Question

• Although the increasing popularity of the Southport neighborhood has generally been a very positive development, there are a few negatives associated with it. You already addressed parking concerns. Another serious issue involves criminal activity. Southport has always had low levels of violent crime, and fortunately this doesn't appear to be changing. However, there has been a significant increase in vandalism and graffiti incidents. The police force is already working overtime, but it just can't keep up with the rapid growth.

  Because of these issues, the City Council is considering options to increase monitoring and reduce the load on law-enforcement officers. The budget is limited, which means it is important to make a cost-effective decision. The options being considered are described below:

• Hire additional officers—with more police patrolling the streets, vandals are less likely to cause damage. The officers would be entry-level officers who would patrol night and evening shifts.
• Purchase additional streetlights and security cameras—these items would work together to deter criminal activity. The streetlights would make it more difficult to damage property without being noticed, while the cameras would allow police to "catch them in the act".

• The city has obtained data from other areas regarding the effectiveness of hiring additional officers and installing cameras and lights. The city has estimated that each crime prevented is worth $1,000 to the city (the amount includes the expenses incurred by the police department, courts, and prisons) Each additional police officer would be paid $20,000 per year. Each security camera/light installation would cost $8,000 per year to operate and maintain. A summary of this data is below:

Number of Crimes Prevented Per Year	Number of Officers Hired
21	1
47	2
76	3
104	4
128	5
149	6
165	7
178	8
188	9
195	10

Number of Crimes Prevented Per Year	Number of Camera/ Light Installations
6	1
13	2
25	3
33	4
40	5

Write a 300- to 500-word report to John Becker. In your report, be sure to

• consider the likely effect of the increase in crime on the labor market for police officers in the city
• calculate the marginal product and marginal revenue product of labor for police officers
• consider the optimal number of additional officers that should be hired if the city only hires police officers (be sure to explain your answer using marginal products)
• calculate the marginal product and marginal revenue product for adding security cameras and lights
• consider the optimal number of security cameras and lights the city should install if the city only purchases security cameras and lights (be sure to explain your answer using marginal products)

Answer 1

Number of crimes prevented per year	Number of officers hired	$ Revenue	Marginal Revenue	$ Cost	Marginal Product
21	1	21000		20000
47	2	47000	26000	40000	20000
76	3	76000	71300	60000	20000
104	4	104000	28000	80000	20000
128	5	128000	24000	100000	20000
149	6	149000	21000	120000	20000
165	7	165000	16000	140000	20000
178	8	178000	13000	160000	20000
188	9	188000	10000	180000	20000
195	10	195000	7000	200000	20000

Number of crimes prevented per year	Number of lights/cameras installed per year	$ Revenue	Marginal Revenue	$ Cost	Marginal Cost
6	1	6000		8000
13	2	13000	7000	16000	8000
25	3	25000	12000	24000	8000
33	4	33000	8000	32000	8000
40	5	40000	7000	40000	8000

The revenue earned by the authorites for each crime prevented in $1000. Thus revenue is calculated by multiplying the crimes by 1000

the cost paid by the authorities to appoint each police officer is $20000. Thus the product/cost of the police officers has been calculated by multipying the number of officers recruited by 20000

the cost to install lights and cameras is $8000. Thus the product /cost of the cameras and lights has been calculated by multiplying the number of installations by 8000

The marginal revenue is calculated by Existing Revenue - The older Revenue in simple terms.

The marginal cost l product is calculated in the same way by reducing the older product from the existing product.

By observing the above calculated tables.:

1 More crimes might be prevented by recruiting more police officers because, even though the cost of recruiting the officers is more, the number of crimes prevented and thus the revenue earned thereof is also more.

2. If only police officers are recruited, the optimal number of police officers to be recruited is 6 as the average of marginal revenue as well as the cost is optimal at that level.

3. If only cameras and lights have to be installed then the optimal number of lights and cameras to be installed will be 2 as the average of marginal revenue is the same at 2 cameras as well as 5 cameras but the considering the cost incurred 2 cameras is the best cost as both 2 cameras and 5 cameras yield the same revenue.