Quality/Value Relationship for Imperfect Information in the Umbrella Problem

The so-called umbrella problem (or cost-loss ratio situation), in which an individual must decide whether to take an umbrella in the face of uncertainty concerning whether it will rain today, is sometimes used as a textbook example of decision making under uncertainty.This problem is extended to provide a simple demonstration of the way in which the economic value of imperfect information changes as its quality increases.