2 Consider the lottery that assigns a probability 7 of obtaining a level of consumption Cand a probability 1-7 of obtaining a low level of consumption c1, with CH > C1. Consideran individual facing such a lottery with utility function u(c) that has the properties thatmore is better (that is, a strictly positive marginal utility of consumption at all levels ofc) and diminishing marginal utility of consumption, u"(c) < 0. As usual, we are usingthe shorthand u'(c) = du@ for the first derivative of the utility function with respect todu' (c) to be the second derivative of the utility functionconsumption and u"(c) = Puc)(which is also the derivative of the first derivative of the utility function).de1. Provide a definition for the certainty equivalent level of consumption for the simplelottery described above.2. Using the definition of the certainty equivalent level of consumption provide anexpression for the ratio,u(Cce) u(€L)u(cH) u(c1)*3. Define the risk premium p = č – Cee where č = rCH + (1 – 7)c, is the expectedlevel of consumption from the lottery (7 = E[c]). Consider the following exercise.There are three lotteries characterized by different probabilities of obtaining cH -Let these probabilities be given by a" > n' > a. Using a single diagram, plot therisk premium for each of these three lotteries. Does the risk premium increase ordecrease as we increase a across these three lotteries? Provide the intuition foryour result.

a. The certainty equivalent of a lottery is the amount of money you would have to be given with the…

Answered: 1. Provide a definition for the…

Math

Probability

1. Provide a definition for the certainty equivalent level of consumption for the simple lottery described above.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.2: Probability

Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...

See similar textbooks

Related questions

Q: 1. Let X be a random variable that denotes the number of passengers in a train station for a given h...

A: let x be a random variable denotes number of passengers in a train station for a given hours.T

Q: 2. A family has four children. If X is a random variable that pertains to the number of female child...

A: It is given that X = Number of female children in the family. Note : Since you have asked multiple q...

Q: The probability function for the number of seizures, X, of a typical epileptic person in any given y...

A: The variance of X is calculated as Var(X) = E(X2) - (E(X))2

Q: Suppose the number of motor vehicle fatalities in a city during a week is poisson distributed with a...

A: Given,A random variable X~Poisson(λ=8)P(X=x)=e-8 8xx! ; x≥0

Q: lim 1 12 Evaluate 2 X →2 -3x + 2 x - 8 3

Q: A genetic experiment with peas resulted in one sample of offspring that consisted of 443 green peas ...

A: a)Givenn=443x=164p^=xn=164443=0.3702Confidence interval = 95%

Q: Determine the cumulative distribution function for f(x) = - wherex is thetimeto failure of an electr...

A: Given,f(x)=13000e-x3000 ; x>0

Q: 28. A box contains 5 green, 3 blue, and 2 yellow marbles. Two marbles are chosen at random, without ...

A: As per bartleby guideline expert have to answer first three subparts only dear student please upload...

Q: Given is the reduced prime implicant chart of a function f3(u,v,w,x,y) after the essential prime imp...

Q: 1. Which formula represents the combination of n taken r at a time? A. C(n,r) =: n! C. C(n,r) = ! (n...

Q: The z-score for the sampling distribution is given by z = Suppose the population mean amount of hour...

Q: 1. Find the probability of the given situation. Dario puts 44 marbles in a box in which 14 are red, ...

A: Givena)Total no.of marbles in a box = 44No.of red marbles = 14No.of blue marbles = 12No.of yellow ma...

Q: The distribution of cell phones calls is normally distributed with mean 79 and a standard deviation ...

Q: 31. A survey on eating habits conducted at the local mall produced the following information: Fast F...

A: Note: If the post contains multiple subparts only allow to do first three subparts as per guidelines...

Q: (a) Calculate Tom's point estimate. (b) Given that the estimated standard er- ror of (p1 + p2)/2 is ...

Q: r Repair: The manager at Arango Automotive has found the probability that a car brought into the sho...

Q: The probability function for the number of seizures, X, of a typical epileptic person in any given y...

Q: A student knows correct answers to 6 questions out of 9 questions from the book. If a professor asks...

Q: Problem 3: Find the Sample Size a. A pizza shop owner wishes to find the 95% confidence interval of ...

Q: 2) From a deck of 52 playing cards, 5 cards are to be drawn. How many sets of 5 cards are possible i...

A: As per our guidelines we are supposed to answer only 3 sub-parts of any question so I am solving fir...

