Johnsson, Richard (2004). ”The Cost of Relying on the Wrong Power – Road Wear and the Importance of the Fourth Power Rule (TP446).” Transport Policy, 11: 345-353.

Abstract: This paper investigates the effect on road wear and deformation of alternatives to the Fourth Power Law in a computable general equilibrium model of Sweden. The alternatives considered are the first through fifth powers, and the results indicate that the results are similar in all cases but when the first power is employed. This follows from the fact that designing the charge according to the first power amounts to a weight-distance charge rather than an axle-weight-distance. The paper also investigates the cost of designing a charge according to the wrong power, i.e. not according to the true relationship between road wear and road use. The results indicate that the cost of choosing the wrong power is relatively small, but slightly higher in the case of the first power. Indeed, there are several implicit costs that seem to have to be taken into account when implementing a charge according to the former power, i.e. a weight-distance charge.