• You offer a lottery ticket {$64, .125}, i.e., 12.5% to win $64 or nothing, to three persons with different utility functions. What maximum price (Pm) each person is willing to pay? Show the solution steps. Person 1 U = x13 1/3 P" = Person 2 U = .3X p" = Person 3 U=x pm = %3D
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- A person has a 2-period utility consumption function U(c1, c2), with a budget function W = c1+c2/1+ra. Explain with pictures how one should choose c1 and c2 such that MRS(from c1 to c2) equals 1+r.b. Also explain with pictures how when the individual receives income, whileconditions at that time was a crisis.***PLEASE NOTE: QUESTION HAS TWO PARTS REQUIRING ANSWER*** Q: Johnny Football has a utility function of the form ? = √?. Johnny is beginning his senior year of college football. If he is not seriously injured, he will receive a $1,000,000 contract for playing professional football. If any injury ends his football career, he will take a job as a refuse removal facilitator in his hometown that pays $10,000. There is a 10% chance that Johnny will be injured badly enough to end his career. a. What is Johnny’s expected utility? b. How much would Johnny be willing to pay to remove the financial riskhe faces? That is, what $p would he pay for a $1,000,000 insurancepolicy so that he would have $1,000,000-$p even if he had a seriousinjury? Assume he wouldn’t work for $10,000 if he had the insuranceand he was injured. Hint: You should set his utility with certainty(U($1,000,000-$p)) equal to his expected utility with risk (found inpart a) and solve for p.An individual is o ered a choice of either $50 or a lottery which may result in $0and $100, each with equal probability 1/2 . If the individual has a utility function u(w) = 5 + 2w, which one would they choose? If the individual has a utility function u(w) =w1/2 + 1?
- Present the classical model of choice under uncertainty. What are the five assump- tions which characterize the Von-Neumann-Morgenstern expected utility repre- sentation?1- A consumer who starts (i.e. has an endowment) at point B, and has preferences shown by IC1, will want to borrow. Select one: True False 2-Assuming a mix of present and future consumption is preferred, ANY consumer who starts (i.e. has an endowment) at point A will gain utility from a rise in interest rates. Select one: True False 3-A consumer who starts at point B will want to borrow, but as little as possible in order to minimise the cost of interest. Select one: True False 4-If a consumer starts at point A, and then receives extra income in the present, this would appear as an outward shift of the budget constraint. Select one: True Falsehow then can we find the total utility given q1=24, q2=30 and q3=15
- EXPECTED UTILITY THEORY • Goal utility and goal difficulty are combined to determine goal selection according to expected utility theory according to this theory, the goal that is selected is based on its utility and estimated probability of being achieved. Utility refers to the usefulness of the goal in providing satisfaction or happiness • Expected utility = Utility × subjective probability . Question- Explain what you understand from this theory above and give an example of how it can be useful .Economics Consider a potential criminal with a lawful income of $121. Potential loot from robbery is $75. The probability of being caught and imprisoned is 0.50 and a prison term for this type of crime is 0.33 units of time. Round to one decimal place in all calculations. Utility is given by: Utility = (income)1/2 A. Calculate the guaranteed utility from lawful income and the expected utility of committing the crime. What will the potential criminal do? Explain why. Would your answer change if there were an anguish cost of 1 util involved? Explain. B. Suppose all the information given above holds true, except there is no anguish cost. You are a city official who has some extra room in the budget to dedicate towards fighting crime. For the use of these resources, you can choose between either increasing the length of prison term for criminals to 0.595 units of time or investing in GIS technologies and improved policing strategies that will increase the probability of criminals being…Using a basic illustration, explain your understanding of utility theory given uncertainty
- Alex preferences over cake, c, and money, m, can be represented by the utility functionu (c, m) = c + m + µ (c − rc) + µ (m − rm)where rc is his cake reference point, rm is his money reference point, and the function µ (·) isdefined as µ (z) = z , z ≥ 0 and λz, z < 0 where λ > 0. 1. If his reference point is the status quo (that is, his initial endowment), what is themaximum price Sam would be willing to pay to buy a cake?2. If his reference point is the status quo, what is the minimum price Sam would be willingto accept to sell a cake he already owned?Now,suppose N=3 with a market clearing interest rate. The first two agents are the same as earlier. The third agent has an endowment of 20 in the first period and consumes 15 in the second period. If the first two agents each consumed 21 units in the first period, how much did the third agent consume in the first period? Plz do fastSuppose a consumer has S100 today and he tells you he is willing to wait X amount of time for another $50. The same consumer also tells you that in the future if he has $10 he ts willng to wait Y amount of time for another $50.If Y is greater than X, does the individual exhibit hyperbolic discounting, exponential discounting, or is there not enough information to determine? Briely explain your answer.