Question

A. El Guapo is terrorizing Santo Poco, a small Mexican village of 100. Carmen, the daughter of the village leader, decides that the village must hire some gunslingers to protect them from El Guapo. Explain why the individual villagers haven’t already hired their own gun fighters and why Carmen must convince all the other villagers to donate to hiring the gun slingers.

B.Given the information below, calculate the marginal cost, individual marginal benefit for each villager, and the marginal social benefit for the village of the hired guns.

Number of Gunslingers	Total Cost	Total individual benefit to each resident
0	$0	$0
1	150	10
2	300	16
3	450	18
4	600	19

C.What is the optimal number of gunslingers for the villagers to hire? Show your reasoning.

Answer 1

Marginal benefit and costs are found from sucessive changes in total benefit and cost. MSB is found by multiplying individual MB with 100 (for whole society)

Now MSB > MC and the difference is minimized at 3 gunslinger. Hence the optimal number of gunslingers for the villagers to hire is 3. (MSB = 200 is greater than MC = 150)(Fourth gunslinger will raise cost and reduce benefits.

Number of Gunslingers	TotalCost	Marginal cost	Total individual benefit to each resident	Marginal benefit	Social marginal benefit
0	0		0
1	150	150	10	10	1000
2	300	150	16	6	600
3	450	150	18	2	200
4	600	150	19	1	100