Dalia owns a small public relations firm and wants to contract with her insurance provider to offer her employees the option to purchase short-term disability insurance.

The insurance will pay out $5,000 to any worker who has to miss at least three consecutive weeks of work due to an illness or accident that occurred outside the work place. Her employees’ probabilities of using the insurance in any year are in the accompanying table.

a. If the insurance company can easily figure out the probabilities of each employee using the short-term disability insurance, and it can tailor its price to each customer, what is the lowest price it’s willing to charge each person?

b. Now suppose that each of Dalia’s employees knows their own probability of using the insurance, but the insurance company only knows that, on average, the probability of a worker suffering a qualifying injury or illness is about 40%. Based on this, how much on average does the insurance company expect to pay out per policy if everyone buys it?

c. Who will purchase the insurance at the price you calculated in part (b) and how much expected profit will the insurance company earn?

d. How much will the insurance company need to increase the premium it charges to each person in order to avoid making a loss? Who will continue to buy the insurance and how much profit will the insurance company now earn?

e. How much will the insurance company need to increase the premium charged to each person in order to earn zero profits? Who will continue to buy the insurance?

f. What is happening to the size of the insured population? What is this called?