Economics of CrimeEconomics of Crime

by Anthony Muirby Anthony Muir

Crime FactsCrime Facts

The FBI collects data from local police The FBI collects data from local police departments on seven index crimes. departments on seven index crimes. These are divided into:These are divided into:

• Personal CrimesPersonal Crimes• Property CrimesProperty Crimes

Crime Facts, 7 indexesCrime Facts, 7 indexes

Victims of CrimeVictims of Crime

Victims of Crime vary depending on Victims of Crime vary depending on the following factors:the following factors:

• IncomeIncome• Place of ResidencePlace of Residence• RaceRace

Costs of CrimeCosts of Crime

Cost of the War on DrugsCost of the War on Drugs

Estimations from Estimations from www.drugsense.org• People People Arrested for Drug Law Arrested for Drug Law

OffensesOffenses this Year: 524,000 this Year: 524,000• People People Arrested for CannabisArrested for Cannabis Law  Law

Offenses this Year: 270,000Offenses this Year: 270,000• People People IncarceratedIncarcerated for Drug Law  for Drug Law

Offenses this Year: 3,400Offenses this Year: 3,400• Money SpentMoney Spent on the War On Drugs this  on the War On Drugs this

Year: over $12 billion Year: over $12 billion 

Expected Utility and Decision to Expected Utility and Decision to Commit CrimeCommit Crime

• Crime decision is based on Crime decision is based on utility maximizationutility maximization

This graph shows the This graph shows the relationship between relationship between income (on the horizontal income (on the horizontal axis) and utility (on the axis) and utility (on the vertical axis).vertical axis).

Concave, because of Concave, because of diminishing marginal utility diminishing marginal utility of income: as income of income: as income increases, utility increases increases, utility increases but at a decreasing ratebut at a decreasing rate

Utility = (Income)^(1/2)Utility = (Income)^(1/2) Utility is the square root of Utility is the square root of

incomeincome

Application of UtilityApplication of Utility

Consider the baseline Consider the baseline lawful income to be 100 lawful income to be 100 (point c)(point c)

The potential loot is $44 The potential loot is $44 Probability of Prison is Probability of Prison is

0.50.5 Lawful utility is 10Lawful utility is 10 Utility from successful Utility from successful

crime is 12 (point s)crime is 12 (point s) Utility from failed crime Utility from failed crime

is 8 (point f)is 8 (point f)

Application of UtilityApplication of Utility

The individual is indifferent between crime The individual is indifferent between crime and lawful livingand lawful living

EU{U1, U2, p1, p2} = p1 x U1 + p2 x U2EU{U1, U2, p1, p2} = p1 x U1 + p2 x U2

0.5 x 12 + 0.5 x 8 = 10 utils0.5 x 12 + 0.5 x 8 = 10 utils

Due to diminishing marginal returns, one is Due to diminishing marginal returns, one is indifferent between crime in the two cases.indifferent between crime in the two cases.

Preventing CrimePreventing Crime

If we change the probability of getting If we change the probability of getting caught for the crime from 0.5 to 0.75, the caught for the crime from 0.5 to 0.75, the incentive of crimes lessens. incentive of crimes lessens.

EU{U1, U2, p1, p2} = p1 x U1 + p2 x U2EU{U1, U2, p1, p2} = p1 x U1 + p2 x U2

0.25 x 12 + 0.75 x 8 = 9 utils0.25 x 12 + 0.75 x 8 = 9 utils

9 utils is now less than the baseline for utils, 9 utils is now less than the baseline for utils, meaning that you will not commit the meaning that you will not commit the crime logicallycrime logically

Preventing CrimePreventing Crime

This can also be slanted by increasing prison time This can also be slanted by increasing prison time from 0.36 to .51. This causes failed utility to be 7 from 0.36 to .51. This causes failed utility to be 7 utils, changing the model:utils, changing the model:

EU{U1, U2, p1, p2} = p1 x U1 + p2 x U2EU{U1, U2, p1, p2} = p1 x U1 + p2 x U2

0.50 x 12 + 0.50 x 7 = 9.5 utils0.50 x 12 + 0.50 x 7 = 9.5 utils

This is also less than the baseline utilThis is also less than the baseline util

Note: Those with higher income will have a higher Note: Those with higher income will have a higher opportunity cost of being in prison and will opportunity cost of being in prison and will therefore be less willing to take the risktherefore be less willing to take the risk

Anguish CostsAnguish Costs

Anguish costs explain why people do not Anguish costs explain why people do not commit crimes when it would otherwise be commit crimes when it would otherwise be profitable to do so. For example, take row 6 profitable to do so. For example, take row 6 of table 13-3of table 13-3

12 (.75) + 8 (.25) = 11 utils12 (.75) + 8 (.25) = 11 utils

This is above the base, however if one would This is above the base, however if one would feel 2 utils of anguish about the crime, then feel 2 utils of anguish about the crime, then the crime would be equal to 9 utils and not the crime would be equal to 9 utils and not worth committing for moral reasons.worth committing for moral reasons.

