Cost-Benefit Analysis under Uncertaity

Abstract

The conventional theory of cost-benefit analysis had held that in a world of perfect certainty, the appropriate measure of benefit for a project is the aggregate willingness-to-pay, that is the sum of the revenues collected plus the price conpensating measures of consumers' surplus for all consumers. However, B. Weisbrod asserted in his paper that when there is uncertainty in demand, there may be an additional form of benefit that must be added to the consumer surplus measure. He called this benefit ‘option value’. After many attempts to clarify the concept of option value had be made, option value was usually defined as the difference between option price and expected consumer's surplus. Resently, D. Graham showed with willingness-to-pay locus that option price is one of an infinite number of contingent schemes. This paper has two purposes; firstly to show that the willingness-to-pay locus depicted by Graham was so rough that some important properties of it were missed. If these properties are considered, some types of willingness-to-pay locus can be obtaind and any types have not option value because option price cannot exit. Secondly to extend the option demand theory to wider situation. That is the situation in which not only utilty function but also probability measure will change in response to the enforcement of a project. For example, we assume a situation where a road is usually croweded with the probability of p0% and normal with the probability of 1-p0%, and a road user can obtain income of ec yen in crowded state and en yen in normal state. If road investment is enforced, the probability of crowded state will decrease and that of normal state will increase. The road user's income will increase in both states. Then, the road user may be willing to pay for the road investment. To examine this example, conditional expected utility theory can be applied. Then, we get the conclusion that there are three cases about option price if option price exits; option price is positive, zero or negative. The last case in which option price is negative is new result in the option demand theory.