Transport user benefits calculation with the “Rule of a Half” for travel demand models with constraints

The importance of user benefits in transport projects assessments is well-known by transport planners and economists. Generally they have the greatest impact on the result of cost-benefit analysis. It is common practice to adopt the consumer surplus measure for calculating transport user benefits. Normally the well-known “Rule of a Half”, as a practical approximation for the integral of the demand curve, is used to determine the change of consumer surplus. Changes in travel demand and consumer surplus are influenced by all modeled changing variables, which primarily comprise the generalized costs. However, travel demand models with multiple constraints additionally contain variable “shadow prices”, added to the generalized costs. Such models are often used for travel demand modeling of large-scale areas. The most discussed and well-known model in the field of transport modeling is the doubly constrained gravity model. Beside this model with inelastic constraints, there are also more flexible models with elastic constraints. In this paper we enter into the question of whether applying the Rule of a Half with regard only to the generalized costs and neglecting the shadow prices is valid in the case of travel demand models with multiple constraints. For this purpose, a theoretical analysis in this paper provides a mathematical proof.