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?
Farmer Brown grows wheat on his farm in Kansas, and the weather during the growing
season makes this a risky venture. Over the many years that he has been in business, he
has learned that rainfall patterns can be categorized as highly productive (HP) with a
probability of .2, moderately productive (MP) with a probability of .6, and not
productive at all (NP) with a probability of .2. With these various rainfall patterns, he
has also learned that the inflation adjusted yields are $25,000 with NP weather, $10,000
with MP weather, and $50,000 with HP weather. Calculate the expected yield from
growing wheat on Farmer Brown’s farm. What can be learned about Brown’s attitude
toward risk from this problem? Explain.