In class, we showed that if a risk adverse consumer was offered "fair" insurance (i.e. 7 = ), she would fully insure against the risk. Show that if the insurance is not fair (i.e. <7), the consumer may still insure, but not fully against the risk.
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- 1 Consider an individual for whom utility is U = ln(I) There are two states of the world (G,B): Outcome G = 2000 with probability .4 Outcome B = 1000 with probability .6 W1 = 2000 L = 1000 π = .6 Option = invest $50 to lower π to .2 An insurance company is willing to offer a contract in which the individual pays a premium and gets full compensation for the loss (1000) in the bad state. a) With no insurance but the option of investing the $50, what is the utility of the individual? b) What is the first-best outcome for utility of the individual, insurance premium, and profits of the insurance company?Suppose that the buyers do not know the quality of any particular bicycle for sale, but the sellers do knowthe quality of the bike they sell. The price at which a bike is traded is determined by demand and supply.Each buyer wants at most one bicycle.(ii) Assuming that each buyer purchases a bike only if its expected quality is higher than the price,and each seller is willing to sell their bike only if the price exceeds their valuation, what is theequilibrium outcome in this market?Khalid has a utility function U = W1/2, where W is his wealth in millions of dollarsand U is the utility he obtains from the wealth. In a game show, the host offershim a choice between (A) $4 million for sure, or (B) a gamble that pays $1million with probability 0.6 and $9 million with probability 0.4.i. Graph Khalid’s utility function with the help of above utility function. Ishe risk lover? Explain. ii. Does A or B choice offer Khalid a higher expected prize? Explain yourreasoning with appropriate calculations. iii. Does A or B offer Khalid a higher expected utility? Again, show yourcalculations. iv. Should Jamal pick A or B choice? Why?
- If a risk‐averse individual owns a home worth $100,000, and that individual iswilling to pay a maximum of $1,000 for an annual fire insurance policy that covers theentire loss in the event of a fire, then we know that:A. There is a one percent chance that the home will be destroyed by fire inthe next yearB. There is a greater than a one percent chance that the home will bedestroyed by fire in the next yearC. There is less than a one percent chance that the home will be destroyedby fire in the next yearD. None of the above is correctAssume that there are two parties, I and V. I engages in an activity that tends to injure V. V and I both can take care to reduce the expected harm from accidents. Specifically, suppose that if I takes no care (i.e., spends $0 on accident precautions), expected injury to V is $250. If I spends $40 on accident precautions, however, the expected injury to V is reduced to $175. Further suppose that V has a choice between taking no care or spending $50 in care to avoid accidents. If V spends $50 in care, V’s expected harm falls by $20 regardless of the level of care that I takes. Assume that courts adopt the socially‐optimal level of injurer care as the negligence standard. That is, if I takes less than the socially‐optimal level of care, she will be found negligent and must pay for all damages to V. If I takes at least the socially optimal level of care, she will not have to compensate V for his damages. 1. Under a negligence standard, what is I’s dominant strategy? a) I does not have a…A person's utility function is U = C1/2 . C is the amount of consumption they have in a given period. Their income is $40,000/year and there is a 2% chance that they'll be involved in a catastrophic accident that will cost them $30,000 next year. a. Calculate the actuarially fair insurance premium. What would your expected utility be if you were to purchase the actuarially fair insurance premium? b. What is the most you would be willing to pay for insurance, given your utility function?
- Governments often require people to obtain insurance; for example, all drivers are required to carry auto insurance to cover damages to others in the event of a crash. Homeowners are often required by banks to carry insurance on their home. (a) Why do these requirements exist? (b) Would they be necessary if people truly recognized the risk they faced? (c) One characteristic of an overconfident person is that she is continually surprised when what she thought was unlikely orScenario 2 Tess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function (sqrt c) . Both could experience an adverse event that results in earnings of $0 per year. Tess has a 1% chance of experiencing an adverse event and Lex has a 12% chance of experiencing an adverse event. Tess and Lex are both aware of their risk of an adverse event. Refer to Scenario 2 If an insurance company knows the probability of Tess experiencing an adverse event, what is the actuarially fair premium charged to Tess per $1 of benefit? Round to two decimal places2. Maria has $100. There is a 50% that she will lose all of it. Her utility as a functionof wealth is u(c) = √c. a. What is the maximum amount she would be willing to pay to fully insure againstthe 50% probability of the loss? b. Is she risk averse, risk loving, or risk neutral?
- Suppose Grace and Lisa are to go to dinner. Lisa is visiting Grace from outof town, and they are to meet at a local restaurant. When Lisa lived in town,they had two favorite restaurants: Bel Loc Diner and the Corner Stable. Ofcourse, Lisa’s information is out of date, but Grace knows which is betterthese days. Assume that the probability that the Bel Loc Diner is better isp > 1/2 and the probability that the Corner Stable is better is 1 - p. Naturedetermines which restaurant Grace thinks is better. Grace then sends amessage to Lisa, either “Let’s go to the Bel Loc Diner,” “Let’s go to theCorner Stable,” or “I don’t know [which is better].” Lisa receives the message, and then Grace and Lisa simultaneously decide which restaurant to go to. Payoffs are such that Grace and Lisa want to go to the same restaurant, but they prefer it to be the one that Grace thinks is better. More specifically, if, in fact, the Bel Loc Diner is better, then the payoffs from theiractions are as shown in the…Seung's utility function is given by U - C^(1/2), where C is consumption and C^(1/2) is the square root of consumption. She makes $50,625 per year and enjoys jumping out of airplanes. There's a 5% chance that in the next year, she will break both legs, incur medical costs of $30,000, and lose an additional $5,000 from missing work. a. What is Seung's expected utility without insurance? b. Suppose Seung can buy insurance that will cover the medical expenses but not the forgone part of her salary. How much would an actuarially fair policy cost, and what is the expected utility if she buys it? Policy cost: $___ Expected utility: ___ c. Suppose Seung can buy insurance that will cover her medical expenses and foregone salary. How much would such a policy cost if it's actuarially fair, and what is her expected utility if she buys it? Policy cost: $___ Expected Utility: ___Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)
