Chapter 5

Q1)  An expected utility maximiser owns a car worth £60000£60000 and has a bank account with £20000£20000. The money in the bank is safe, but there is a 50%50% probability that the car will be stolen. The utility of wealth for the agent is u(y)=ln(y)u(y)=ln⁡(y) and they have no other assets.

 Time remaining: 01 :51 :45 Economics A dealer decides to sell an antique automobile by means of an English auction with a reservation price of $900. There are two bidders. The dealer believes that there are only three possible values, $7,200, $3,600, and $900, that each bidder’s willingness to pay might take. Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other’s valuation. Assuming that the two bidders bid rationally and do not collude, the dealer’s expected revenue from selling the car is approximately Group of answer choices $3,600. $2,500. $3,900. $5,400. $7,200.

Suppose that an individual is just willing to accept a gamble to win or lose $1000 if the probability ofwinning is 0.6. Suppose that the utility gained if the individual wins is 100 utils. What is expected gains/loss.

A lottery has a grand prize of $1,000,000, 2 runner-up prizes of $100,000 each, 6 third-place prizes of $10,000 each, and 19 consolation prizes of $1,000 each. If a 4 million tickets are sold for $1 each, and the probability of any ticket winning is the same as that of any other winning, find the expected return on a $1 ticket. (Round your answer to 2 decimal places.

Question 2   A potential criminal enjoys a gain of g > 0 from committing an illegal act. If the potential criminal does not commit the act, he gets a gain equal to g = 0. The expected punishment upon conviction is p (e.g. number of years in prison), but there is the possibility of legal error. In particular, if the criminal commits the act, there is a probability r that he will not be punished, and if the criminal did not commit the act, there is a probability q that he will be punished regardless. a. Derive the net gain (i.e. gain minus expected punishment) for the criminal from not committing the illegal act. b.   Use your answer in a. to derive the condition for the criminal to commit the illegal act. Show and explain every step of your calculations. c.   Lawmakers decided to further increase the standard of proof for a criminal conviction. How will this change a ect the criminal’s decision to commit the illegal act in your answer in b.?

Given the following data with 25 % probability Bidder 1 bids 100 and Bidder 2 bids 80. What is the winning bid? Select the correct response 80 45 100 25

‘Lottery A’ refers to a lottery ticket that pays $2,000 with a probability of 0.3, $8,000 with a probability of 0.4, $12,000 with a probability of 0.2, and $18,000 with a probability of 0.1. Lottery B pays $3,000 with a probability of 0.3, $8,000 with a probability of 0.4, $12,000 with a probability of 0.2, and $15,000 with a probability of 0.1. Which of the following is true? A) A risk-averse person would definitely prefer lottery A to lottery B.B) A risk-averse person would definitely prefer lottery B to lottery A.C) Whether a risk-averse person prefers lottery A to lottery B depends on his degree of risk-aversion.D) A risk-averse person would prefer to pay $50 to switch from lottery B to lottery A.E) We do not have enough information to judge whether any of the statements listed in A-D, above, are correct.

Deborah is at the casino and is considering playing Roulette. In Roulette, a ball drops into one of 36 slots on a spinning wheel. 17 of the slots are red, 17 are black, and 2 are green. Each slot is equally likely and occurs with probability 1/36. Deborah bets $1.00 on black. If the ball drops into a black slot she receives $2.00 and if it drops into a red or green slot, she receives nothing. a) The expected value of Deborah’s bet (after subtracting the $1.00 she bet) is $________________ b) Given that Deborah makes this bet, is she risk adverse, risk neutral, or risk loving?

Suppose that there are two types of workers: high and low. Employers cannot distinguish between different types during an interview. Employers value high type at $200,000 and low type at $100,000. Employers are in a competitive market (i.e. zero profit applies). High type workers have a reservation wage of 140,000 and low type workers have a reservation wage of 80,000. Suppose that 50% of all workers are high type. The productivities, reservation wages, and the probabilities are common knowledge). What wage would the employers offer? Please explain the solution!

A poker hand (5 cards) is drawn from an ordinary deck of 52 cards. Find the probability of each event, showing your reasoning carefully. a. The first four cards are aces. b. Any four cards are the four aces.

