Suppose the actuaries and executives at a brand new insurance company, Bumbly Dex Insurance, have watched Everest and other high mountain climbers for years. In their research, they have found that 5% of climbers get themselves into serious trouble while climbing. When a high-altitude climber gets in trouble, it usually amounts to a stranding at extreme altitudes and temperatures, or a fall, or worse. Suppose that our actuaries estimate that the typical damages incurred by high mountain climbers around the world amount to $0 for the 95% who do not get into serious trouble on a trip, and $500,000 for those who do get themselves into trouble on a trip.

What would be the cheapest per-trip insurance premium that Bumbly Dex would offer to high mountain climbers? Explain.

Explain why, even if Bumbly Dex has zero administrative expenses, why charging the premium in Part (a) would very likely ensure the rapid bankruptcy of the company, even if every single high mountain climber purchases, and maintains, insurance each year. You might think about things Bumbly could do to prevent this, assuming it can’t raise its price.