Suppose that optimal deterrence of a particular crime requires setting the expected punishment equal to $2000. Assume that the probability of apprehension is fixed at .2 Suppose an offender has a wealth of $5000 and incurs a cost of 1000 per month spent in prison. What combination of a fine and prison term achieves optimal deterrence at the lowest cost? What combination of a fine and prison term is optimal for an offender with a wealth of $7000 (assuming the same monthly cost of imprisonment)? Suppose considerations of fairness dictate that the prison term of offenders who commit the same crime must be the same. What fine and prison term must be imposed on the two offenders to maintain optimal deterrence?

Suppose that optimal deterrence of a particular crime requires setting the expected punishment equal to $2000. Assume that the probability of apprehension is fixed at .2 Suppose an offender has a wealth of $5000 and incurs a cost of 1000 per month spent in prison. What combination of a fine and prison term achieves optimal deterrence at the lowest cost? What combination of a fine and prison term is optimal for an offender with a wealth of $7000 (assuming the same monthly cost of imprisonment)? Suppose considerations of fairness dictate that the prison term of offenders who commit the same crime must be the same. What fine and prison term must be imposed on the two offenders to maintain optimal deterrence?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter16: Labor Markets

Section: Chapter Questions

Problem 16.9P

See similar textbooks

Similar questions

Question 4 Suppose a prosecutor expects to convict a defendant with probability 0.5 and that the sentence on conviction is 10 years in prison. Assume the prosecutor values prison time at $1,000 per year (its value as a deterrent of crime), and incurs a cost of trial equal to $2,000. a. What is the minimum prison sentence the prosecutor will o er as part of a plea bargain if her objective is to maximize the expected value of the sentence imposed, less the cost of trial (ignore the information provided in b. below to answer this question a.)? b. Suppose the defendant believes his chances of being convicted are 0.3, his cost of prison time is $5,000 per year, and his cost of a trial is $1,000. Will he accept the plea bargain in a.?
Say there are two individuals; Hala and Anna who are deciding on either to buy health insurance on a pooling arrangement basis or otherwise. Both face a 30% probability of losing RM40 on medical services and 70% of losing nothing. With these information discuss whether Hala and Anna should join this arrangement or pay the medical services costs out of their own pocket money.
Consider the St. Petersburg Paradox problem first discussed by Daniel Bernoulli in 1738. The game consists of tossing a coin. The player gets a payoff of 2^n where n is the number of times the coin is tossed to get the first head. So, if the sequence of tosses yields TTTH, you get a payoff of 2^4 this payoff occurs with probability (1/2^4). Compute the expected value of playing this game. Next, assume that utility U is a function of wealth X given by U = X.5 and that X = $1,000,000. In this part of the question, assume that the game ends if the first head has not occurred after 40 tosses of the coin. In that case, the payoff is 240 and the game is over. What is the expected payout of this game? Finally, what is the most you would pay to play the game if you require that your expected utility after playing the game must be equal to your utility before playing the game? Use the Goal Seek function (found in Data, What-If Analysis) in Excel.
A risk-neutral plaintiff in a lawsuit must decide whether to settle a claim or go to trial. The defendants offer $50,000 to settle now. If the plaintiff does not settle, the plaintiff believes that the probability of winning at trial is 50% if the plaintiff wins, the amount awarded to the plaintiff is X Will the plaintif settle if x is $62,500? What if X-$250,000? What is the critical value of X that would make the plaintiff indifferent between setting and going to trial? it the plaintiff were risk averse instead of risk neutral, would this critical value of X be higher or lower? If the amount to be awarded at trial with a win (X) were $62,500, then the plaintiff would settle If the amount to be awarded at trial with a win (X) were $250,000, then the plaintiff would not settle The critical value of X that would make the plaintiff indifferent between settling and going to trial is $ (Enter your response using rounded to wo decimal places)
Suppose that the buyers do not know the quality of any particular bicycle for sale, but the sellers do knowthe quality of the bike they sell. The price at which a bike is traded is determined by demand and supply.Each buyer wants at most one bicycle.(ii) Assuming that each buyer purchases a bike only if its expected quality is higher than the price,and each seller is willing to sell their bike only if the price exceeds their valuation, what is theequilibrium outcome in this market?
