A risk-neutral individual has the utility function u(w) = aw, where w is her wealth, and a>0 a parameter.Her initial wealth is equal to W. There might be a fire which would destroy the dollar amount L of thiswealth. The fire occurs with probability p. The individual can buy insurance to cover the amount K, withKE[0,L]. The insurance premium is given by g, so that if she buys insurance to cover an amount K, shemust pay the insurance company the amount gK.Solve the expected utility maximization problem of this individual to determine how much insurance shewould buy. From the first-order condition you obtain, determine how much insurance she will buy in eachof the following cases:a) The insurance market is competitive.b) The insurance market is characterized by imperfect competition, so that insurance companies havemarket power.c) The insurance market is competitive, but the government subsidizes insurance companies, so that whena firm sells insurance for a coverage of K, it receives from the government the amount sK.

Answered: Image /qna-images/answer/cfee8c0b-0278-4b2f-9c43-9f1301b2aea2.jpg

Answered: A risk-neutral individual has the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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a) A university projects that enrollments are going to decline as the pool of college-aged applicants begins to shrink. They have estimated the number of applications for coming years to behave according to the function a = f(t) = 6,500 – 250t where a equals the number of applications for admission to the university and t equals time in years measured from this current year (t = 0). i. What class of function is this? ii. What is the expected number of applications 5 years from today? 10 years? iii. Do you think this function is accurate as a predictor indefinitely into the future? iv. What kinds of factor would influence the restricted domain on t?
According to the U.S. Customs and Border Protection Agency, the average airport wait time (time from arrival at the airport until the completion of security screening) at Chicago's O'Hare Inter- national airport is 32 minutes for a passenger arriving during the hours 4-5 PM. Assume the wait time is exponentially distributed so that p(t) = ke-kt for 0≤t<∞, where k is the reciprocal of the average wait time. Assume t is measured in minutes. 1. Sketch a labeled plot of the relevant pdf on the interval [0, 90] minutes (while remembering that it is defined for all t≥ 0.) 2. Set up integrals (you can write p(t) for the integrand) for the following probabilities: (a) Waiting longer than 60 minutes. (b) Waiting shorter than 30 minutes. (c) Waiting between 20 and 40 minutes. 3. Evaluate the probability that the waiting time is longer than 60 minutes (part 2(a) above) and convert to a percentage with two decimal places.
if P(E and F)= 0.04 P(E|F)= 0.16 P(F|E)= 0.2 then P(E) is
An individual has a vNM utility function over money of u(x) = Vx, where x is final wealth. Assume the individual currently has $16. He is offered a lottery with three possible outcomes; he could gain an extra $9, lose $7, or not lose or gain anything. There is a 15% probability that he will win the extra $9. What probability, p, of losing $7 would make the individual indifferent between to play and to not play the lottery? (Make sure to answer in the form, 0.X, i.e. 0.25) Enter your answer here
Farmers face uncertainty over their earnings because rain is random. Let a farmer's yield be Y= 0 in the dry outcome and Y = 1 in the wet outcome. However, not all farmers are the same: Probability(Y= 1) = p1= 2/ 3 if type = 1 p0= 1/ 3 if type = 0 All farmers are risk averse, with utility U(Y) = √Y as their utility function. Farmers know their type. (a) Calculate each farmer's expected yield, E(Yi) =pI1 + (1- pi)0, expected utility ,E(Ui) =piU(1) + (1 - pi)U(0), and calculate the utility at E(Yi), U(E(Yi)), for i= 0, 1. Show these all on a graph with utility on the vertical axis and yield on the horizontal axis.
A. Calculate the value of t for each of the following. 1p=8, s 5,n = 16, and X = 7.5 2. p= 98, s 6, n 13, and X = 97 3. p = 200, s = 50, n 27, and X 197 4. p= 89, s 30. n 16. and X 90 5. p = 75, s = 22, n 25, and X = 77 %3D
A research center claims that 31% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 800 adults in that country, 34% say that they would travel into space on a commercial flight if they could afford it. At a = 0.10, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state H, and H Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) O A. At least % of adults in the country would travel into space on a commercial flight if they could afford it. O B. % of adults in the country would travel into space on a commercial flight if they could afford it. %. O C. The percentage adults in the country who would travel into space on a commercial flight if they could afford it is not O D. No more than % of adults in the country would…
A chemical supply company currently has in stock 100 Ib of a certain chemical, which it sells to customers in 7-lb batches. Let x = the number of batches ordered by a randomly chosen customer, and suppose that X has the following pmf. 1 2 3 4 p(x) 0.3 0.5 0.1 0.1 Compute E(X) and V(X). batches | batches? E(X) = V(X) = Compute the expected number of pounds left after the next customer's order is shipped and the variance of the number of pounds left. [Hint: The number of pounds left is a linear function of X.] expected weight left Ib variance of weight left Ib2
Let X; be random variables and M; (t) be their respective moment generating functions, for i = 1, 2, 3. Solve: Suppose that M₁ (t) = 1 +t+t² + t³+... Is this enough information to determine the type of random variable that X₁ is? Explain why or why not. Determine the type of random variable if there is enough information. Determine if it is possible for M₂ (t) = (-1)" -0 (2n)! possible, determine the type of random variable that X₂. -+2n. Explain why or why not. If it is Suppose that that the expectation of X3 is -1 and its second moment is 1. Determine if this is enough information to find the moment generating function of X3 explicitly. Explain why or why not. If it is enough information, compute it explicitly.

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