Jim’s Hardware Supply has theft insurance. Jim also has an alarm syste

Jim’s Hardware Supply has theft insurance. Jim also has an alarm system. The alarm system has just recently malfunctioned. If Jim has the alarm system repaired, it will cost him $100. The probability of a theft occurring is p = 0.0001.

If a theft occurs and there is no alarm system, the value of stolen materials will be $125,000. However, Jim’s insurance will compensate him fully for the loss. No thefts will occur if the alarm system is in place. What is the expected cost to Jim of repairing the alarm system? What is the expected cost to society of not repairing the alarm system?

ANSWER

Jim’s private costs and the costs to society of repairing the alarm system are given in the table below. As the table illustrates, Society’s expected costs are minimized if Jim has the alarm repaired. However, Jim’s expected costs are minimized if he does not repair the alarm.

Alarm Repaired Alarm Unrepaired
Jim’s Expected Cost $100 $0
Society’s Expected Cost $100 $125