Question

Jack and Jill are the only two residents in a neighborhood, and they would like to hire a security guard. The value of a security guard is $50 per month to Jack and $150 per month to Jill. The competitive wage for a security guard is $120 per month, and irrespective of who pays the guard, the guard will protect the entire neighborhood. Furthermore, suppose Jack earns $1,000 per month and Jill earns $11,000 per month.

Required:
a. What is the most a guard can charge per month and still be assured of being hired by at least one of them?
b. Suppose the competitive wage for a security guard is $120 per month. The local government proposes a plan whereby Jack and Jill each pays 50 percent of this monthly fee, and asks them to vote on this plan. Will the plan be voted in? Would economic surplus be higher if the neighborhood had a guard?

Answer 1

The guard can charge up to $150 per month. Jack would likely vote against, while Jill would vote for the cost-sharing plan at $60 each since it's less than her valuation. Economic surplus is higher with a guard.

Step-by-step explanation:

Analysis of the Security Guard Hiring Scenario

Given the scenario where Jack values the security guard at $50 per month and Jill values it at $150 per month, the most a guard can charge and be assured of being hired is $150 per month, as that is the maximum value the guard provides to either resident. As for the cost-sharing proposal, we look at whether each person's valuation exceeds their share of the cost. The plan suggests that Jack and Jill each pay 50 percent of the competitive wage, which is $120 per month, meaning each would pay $60.

For Jack, who values the guard at $50 per month, this is above what he values the service ($60 > $50), and he would likely vote against it. For Jill, who values the service at $150 per month, the cost is significantly lower than her valuation ($60 < $150), so she would likely vote for it. However, because both votes are needed and the proposal costs more to Jack than the service is worth to him, the plan would not be voted in unless alternative arrangements or negotiations could bring Jack onboard.

Economic surplus, defined as the sum of consumer and producer surplus, would be higher with a security guard than without one, assuming the guard is paid less than the total value provided ($50 + $150 = $200).