Suppose that the consumer is asked to contemplate a gamble with a probability of 60% of winning Birr 10,000 with a utility of 10 utils, and a 40% probability of winning Birr 15,000 with a utility of 12 utils. A. What will be the expected income and expected utility of the consumer? B. If the utility of this consumer from a risk free alternative which gives him an income equal to the expected income of the risky alternative given above is equal to 11 utils, is this consumer risk lover or risk averse? Why? Illustrate your answer with the help of a diagram
Eunice, the industry analyst of H&M, wants to determine the propensity of Major Clothingcompanies toward risk. She was able to determine the utility distribution of H&M, Uniqloand Dickies. For H&M, If the expected payoff of a venture is a loss of 125,000, the utilityvalue is 0.00, if a loss of 75,000, the utility value is .2, if breakeven, the utility value is .5,if gain of 75,000 .8 and if gain of 125,000 utility value is 1. For Uniqlo, if loss of 125,000utility value is 0, if loss of 75,000 utility value is .1, breakeven is .4, if a gain of 75,000,utility value is .7 and if gain of 125,000 utility value is 1. For Dickies, if loss of 125,000,utility value is 0, if loss of 75,000, utility value is .3 breakeven is .6, if gain of 75,000, utilityvalue is .9 and gain of 125,000, utility value is 1. What is the propensity to risk of the threeinternet companies? Explain your graph.
The manager of XYZ Company is introducing a new product that will yield N$1000 in profits if the economy does not go into a recession. However, if a recession occurs, demand for normal good will fall so sharply that the company will lose N$4000. If economists project that there is a 10 percent chance the economy will go into a recession, what are the expected profits to XYZ Company of introducing the new product? How risky is the introduction of the new product?
Consider a medieval Italian merchant who is a risk averse expected utility maximiser. Their wealth will beequal to y if their ship returns safely from Asia loaded with the finest silk. If the ship sinks, their incomewill be y − L. The chance of a safe return is 50%. Now suppose that there are two identical merchants, A and B, who are both risk averse expected utilitymaximisers with utility of income given by u(y) = ln y. The income of each merchant will be 8 if theirown ship returns and 2 if it sinks. As previously, the probability of a safe return is 50% for each ship.However, with probability p ≤ 1/2 both ships will return safely. With the same probability p both willsink. Finally, with the remaining probability, only one ship will return safely.(iv) Compute the increase in the utility of each merchant that they could achieve from pooling theirincomes (as a function of p). How does the benefit of pooling depend on the probability p? Explainintuitively why this is the case.
Givenu(x)=x0.5 Lottery A Probability 0.50 0.25 0.25 Outcome 64 16 0 For automatic grading, give all numerical answers to exactly two decimal places. Do not include currency signs 1) What is the expected value? (Give the answer as 36.00, not 36) 2) What is the expected utility? 3) What is the certainty equivalent? (Number only) 4) What is the risk premium? 5) Would this person rather receive 20 for sure than play Lottery A? (Answer should be Y or N for auto-grading to work) 6) (Harder) In many applications of expected utility, it is possible to lose money. The usual way of handling this is to interpret utility in terms of final wealth. Suppose it costs money to play this lottery. If starting wealth is 100, calculate the expected utility of playing lottery A if the price of playing is 15. Your answer should be to two decimal places. (Note: calculating the certainty equivalent of the lottery would be a little different than we've done in class. Squaring your EU result would give…
Your friend is contemplating buying a local restaurant. He has assessed the lifetime profits, including resale, to be $11 million with 20% chance, $6 million with 60% chance or $3 million with 20% chance. Knowing the most your friend would pay for the restaurant is $6.4 million, what can you infer about the situation? O A. The expected payoff of the restaurant is $6.333 million, the risk-discount being offered by your friend is $77.000 and your friend is risk averse with respect to this purchase. O B. The expected payoff of the restaurant is $6.4 million, the risk-premium being required by your friend $0 and your friend is risk neutral with respect to this purchase. o C. The expected payoff of the restaurant is $6.4 million, the risk-premium being required by your friend $200,000 and your friend is risk seeking with respect to this purchase. O D. The expected payoff of the restaurant is $6.333 million, the risk-premium being required by your friend is $333,000 and your friend is risk…
In the Hawaiian Beach Boy surf board vendor scenario, what if the fine was increased to $190 but the probability of a fine decreased to one in 20 days, 5%? What would be the expected value – Exp(RS) -- of continuing to rent surfboards? Assume the other numbers stay the same. He makes $300/day and to rent boards from friends costs him $100 a day. So, he makes $200 a day. Write out the expected value formula, plug in the numbers, and show the math. Hint: the Exp(RS) should be higher than the previously calculated $160.