Analytic approaches to welfare measurement in logit with income effect have attracted researchers for the higher ease of computation compared with the approach based on simulation. Different analytic approaches are possible, each being identified by the quantity adopted as welfare measure. The most natural candidate is the expectation of the compensating variation, which is provided by the formulas developed by Karlström and by De Palma and Kilani.

Other welfare measures are based on the representative consumer (RC) approach. The first considers the compensation in income that equates the expected maximum utility (EMU) after the price and quality change with the EMU in the initial state. This measure is already found in the literature. Another measure can be defined based on the classical interpretation of the RC that is adopted in economic theory. The RC is the consumer whose utility maximisation problem yields the aggregate demand. The compensating variation of the RC can be computed once her indirect utility is recovered from the aggregate demand. This welfare measure is new because the RC’s indirect utility is to be found. Mathematically, the problem is equivalent to solving the system of partial differential equations which is set based on Roy’s identity. The paper fills this gap and provides for multinomial logit the closed-form expressions of the RC’s indirect utility for specification of the individual utilities of practical interest.  

The formulas of the expectation of the compensating variation require numerical integration while the two RC’s measures require only to solve a non-linear equation. Therefore, an interesting experimental question is to investigate the magnitude of the error that is made when the RC’s measures, which are easier to compute, are used to approximate the expectation of the compensating variation. The investigation is carried out with the use of a synthetic dataset generated to simulate the choice of the transport mode. The welfare change associated with road pricing policies is considered. In the case of a linear-in-income specification of the utility, the results are indicative that the two RC’s measures are a biased approximation and that the RC’s measure based on the classical interpretation has better approximation performance than the RC’s measure based on the EMU.