The theory of approximate prices: Analytical foundations of experimental cost–benefit analysis in a fuzzy-decision space

The essay presents a theory of efficient prices for cost–benefit analysis in a fuzzy space. The approach proceeds by taking consumers' income, and producers' outputs and costs as given. The price preferences of consumers and producers are elicited and then embedded in a fuzzy space through fuzzy mappings to obtain a fuzzy compact price space where fuzzy price decisions are constructed. Solutions to the fuzzy price decision problems are abstracted through fuzzy mathematical programming to obtain fuzzy equilibrium prices. From the fuzzy price space measures of price disagreement, fuzzy consumer surplus and fuzzy producer surplus are advanced. Theorems of existence and uniqueness are stated. The total result is a theory of fuzzy prices for cost–benefit analysis for decision problems, in general including cases where market imputations of prices may not be available to us as well as those cases where market failure may yield price distortions. The theory is not only compactible with either contingent variation method (direct information elicitation) and revealed preference method (market-based evaluation) but provides a direction for cases where problems may exist in both. A computational example is provided to illustrate the working mechanism of the theory.