Breaking BadBreaking Bad http://www.youtube.com/watch?v=iRlI

Or1N5kM#t=4m6s

Walter White is a high school Walter White is a high school chemistry teacher in New Mexico, chemistry teacher in New Mexico, making an approximate average of making an approximate average of $40 a year (in thousands) $40 a year (in thousands)

Over the course of a year, Walter has Over the course of a year, Walter has the potential to make $737 selling the potential to make $737 selling Crystal Meth, in addition to his $40 Crystal Meth, in addition to his $40 from being a teacherfrom being a teacher

Walter has a 0.75 probability of being Walter has a 0.75 probability of being caughtcaught

He will serve the rest of his life in He will serve the rest of his life in prison if caught, where he will most prison if caught, where he will most likely die from Cancer in one yearlikely die from Cancer in one year

http://www.youtube.com/watch?v=iRlIOr1N5kM#t=4m6s

Walter White is a high school Walter White is a high school chemistry teacher in New Mexico, chemistry teacher in New Mexico, making an approximate average of making an approximate average of $40 a year (in thousands) $40 a year (in thousands)

Over the course of a year, Walter has Over the course of a year, Walter has the potential to make $737 selling the potential to make $737 selling Crystal Meth, in addition to his $40 Crystal Meth, in addition to his $40 from being a teacherfrom being a teacher

Walter has a 0.75 probability of being Walter has a 0.75 probability of being caughtcaught

He will serve the rest of his life in He will serve the rest of his life in prison if caught, where he will most prison if caught, where he will most likely die from Cancer in one yearlikely die from Cancer in one year

Breaking BadBreaking Bad Lawful Income = 40Lawful Income = 40 Loot = 737Loot = 737 Probability of Prison = 0.75Probability of Prison = 0.75 Prison Time = 1Prison Time = 1 Lawful Utility = 6.3Lawful Utility = 6.3

Utility from Successful CrimeUtility from Successful Crime Legal Income + Loot = 777Legal Income + Loot = 777 Utility = 27.9Utility = 27.9

Utility from failed crimeUtility from failed crime Prison Cost = 40Prison Cost = 40 Net Income = 0Net Income = 0 Utility = 0Utility = 0

0.25 x 27.9 + 0.75 x 0 = 6.9750.25 x 27.9 + 0.75 x 0 = 6.975

6.975 > 6.36.975 > 6.3

Walter would be better off committing the crimeWalter would be better off committing the crime

The Equilibrium Quantity of CrimeThe Equilibrium Quantity of Crime

• Shows how the number of crimes one Shows how the number of crimes one commits increases with loot.commits increases with loot.

• First crime at point m, when loot First crime at point m, when loot reaches $400reaches $400

• As loot increases, quantity of crime will As loot increases, quantity of crime will increaseincrease

• The supply curve is positively sloped The supply curve is positively sloped because various criminals differ in because various criminals differ in terms of their opportunity cost and terms of their opportunity cost and anguish costsanguish costs

• Model of rational criminal is Model of rational criminal is determined by: 1) the probability of determined by: 1) the probability of being caught and imprisoned 2.) the being caught and imprisoned 2.) the length of the prison term 3.) the length of the prison term 3.) the opportunity cost of time spent in opportunity cost of time spent in prison, which varies with income. 4.) prison, which varies with income. 4.) The anguish cost of crime, which varies The anguish cost of crime, which varies across individualsacross individuals

QuestionsQuestions

1.) The text states that the justice system in the United States 1.) The text states that the justice system in the United States costs tax payers $74 billion dollars. Sources claim that costs tax payers $74 billion dollars. Sources claim that nearly $15 billion of this was spent on the “War on Drugs” nearly $15 billion of this was spent on the “War on Drugs” Is this a wise investment when taking opportunity cost and Is this a wise investment when taking opportunity cost and morality into consideration?morality into consideration?

2.) Suppose you have an opportunity to buy the last ticket to 2.) Suppose you have an opportunity to buy the last ticket to the concert, but in order to do so you must commit the the concert, but in order to do so you must commit the crime of double parking, in which you have a 50% chance crime of double parking, in which you have a 50% chance of receiving a $36 fine. The concert ticket gives you a of receiving a $36 fine. The concert ticket gives you a surplus of $44 dollars. How would you act in this scenario? surplus of $44 dollars. How would you act in this scenario?

3.) Walter White is better off selling Crystal Meth than not 3.) Walter White is better off selling Crystal Meth than not selling Crystal Meth. Why don’t you (or the average person) selling Crystal Meth. Why don’t you (or the average person) sell meth outside the law rather than working legally? Do sell meth outside the law rather than working legally? Do anguish costs play a factor here? What if you only had 0.25 anguish costs play a factor here? What if you only had 0.25 chance of getting caught rather than 0.75?chance of getting caught rather than 0.75?