Question

1. An evil man is tormenting a small city of 100. Lydia who is the president’s daughter says the city has to hire security guards with guns to protect the city from the evil man. Explain why the citizens of the city have not hired their own security guards with guns and why Lydia has to convince the citizens to donate money to help in hiring for protection

2. With the info below calculate the marginal cost, individual marginal benefit for each citizen, and the marginal social benefit for the city of the hired protection.

Number of Gunslingers	Total Cost	Total individual benefit to each resident
0	$0	$0
1	100	10
2	250	16
3	400	18
4	550	19

3. What is the optimal number of security guards with guns for the city to hire? Show your reasoning.

Answer 1

1.

Security guards should be hired from outside, because own guards are already occupied with their routine works; therefore, if they are entrusted with more works they may not perform well and their marginal productivity may diminish. Such hiring from outside may be expensive but it gives higher amount of benefits to each citizen.

2.

Marginal cost (MC) is the difference of total cost of two consecutive security guards.

Marginal benefit (MB) is the difference of total benefit of two consecutive security guards.

Marginal social benefit (MSB) = MB – MC for each citizen

MC for each citizen = MC / 100 citizens

Number	TC	TB	MC = TCn – TC(n-1)	MB = TBn – TB(n-1)	MSB
0	0	0	---	---	---
1	100	10	100 – 0 = 100	10 – 0 = 10	10 – (100/100) = 10 – 1 = 9
2	250	16	250 – 100 = 150	16 – 10 = 6	6 – (150/100) = 6 – 1.5 = 4.5
3	400	18	400 – 250 = 150	18 – 16 = 2	2 – (150/100) = 2 – 1.5 = 0.5
4	550	19	550 – 400 = 150	19 – 18 = 1	1 – (150/100) = 1 – 1.5 = - 0.5

3.

Optimal number is 1, since its MSB is the highest.