Question

7. Three thousand senior citizens live in Golden Years retirement community. They are concerned about public safety and plan to hire security guards to patrol their community. The security guards would be a public good to all residents. One thousand residents are very concerned about safety, another one thousand are somewhat concerned, and the final one thousand are not that concerned at all. The table below shows the marginal benefit of a security guard for each type of resident. For example, the marginal benefit of a third security guard is $50 for a "very concerned" senior citizen. The cost of hiring a security guard is $70,000. To maximize social profits, how many security guards should Gold Years hire? Security Guards Very Concerned Somewhat Concerned Not So Concerned $70 S60 $50 2 SGO $50 $40 3 $50 $40 $30 4 $40 S30 $20 5 $30 $20 $10

Answer 1

Solution :

In an equilibrium, the Marginal Benefit must be equal to marginal cost.

MC = MR

Marginal Benefit for hiring 1 security guard, the total marginal benefit equals = 1000(70) + 60(1000) + 50(1000) = 180,000

Marginal Cost = 70,000

Marginal Benefit for hiring 2 security guards = 1000(60) + 50(1000) + 40(1000) = 150,000

Marginal Cost for hiring 2 guards = 70,000 * 2 = 140,000

Marginal Benefit for hiring 3 security guards = 1000(50) + 40(1000) + 30(1000) = 120,000

Marginal Cost for hiring 3 guards = 120,000 * 3 = 360,000

For any further number of guards, the marginal cost will always be more than marginal benefit of hiring a guard.

Thus, 2 guards will be hired but the outcome will still not be an efficient one since marginal benefit is less than the marginal cost when 2 guards are hired.

Thus, Gold's will hire 2 guards.