Q: Find the probability of the following card hands from a 52-card deck In poker, aces are either high ...

A: General formula of probability is , Probability =Number of favorable outcomes Total outcomes

Q: A player is dealt by 4 cards from a deck of 52 cards. What is the probability of having a flush? Sel...

A: A player is dealt by 4 cards from a deck of 52 cards. We have to find out the probability of having ...

Q: 1. In how many ways can you create 2 letter words from the letters in the word DAVE? Answer: 2. How ...

A: The number of ways to select r elements out of n distinct elements is computed using the combination...

Q: Game of Craps played in a casino. Stage 1- Roll 1- The player rolls a pair of standard 6-sided dice...

A: Given Information: Consider that a player who rolls a pair of standard 6-sided dice and takes their ...

Q: percent of those that play FIFA also play DOTA?

A: Here use Bayes rule

Q: What are the laws of repetition of categories in statistics?

A: The law of averages is the commonly held belief that a particular outcome or event will, over certai...

Q: 2. A professor posts the grades for a class using the last four digits of the Social Security number...

A: Here Given Professor posts the grades for class using the last 4 digits of social security Number of...

Q: The probability of illness depends on the preventive healthcare investments made till that period an...

A: The illness depends on the preventive healthcare investments made till that period. It also depends ...

Q: If you roll a fair die twice and observe the numbers that face up, then the probability that the pro...

A: The sample space is, S={ (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (...

Q: 2-A card is drawn at random from a deck consisting of cards numbered 2 through 10. A player wins 1 d...

A: Probability of an event is computed by taking the ratio of number of favourable outcomes to total nu...

Q: In the experiment of rolling two dice, what is the probability that the difference between the large...

Q: i) If you have twenty ones and fifteen zeroes how many ways can we arrange these digits such that no...

Q: Find the probability that in five tosses of a dice a 6 appears (a) at no time, (b) once, (c) twice, ...

Q: What is non probability sampling and explain the types of the same

A: Probability sampling is the sampling technique that allows a researcher to select a sample where the...

Q: Little Peten'ka refuses to eat broken spaghetti, so his monm wants so compare two brands "M" and "A"...

A: Given that, Little Peten 'ka refuses to eat broken spaghetti, so his mom wants so compare two brands...

Q: , what is the probability of obtaining not more than 2 heads if it is known that the last two tosses...

A: Here use basic probability Probability of head = 1/2 Probability of tail = 1/2 Here each toss outco...

Q: Evaluate each combination in column A, then match your answer in column B. A B 1. С(8,3) 2. С(15,4) ...

Q: 3(6x- x) Determine the mean and variance of the random variable for f(x) = 0<x< 6. 108 Round your an...

Q: Jill and Pete come to the bookstore and each of them can buy one English-Chinese dictionary with the...

Q: B. Find the z value that corresponds to each of the following. Show the raw scores and the z scores ...

A: As per bartleby guideline expert have to answer first three subparts only dear student please upload...

Q: Solve the following problems. Round off your answer to the nearest hundredths. he number of computer...

Q: 36. Consider all courtroom trials with a single de- fendant who is charged with a felony. Suppose th...

Q: A multuple choice questions exam consist of question with 6 choices. Supose that 80% of the class kn...

A: The likelihood of the occurrence of an event resulting from such a statistical experiment is evaluat...

Q: You want to raise $200,00. How many contacts do you have to make based on the expected value of each...

A: Here AS per your requirement I have calculated Q.3 Here use given answer from Q.2

Q: A biased die is thrown thirty times and the number sixes seen is eight. If the die is thrown a furth...

A: List of formulae : Expected value : E(X) = np Variance : Var(X) = np(1-p)

Q: The table shows the distribution, by age, of a random sample of 2520 moviegoers ages 12-74. If one m...

A: Given Total number of random sample of 12-74=2520

Q: Identify each problem as Permutation, combination, or both permutatin and combination problem. 1 A ...

A: Given some problems and we have to identify each problem as Permutation, combination, or both permut...

Q: DIRECTION: Analyze the problem carefully. Fill in the table correctly. You are holding a die. Your c...

A: The table is : Sides of a die 1 2 3 4 5 6 1 1,1 2,1 3,1 4,1 5,1 6,1 2 1,2 2,2 3,2 4,2 5,2 6,2...

Q: Auditors make assessments on the basis of their individual experience, the experience of others, or ...

