Consider a Police Department Trying to Decide How to Allocate

question 61

Multiple Choice

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?

• A)4 detectives to motor vehicle theft and 0 to burglary.
• B)3 detectives to motor vehicle theft and 1 to burglary.
• C)4 detectives to motor vehicle theft and 2 to burglary.
• D)0 detectives to motor vehicle theft and 4 to burglary.

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Definitions:

N Th Partial

Relates to the nth term in a sequence, often used in the context of partial sums.

N Th

Pertaining to an unspecified member of a sequence or series, representing a general or particular position.

Geometric Sequence

A series of numbers in which each subsequent term is derived by multiplying the term before it by a constant, non-zero figure referred to as the ratio.

Population

In statistics, population refers to the entire group of individuals or items that a study intends to investigate or draw conclusions from.