Question

Sabrina, Kris, and Kelly are the only three residents of the small town of Charleston. They are considering whether to hire a police officer to patrol the town. Sabrina values the police officer at $610 per week, Kris values the police officer at $230 per week, and Kelly values the police officer at $150 per week. The competitive wage for a police officer is $900 per week.

a. If the protection provided by the police officer to one resident does not diminish the protection provided to the other residents, then the police officer is   (Click to select)  a commons  an excludable  a rival  a nonrival  a nonexcludable  good.

b. Suppose Sabrina proposes a tax whereby all three residents split the cost of the police officer equally.

Will the majority of them support this tax?

• No, they will not support the tax.

• Yes, they will support the tax.

Is this outcome socially efficient?

• This outcome is not socially efficent.

• This outcome is socially efficient.

c. Suppose Kris suggests a proportional tax on income to pay for the police officer. If Sabrina earns $4,000 per week, Kris earns $1,500 per week, and Kelly earns $500 per week, what proportional tax on income would just cover the cost of the police officer?

Instructions: Enter your response as a percent.

A proportional tax rate:  %

Will the majority of them support the tax?

• Yes, all three would support the tax.

• No, all three would not support the tax.

• No, two of them would not support the tax.

• Yes, two of them would support the tax.

d. Is a regressive tax system likely to lead to the socially optimal outcome in this case?

• No

• Yes

Answer 1

a) The characteristic of police officer as given in the question makes him a non-rival good. His services to one person does not diminish benefits to the other person.

b) No, they will not support the tax because if they split equally, all of them have to pay $300. Cost is more than benefits for Kris and Kelly. Their net benefits would be-&70 and -$150 respectively, so their private net benefits are negative.

This outcome is socially efficient because joint profits are maximized when costs are split equally.

Net benefits of the society as whole is maximized here. Net benefits to society is: Total Marginal Benefits to all 3 people- cost of the police officer= 610+230+150-900=90

Whereas after taxation, net benefits to society will be: Sum of net benefits of all 3 people= (610-300)+(230-300)+(150-300)= 90

c) From hit and trial method, we find that a 15% proportional tax on income will just cover cost. Each person will pay as follows:

Sabrina: $4000*15%= 600

Kris: $1500*15%= 225

Kelly: $500*15%= 75

Total tax: 600+225+75= 900

Yes, all of them will support the tax because the cost is below their respective valuation.

d) We see that regressive tax system is leading to a socially efficient outcome (because net benefits are maximized when costs are split equally), so it is likely to lead to socially efficient outcome in this case