If the farmer uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 50,000 bushels.  The cost of pesticides is $30,000 and the other costs associated with planting and harvesting the crop total $450,000. The price of corn at harvest time will either be $9.00 with probability of 0.50 or it will be $11.00 with probability 0.50, so if the farmer decides to sell the crop at harvest, the expected price per bushel that he will receive is $10.00.  The corn farmer is considering two alternatives for selling his crop.  The first is a contract where he can sell the rights to the future crop at planting.  The second is to sell the crop after harvest. What is the maximum a purchaser would be willing to pay to the farmer for the rights to the future corn crop assuming they cannot monitor the farmer after purchasing the contract?     a. $600,000.00   b. $550,000.00.   c. $500,000.00   d. $540,000.00

If the farmer uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 50,000 bushels.  The cost of pesticides is $30,000 and the other costs associated with planting and harvesting the crop total $450,000. The price of corn at harvest time will either be $9.00 with probability of 0.50 or it will be $11.00 with probability 0.50, so if the farmer decides to sell the crop at harvest, the expected price per bushel that he will receive is $10.00.  If the farmer does not use pesticides and decides to sell the crop at harvest, what is his expected profit?     a. $180,000.00   b. $100,000.00   c. $50,000.00   d. $20,000.00 If the farmer uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 50,000 bushels.  The cost of pesticides is $30,000 and the other costs associated with planting and harvesting the crop total $450,000. The price of corn at harvest time will either…

If the farmer uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 50,000 bushels.  The cost of pesticides is $30,000 and the other costs associated with planting and harvesting the crop total $450,000. The price of corn at harvest time will either be $9.00 with probability of 0.50 or it will be $11.00 with probability 0.50, so if the farmer decides to sell the crop at harvest, the expected price per bushel that he will receive is $10.00. If the farmer decides to sell the crop at harvest, then:     a. He should not use pesticides because not using pesticides ensures greater expected profit.   b. He should not use pesticides because not using pesticides ensures lower expected profit.   c. He should use pesticides because using pesticides ensures greater expected profit.   d. He should use pesticides because using pesticides ensures lower expected profit.

In a game, there are three values 1, 000, 2.500 and 5,000 and the cost of the game is 1, 500 . If each outcome has an equal probability of occurring, then what is the expected value of playing the game?

If the farmer uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 55,000 bushels.  The cost of pesticides is $20,000 and the other costs associated with planting and harvesting the crop total $450,000. The price of corn at harvest time will either be $10.00 with probability of 0.50 or it will be $12.00 with probability 0.50, so if the farmer decides to sell the crop at harvest, the expected price per bushel that he will receive is $11.00.  If the farmer uses pesticide and decides to sell the crop at harvest, what is his expected revenue?     a. $720,000.00   b. $600,000.00   c. $605,000.00   d. $660,000.00

If the farmer uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 55,000 bushels.  The cost of pesticides is $20,000 and the other costs associated with planting and harvesting the crop total $450,000. The price of corn at harvest time will either be $10.00 with probability of 0.50 or it will be $12.00 with probability 0.50, so if the farmer decides to sell the crop at harvest, the expected price per bushel that he will receive is $11.00.  If the farmer uses pesticide and decides to sell the crop at harvest, what is his expected profit?     a. $135,000.00   b. $250,000.00   c. $210,000.00   d. $190,000.00 If the farmer uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 55,000 bushels.  The cost of pesticides is $20,000 and the other costs associated with planting and harvesting the crop total $450,000. The price of corn at harvest time will either be…

If the farmer uses pesticides he expects a crop of 60,000 bushels; if he does not use pesticides he expects a crop of 55,000 bushels.  The cost of pesticides is $20,000 and the other costs associated with planting and harvesting the crop total $450,000. The price of corn at harvest time will either be $10.00 with probability of 0.50 or it will be $12.00 with probability 0.50, so if the farmer decides to sell the crop at harvest, the expected price per bushel that he will receive is $11.00.  If the farmer does not use pesticides and decides to sell the crop at harvest, what is his expected revenue?     a. $550,000.00   b. $660,000.00   c. $600,000.00   d. $605,000.00

SOLVE STEP BY STEP IN DIGITAL FORMAT 2. A client for an $85,000 fire insurance policy owns a home in an area that can sustain a total loss with probability 0.001 and a 50% loss with probability 0.01.What premium should the insurance company charge for an annual policy so that there is no gain or loss on all $85,000 policies in this area?

In the final round of a TV game show, contestants have a chance to increase their current winnings of$1 million to $2 million. If they are wrong, their prize is decreased to $500,000. A contestant thinks his guess will be right 50% of the time. Should he play? What is the lowest probability of a correct guess that would make playing profitable?

"Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $1,480,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.The probability of a small box office earning $203,000 is 0.27. The probability of a medium box office of $1,660,000 is 0.49, and the probability of a large box office of $2,950,000 is 0.24.Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $20,000 to get the novel evaluated by the movie critic.The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.If the movie will have a large box office, there is a 0.75 probability the critic will have a favorable opinion.If the movie will have a medium…

A construction company needs to move lumber onto the roof of a building. If the lumber falls and hits someone it will cause $1,200,000 in damage. Assume that company must choose between the following levels of precaution: Spend $500 and the probability of an accident is .05 Spend $5,000 and the probability of an accident is .01 Spend $8,000 and the probability of an accident is .008 Spend $10,000 and the probability of an accident is .003 If the construction company is strictly liable for the costs of the accident, how much would they spend on precaution? A. $500 B. $5,000 C. $8,000 D. $10,000

"Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $1,460,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.The probability of a small box office earning $210,000 is 0.27. The probability of a medium box office of $1,530,000 is 0.64, and the probability of a large box office of $3,190,000 is 0.09.Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $21,000 to get the novel evaluated by the movie critic.The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.If the movie will have a large box office, there is a 0.61 probability the critic will have a favorable opinion.If the movie will have a medium…

John is a farmer with $225 of wealth. He can either plant corn or beans. If he plants corn, John earns an income of $675 if the weather is GOOD and $0 if the weather is BAD. If he plants beans, John earns an income of $451 under both GOOD and BAD weather. The probability of GOOD weather is 0.7. The probability of BAD weather is 0.3. John’s utility function is U(c) = 5√c , where c is the value of consumption.  Mae owns an insurance company in a nearby town and has decided to offer conventional crop insurance to corn farmers in the area. Assume that Mae has perfect information and can write and enforce an insurance contract that requires the farmer to plant corn. Here’s how the insurance contract works. At the beginning of the year, the corn farmer pays an insurance premium of $202.5. If the weather is GOOD, Mae makes no payment to the farmer. If the weather is BAD, Mae makes an indemnity payment of $675 to the farmer.   a. If a farmer buys this insurance contract,what is Mae’s expected…

Consider a city where everyone commutes to the city center and commuting cost per mile per month is $40. Each household occupies a 1,000-square-foot dwelling and has $7,000 worth of possessions in its dwelling. The probability that any particular household will be burglarized (involving the uninsured loss of all possessions) is 0.10 at the city center and decreases by 0.01 per mile (to 0.09 at one mile, 0.08 at two miles, and so on). The housing price is $1.00 per square foot at the city center. a) Draw the housing-price curve for locations up to five miles from the city center.

Exercise 3: Risky Investment   Charlie has von Neumann-Morgenstern utility function u(x) = ln x and has wealth W = 250, 000.   She is offered the opportunity to purchase a risky project for price P = 160, 000. 1                                                                                                                    1 With probability p = 2 the project will be a success and return V  > 160, 000. With probability 1 −p = 2 the project will fail and be worthless (i.e. it returns 0). For simplicity assume there is no interest between the time of the investment and the time of its return, that is r = 0 . How large must V be in order for Charlie to want to purchase the risky project? [Hint: What is Charlie’s expected utility is she does not purchase the project? What is Charlie’s expected utility is she purchases the project?]

Bob earn 60,000 a year and an accounting firm each year he receives Reyes Bob has determined that the probability that he receives a 10% raise is .7 the probability that he earns a 3% raise is .2 and the probability that he earns a 2% raise is .1 a competing company has offered Bob a similar position for 65,000 a year Bob wonders if he should take the new job or take his chances with his current job. a. Find the mathematical expectation of the dollar amount of his raise at his current job b.

Deborah Mitz buys Breathalyzer test sets for the Police Department. The quality of the test sets from her two suppliers is indicated in the following table: (image attach)    For example, the probability of getting a batch of tests that are 1% defective from Loomba Technology is .70. Because Mitz orders 10,000 tests per order, this would mean that there is a .7 probability of getting 100 defective tests out of the 10,000 tests if Loomba Technology is used to fill the order. A defective Breathalyzer test set can be repaired for $0.50. Although the quality of the test sets of the second supplier, Stewart-Douglas Enterprises, is lower, it will sell an order of 10,000 test sets for $37 less than Loomba. a) Develop a decision tree.b) Which supplier should Kellogg use?