Question

Twentyfirst 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 following table shows how the number of security guards affects the number of radios stolen per week. # of security guards # of stolen per week 0 50 1 30 2 20 3 11 4 7 5 4 a. If each security guard is paid $400 a week and the cost of a stolen radio is $50, how many security guards should the firm hire? b. If the cost of a stolen radio is $50, what is the most the firm would be willing to pay to hire the first security guard? c. If each security guard is paid $400 a week and the cost of a stolen radio is only $30, how many security guards should the firm hire?

Answer 1

The firm wants to hire the optimal number of security guards.

a. If each security guard is paid $400 a week and the cost of a stolen radio is $50, 3 security guards will be hired by the firm. This is because when the third guard is hired, the cost saved by the guard is 450 and the wages are $400. For the fourth worker the savings are 200 while wage is 400 so it is not worth to hire 4th guard.

Guards	Stolen radios	Cost of radios	Reduction in the cost (marginal)
0	50	2500	2500
1	30	1500	1000
2	20	1000	500
3	11	550	450
4	7	350	200
5	4	200	150

b. If the cost of a stolen radio is $50, the most the firm would be willing to pay to hire the first security guard is the cost saved by hime, it is 1000

c) . If each security guard is paid $400 a week and the cost of a stolen radio is only $30, only 1 security guards will be hired because the reduction in cost is 600

Guards	Stolen radios	Cost of radios	Reduction in the cost (marginal)
0	50	1500	2500
1	30	900	600
2	20	600	300
3	11	330	270
4	7	210	120
5	4	120	90