A: The required hypothesis to be tested is H0:μi=μo=μcH1:At least one of the μi is different Here, μi i...

Q: A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subj...

Question

Consider the lottery that assigns a probability 7 of obtaining a level of consumption C
and a probability 1-7 of obtaining a low level of consumption c1, with CH > C1. Consider
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) < 0. As usual, we are using
the shorthand u'(c) = du@ for the first derivative of the utility function with respect to
du' (c) to be the second derivative of the utility function
consumption and u"(c) = Puc)
(which is also the derivative of the first derivative of the utility function).
de
1. Provide a definition for the certainty equivalent level of consumption for the simple
lottery described above.
2. Using the definition of the certainty equivalent level of consumption provide an
expression for the ratio,
u(Cce) u(€L)
u(cH) u(c1)*
3. Define the risk premium p = č – Cee where č = rCH + (1 – 7)c, is the expected
level of consumption from the lottery (7 = E[c]). Consider the following exercise.
There are three lotteries characterized by different probabilities of obtaining cH -
Let these probabilities be given by a" > n' > a. Using a single diagram, plot the
risk premium for each of these three lotteries. Does the risk premium increase or
decrease as we increase a across these three lotteries? Provide the intuition for
your result.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.
Consider a function F (x ) = 0, if x < 0 F (x ) = 1 − e^(−x) , if x ≥ 0 Is the corresponding random variable continuous?
Consider an individual who is risk-loving instead of risk-averse. a. Is U(I) concave or convex?b. Suppose this person is offered an actuarially fair insurance product that guarantees her a certain income, E[I]. Graph the consumer surplus this person receives from buying this insurance as p, the probability of being sick, varies from 0 to 1. You should plot p on the horizontal axis and consumer surplus on the vertical axis.c. Suppose, finally, that this person is offered a subsidy (perhaps from her parents) for buying insurance so that, if she buys insurance, she will be guaranteed an income γ E[I], where γ >1. With the subsidy, insurance is now actuarially unfair in her favor. Graph how her consumer surplus (M) changes as p, the probability of being sick, varies from 0 to 1. [Hint: draw a coordinate plane with p on the x-axis and M on the y-axis.] Based on this graph, under what conditions is she least likely to buy the subsidized insurance?
A computer store sells 3 computer models priced at P26,000, 32,000, and42,000, and two brands of monitors priced at P3,200 and 3, 800, respectively.The joint pmf of X, the computer price, and Y , the monitor price, is given inthe table below. X\Y 3,200 3,800 26,000 0.30 0.25 32,000 0.20 0.10 42,000 0.10 0.05 Compute the marginal probability functions (pmf’s).
Let X be a random variable with mean μ and variance _2. Show that E[(X − b)2], as a function of b, is minimized when b = μ.
You consider investing £800 in stocks of the company X for a certain period. There is a possibility for X to merge with Y, in which case you expect your investment to appreciate £300, otherwise you expect it to depreciate £200. Also, rather than investing, you can choose to keep your £800. By using a utility function U(x)=x−−√, and by defining pthe probability that X merges with Y, what is the condition that p must satisfy for your investment to be worthwhile (rounded to two decimal places)?
Suppose a quality control expert examines iterms for defects in a series of independent fixates, each of a fixed duration, and suppose that defects are present. Let p be the probability that the defect or flaw is detected and 1-p the probability that a defect or flaw is not detected. Let the r.v. X = the number of defects detected in n fixations. a. What is the pmf of X? b. What is the expected value of X = E(X)? c. What is the moment generating function (mgf) for the r.v. X (Remember to state the interval of validity for t)? d. Use it to find the Variance of X.
Let m(t) be the moment generating function of a random variable X. Show that the random variable W = 10X is m(10t). What is the moment generating function of Z = X-5 in terms of m(t)?
Suppose X is a continuous random variable with p.d.f. fX(x) = kx2(1 − x) if 0 < x < 1. (b) Find the c.d.f FX(x) explicitly.
Let X be an exponential random variable with standard deviation σ. FindP(|X − E(X)| > kσ ) for k = 2, 3, 4, and compare the results to the boundsfrom Chebyshev’s inequality.
Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1 Compute P(X≤4) and P(2≤X≤5)
You and two other people are to place bids for an object, with the high bid winning. If you win, you plan to sell the object immediately for 10,000.(a) How much should you bid to maximize your expected profit if you believe that the bids of the others can be regarded as being independent and uniformly distributed between 7,000 and 10,000?