Antonio has a utility function U = W, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stageof a game show, the host offers Antonio a choice between (A) $9 million for sure, or (B) a gamble that pays $1 million with probability 0.4 and $16million with probability 0.6.Use the blue curve (circle points) to graph Antonio's utility function at wealth levels of $0, $1 million, $4 million, $9 million, and $16 million.?Utility (Thousands)5.04.54.03.53.0252.01.51.00.50+0246810 12 14Wealth (Millions of dollars)16 18True or False: Antonio is risk averse.2020Utility FunctionChoiceTrueO Falseoffers Antonio a higher expected prize. (Hint: The expected value of a random variable is the weighted average of the possible outcomes,where the probabilities are the weights.)Choice offers Antonio a higher expected utility.Antonio should pick choice,

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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.
A pirate is about to set sail on a 2-period journey (trip). He has 100 bags of barley (food). He must decide how much to consume in period 1 and how much to consume in period 2: (C1, c2). He gets all the barley in period 1 and none in period 2. Unfortunately, rats will eat 50% of any barley that he saves to consume in period 2. If the pirate's utility function is U(C1, C2) = C1C2, what levels of consumption does he choose in each period? (Hint: The "price" of barley in each period can be assumed to be 1.)
An individual is offered a choice of either $50 or a lottery which may result in $0 or $100, each with equal probability 1/2. If the individual has a utility function u(w) = w, which one would they choose? If the individual has a utility function u(w) =sqr(w)?
Persons A and B are roommates. Person A smokes and Person B does not. The index s measures how smoky the room is. It varies from s=0, where there is no smoke in the room, to s=1, when the room is filled with smoke. Thus, 1-s measures how "clean" the air in the room is. Person A's utility function is UA(XA,S)=XA+In(1+s), where xA is the amount of money Person A owns. Person B's utility function is uB(XB,1s)%3D3XB+2(1-s), where Xg is the amount of money Person B owns. Each person starts with an endowment of 5 units of money. Persch B has the legal right to a smoke-free room and there is a market for "emission right." At the Walrasian equilibrium, what will be the (per unit of smoke index) price p of the emission rights if the price of money is 1? O a. None of the other answers. O b. p=2/3 O c. p=1 O d. p=3/2 О е. р31/6
Consider a health insurance market. The market has many insurers so that each insurance company offers insurance at the fair insurance premium. Each consumer has utility function, and has an initial wealth of $200. Consumers have access to a (magical) gym that reduces their probability of needing to go to the doctor from 90% to 10%. A gym membership costs $6. A trip to the doctor costs $120. Suppose insurance companies charge the fair insurance premium which assumes all consumers go to the gym. This fair insurance premium is $? and the insurance company makes a profit of $? per consumer. Suppose insurance companies continue to charge the fair insurance premium that assumes all consumers go to the gym, but now charges a copay of $15 for a doctor's visit. The insurance company now makes a profit of $ per consumer. By implementing a copay, the insurance company the problem.
Persons A and B are roommates. Person A smokes and Person B does not. The index s measures how smoky the room is. It varies from s=0, when there is no smoke in the room, to s=1, when the room is filled with smoke. Thus, 1-s measures how "clean" the air in the room is. Person A's utility function is ua(XA,s)=Xa.S, where xA is the amount of money Person A owns. Person B's utility function is ug(xg, 1s)=Xg .(1-s)³, where xg is the amount of money Person B owns. Each person starts with an endowment of 5 units of money. Person A has the legal right to a fill up the room with smoke and there exists a market for smoke "abatements". At the Walrasian equilibrium, how much money will person B be left with? а. Хв31.25 ОБ. Хв32.25 O c. XB=0.25 O d. Xg=0.25 е. None of the other answers.
An individual has a vNM utility function over money of u(x)= x, where x is final wealth. She currently has $8 and can choose among the following three lotteries. Which lottery will she choose? • Lottery 1: Give up her $8 and face the gamble (0.1, 0.5, 0.4) over final wealth levels ($1, $8, $27). • Lottery 2: Keep her $8. • Lottery 3: Give up her $8 and face the gamble (0.2, 0.8,0.0) over final wealth levels ($1, $8, $27) O Lottery 1 O Lottery 2 Lottery 3 O They are indifferent between lotteries 1 and 2 O They are indifferent between lotteries 2 and 3 O They are indifferent between lotteries 1 and 3 O They are indifferent between all three lotteris

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