Consider the St. Petersburg paradox. Decision- maker has an exponential utility function with A=4 and B=2 and the risk tolerance level is R=7,000. What is the highest price that the decision-maker is willing to pay for the lottery?
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- Suppose that the world is populated entirely with rational but amoral individuals that only get utility from wealth. An individual's utility function is U(W) = ln(W + 1) where W is the wealth of the individual. Some individuals start with 0 initial wealth while other individuals start with a wealth of W > 0. Everyone can decide whether or not to steal x units of wealth. The individual know their wealth when they take the decision to steal or not. Stealing has two consequences: first the individual gains x$ of wealth up to 2$ of wealth. Second, with probability p= 0.6 the individual gets caught and has to pay back 2x$, that is twice the amount stolen. The penalty is capped by the individual's wealth: the individual can never get less than 0$ of wealth in that world. a) How much should the individual steal if they have an initial wealth of w >> 0? b) How much should the individual steal if they started with no initial wealth? c) Now suppose that there is no limit to the amount that can…Fred wants to hire Barney to manage his retail store. Barney can apply a high level of effort (at a cost to him of $30), a medium level of effort (at a cost to him of $10), or a low level of effort (at a cost to him of $0). Fred's profits depend not only of the level of Barney's effort but also on the state of consumer demand. Fred believes that demand will be high with probability 50 percent (and therefore demand will be low with probability 50 percent). Fred has determined the following possible profit levels (before paying Barney) will occur depending on Barney's effort and the state of consumer demand: Demand low high effort low 20 40 medium 40 80 high 80 100 Of the choices below, what is the largest percentage range of profit provided to Barney that would ensure Barney would supply high effort? a. any percent greater than 75.00 percent (3/4). b. any percent greater than 66.66 percent (2/3). c. any percent greater than 50.00 percent (1/2).d. any…John wants to buy a used car. He knows that there are two types of car in the market, plums and lemons. Lemons are worse quality cars and are more likely to break down than plums. John is willing to pay £10, 000 for a plum and £2, 000 for a lemon. Unfortunately, however, he cannot distinguish between the two types. Sellers can offer a warranty that would cover the full cost of any repair needed by the car for y ∗ years. Considering the type and likelihood of problems their cars can have, owners of plums estimate that y years of guarantee would cost them 1000y, owners of lemons estimate that the cost would be 2000y. John knows these estimates and decides to offer £10, 000 if a car comes with y ∗ years of warranty, £2, 000 if a car comes without warranty. For which values of y ∗ is there a separating equilibrium where only owners of plums are willing to offer the y ∗ -years warranty? Clearly explain your reasoning.
- Suppose your preferences can characterized by the simple utility function U = √C, where C is consumption. You enjoy rock climbing, where you have a 10% chance of get- ting injured and losing $50,000. Your income (and therefore consumption) in the uninjured state is $90,000. What is the most you are willing to pay for an insurance policy? What is the fee for a fair insurance?Assume, in producing one unit of a good X, an agent can exert either the good effort (G) or the bad effort (L), which cause production defects with probability 0.25 or 0.75 respectively. His utility function in effort e and wage w is U(w, e) = 100 (10/w) c(e) where c(G) = 2 for the good effort and c(L) = () for the bad effort. Production defects are contractible and so can be included in the agent's contract, but effort is not contractible. Good X sells for $20 if there are no defects and $0 otherwise. The principal is risk-neutral and likes profit. Assume the agent has a reservation utility/outside option of U=0. If effort is not contractible then:: Select one: O a. There is insufficient information to know the principal's choice of contract because we do not know the agent's level of absolute risk aversion. O b. the principal will be indifferent between writing a contract to achieve the good effort level and writing a contract to achieve the bad effort level O c. the principal will…Consider the lottery that assigns a probability T of obtaining a level of consumption CH and a probability 1-T an individual facing such a lottery with utility function u(c) that has the properties that more is better (that is, a strictly positive marginal utility of consumption at all levels of c) and diminishing marginal utility of consumption, u"(c) CL. Consider du(c) for the first derivative of the utility function with respect to dc du(c) du' (c) consumption and u"(c) (which is also the derivative of the first derivative of the utility function). to be the second derivative of the utility function dc dc2 1. Provide a definition for the certainty equivalent level of consumption for the simple lottery described above.
- Why do sellers generally prefer a Vickrey auction to a regular sealed bid if sellers don’t receive the highest bid in the Vickrey auction? Sellers only have to sell their item if the bid is the highest-price bid. The second-highest bid in a Vickrey auction is generally higher than the highest bid in a regular sealed-bid auction. The second-highest bid is about the same in both auctions. Sellers prefer the final price is not revealed to all bidders. Sellers would never prefer Vickrey auctions.Shane just bought a house worth $360,000 in an area that is known for floods. A flood occurs with a 5% chance and if it occurs, his home is ✓ for reduced in value to $202,500. Shane has utility function given by U(X)=√√X. He would be willing to pay a maximum of flood insurance. The fair insurance premium for flood insurance is Shane's risk premium is Suppose, instead, that Shane's utility function is given by U(X) = X². Then, the maximum he would be willing to pay for flood insurance isConsider the following game, with a risk-neutral principal with preferences π = q - w hiring an agent with preferences U = √w-e.. The agent's reservation utility is given by Ū = 2, and the agent can choose between an effort level of 0 or an effort level of 10. Output is either 0 or 400 and follows the following probability distribution, a function of effort level and some uncertain factor: e=0 e=10 Probability (q=0) Probability (q=400) 0.6 0.4 0.9 0.1 What would the contract look like if the principal tried to push the wages when q=0 to zero? Would the principal want to do this? Explain.
- Prospect Y = ($6, 0.25 ; $15, 0.75) If Will's utility of wealth function is given by u(x)=x0.25, what is the value of CE(Y) for Will? (In other words, what is Will's certainty equivalent for prospect Y?) (The certainty equivalent represents the maximum amount a person would be willing to pay to acquire a risky prospect, and equivalently, the lowest price for which they would be willing to sell a risky prospect if they already owned it) (Note: The answer may not be a whole number; please round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)1 Q1. Jerry has wealth of $60 and derives utility from this according to the utility function U(w) = 1 - Where w is his wealth. Jerry now finds a lottery ticket (the drawing takes place the next day) that offers a 50% chance of winning $5. W a) What is the expected value of Jerry if he takes the lottery ticket? (pay attention, it's not jerry's wealth) b) What is the minimum amount for which Jerry would be willing-to-sell the ticket? (Hint: sets a price of p, and at the minimum amount, the expected utility of selling and not selling should be the same) c) Which is bigger, your answer to (a) or (b), and suggest whether Jerry is a risk averse person based on the previous conclusion? d) If he does not sell the ticket, what is Jerry's cost of risk? (The cost of risk is the difference between the expected wealth and the certainty equivalence)Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain. b) What would be the highest price (premium) that she would be willing to pay for an insurance policy that fully insures her against the flooding damage?