1. The index of public safety in a city is given by one minus the crime rate. For example, and index of 0.90, or 90%, means that 90% of the population will not be a crime victim during a given year. The public safety index, denoted S, depends on the number of police in a city as well as its population. The relationship isS = 13.2(P.20)(n.30), Where P is the number of police and n is the city population.

a)Using the formula, identify and interpret the elasticity of congestion for public safety.

b)Suppose both P and n double. Does the level of public safety rise or fall? Based on your answer, if n is expect to double, what must happen to the level of police to maintain a constant level of public safety (must the police force more or less than double)?

c)Consider a city of 100,000 people with a police force of 60 officers. Compute the public safety index for this city, and interpret it.

d)Suppose the city population grows to 500,000 but that the police force size remains at 60. Compute the new index of public safety, and compare it to the level in part (c).

e)Suppose the larger city wishes to achieve the same level of public safety as it enjoyed when population was 100,000. How much must the police force be expanded to achieve this goal? Compare the proportional increase in P to the proportional increase in population.

f)Suppose the cost of a policeman is measured in thousands of dollars, with the cost equal to 30. Compute the per capita cost (total cost divided by population) of the original police force. Then compute the per capita cost of the police force from part (e), remembering that the city is now larger. What is the proportional change in the cost?