carefully explain your answer.

Suppose that a person's utility function is the square root of wealth. Suppose the person earns $100,000 per year. He or she has an illness with a probability of 0.2, and the cost of the treatment is $30,000. Would the person pay $6,000 for insurance? Why or why not? What is the most this person would pay to be insured (hint: equate expected utility to utility with certainty)? Suppose their utility function changed to wealth squared (hint: are they now risk averse?). Would they pay $6,000 for insurance? Why or why not?

Q.No.4. If you are supposed to a 40/60 chance of gaining or losing Rs.400 and insurance that removes the risk costs Rs.150; at what level of wealth will you be indifferent relative to taking the gamble or paying the insurance? That is, what is your certainty equivalent wealth? Assuming your utility function is U(W)= In(W).