Consider a police department trying to decide how to allocate its crime preventi

Question

Consider a police department trying to decide how to allocate its crime prevention resources between motor vehicle thefts and burglaries. The marginal benefit of one less motor vehicle theft is $20,000, and the marginal benefit of one less burglary is $1,000. Suppose the annual number of motor vehicle thefts and the annual number of burglaries depends on the number of detectives assigned to each type of crime, as shown in the table below. Each detective costs $35,000 each per year, regardless of whether the detective is assigned to motor vehicle thefts or burglaries.

What is the socially optimal number of detectives to be assigned to each type of crime?

Explanation / Answer

3 detectives to motor vehicle theft and 1 detective to burglary

At socially optimal level

Marginal benefit of less motor vehicle thefts = Cost to hire detective

So, since cost to hire 4th detective is 35000 whereas marginal benefit = (11-10)*20,000 = 20,000

So Marginal ocst to hire > Marginal benefit hence 3 detectives for motor vehicle theft,

since cost to hire 2th detective is 35000 whereas marginal benefit = (60 - 30)*1,000 = 30,000

So Marginal cost to hire detective > Marginal benefit hence 1 detective for burglary.

If you don't understand any thing then comment, I'ill revert back on the same. :)

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