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Twenty first century electronics has discovered a theft problem at its warehouse and has decided to hire security guards
Twenty first century electronics has discovered a theft problem at its warehouse and has decided to hire security guards. The firm wants to hire the optimal number of security guards. the table above shows how the number of security guards affects the number of cellphones stolen per week.
| Number of security guards | Number of phones stolen per week |
|---|---|
| 0 | 0 |
| 1 | 35 |
| 2 | 25 |
| 3 | 20 |
| 4 | 18 |
| 5 | 17 |
a. If each security guard is paid $500 a week and the cost of a stolen phone is $200, how many security guards should the firm hire?
b. If the cost a stolen phone is $100, what is the most the firm would be willing to pay to hire the first security guard?
c. If each security guard is paid $500 a week and the cost of stolen phone is $300, how many security guards should the firm hire?
Expert Solution
The first step is to calculate the marginal benefit (MB) associated with hiring more guards. We will calculate it in units and then in dollars for each of the three cases: if the phones are valued at $100, $200, and $300.
| Guards | Phones Stolen | MB in units | MB @$100 | MB @$200 | MB @$300 |
|---|---|---|---|---|---|
| 1 | 35 | 35 | 3,500 | 7,000 | 10,500 |
| 2 | 25 | 35-25=10 | 1,000 | 2,000 | 3,000 |
| 3 | 20 | 25-20=5 | 500 | 1,000 | 1,500 |
| 4 | 18 | 20-18=2 | 200 | 400 | 600 |
| 5 | 17 | 18-17=1 | 100 | 200 | 300 |
a. If each stolen phone is valued at $200, hiring the fourth guard is not optimal because the marginal cost is $500 while the marginal benefit is only $400. Therefore, the optimal number of guards is three
b. If each stolen phone is valued at $100, the first guard brings the marginal benefit of $3,500. Hence, the firm would be willing to pay up to $3,500 to the first guard
c. If each stolen phone is valued at $300, hiring the fifth guard is not optimal because the marginal cost is $500 while the marginal benefit is only $300. Therefore, the optimal number of guards is four
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