Help Much Appreciated Analyse and explanations

Question

A housing estate has 100 residents who are concerned about security. The accompanying table gives the total cost of hiring a 24-hour security service as well as each individual resident’s total benefit.

(a) Explain using precise economic language, why the security service is a public good for residents of the estate.

(b) If the residents act together, how many security guards will they hire? (use marginal analysis to justify your answer and show all working).

Quantity of security guards Total Cost Total individual benefit to each

resident

0 $0 $0

1. 150 10

2 300 16

3 450 18

4 600 19

Answer 1

(a) The security service is a public good for the residents of the estate because it is both non-rival and non-excludable. This means that the benefits of the service cannot be depleted by one individual's use, and it is not possible to exclude certain individuals from enjoying the benefits of the service. In other words, the security service provides benefits to all residents of the estate, regardless of whether they individually contribute to its cost.

(b) Using marginal analysis, we can determine the optimal number of security guards to hire by comparing the marginal cost and marginal benefit of each additional security guard. The marginal cost is the additional cost of hiring one more security guard, while the marginal benefit is the additional benefit that each resident receives from hiring one more security guard.

At the first level of security guards (1 guard), the marginal cost is $150 and the marginal benefit is $10. The marginal benefit exceeds the marginal cost, so it is profitable to hire one more security guard.

At the second level of security guards (2 guards), the marginal cost is $150 and the marginal benefit is $6. The marginal benefit is now less than the marginal cost, so it is not profitable to hire any more security guards.

Therefore, the optimal number of security guards to hire is 2, as this is the point at which the marginal cost equals the marginal benefit.

Answer 2