Exercise 5: Individual and Aggregate Option Price

A large rural county is considering establishing a medical transport unit that would use helicopters to y emergency medical cases to hospitals. Analysts have attempted to estimate the benefits from establishing the unit in two ways. First, they surveyed a random sample of residents to nd out how much they would be willing to pay each year for the unit. Based on responses from the sample, the analysts estimated a total willingness to pay of $8.5 million per year. Second, the analysts estimated the dollar value of the improvements in health outcomes and avoided medical costs of users of the unit to be $6.2 million per year. Taking the analysts' estimates at face value, specify the following:

(a) The aggregate of individuals' annual option prices for the unit.

(b) The annual total expected gain in social surplus from use of the unit.

(c) The annual aggregate option value for the unit.

(a) The aggregate of individuals' annual option prices for the unit.

If we take the results of the survey at face value, then the $8.5 million annual willingness to pay as the aggregate annual option price would be fair to view. If the unit's costs were certain, then this would be the appropriate measure of gain. However, there are several reasons why we might be suspicious of the precision of such an estimation of readiness to pay.

(b) The annual total expected gain in social surplus from use of the unit.

The analysts' estimate of the annual dollar value of improved outcomes and avoided costs, $6.2 million, can be interpreted as the annual gain in expected social surplus. If this estimate is based on a large number of users, then it is likely to be close the annual gain in social surplus actually realized. It would thus be a reasonable lower bound for the annual benefits of the unit.

(c) The annual aggregate option value for the unit.

The aggregate annual option value would be the difference between the aggregate annual option price and the annual expected gain in social surplus: $8.5 million - $6.2 million =$2.3 million. This large option value for a program that uses helicopters to fly emergency medical cases to hospitals might be expected because the program functions similarly to insurance by helping to reduce the magnitude of unlikely but severe losses.