A key issue in establishing the validity of travel choice models for economic appraisal is whether or not they adhere to the so-called integrability conditions. These conditions ensure that, for any system of demand functions involving a symmetric negative semi-definite substitution matrix, there necessarily exists an underlying utility function from which the demandfunctions can be derived. In short, the integrability conditions ensure that a given observed pattern of demand is consistent with economic theory.Conventionally, these integrability conditions exploit continuous demand theory, wherein preferences are defined on a continuous commodity space. Indeed the integrability conditions are based on the partial derivatives ofHicksian demand functions with respect to price and income, and thus appeal to smooth and continuous demand functions. Travel choice models may be seen as special case of continuous demand theory, such that choice is restricted to a finite and exhaustive subset of the commodity space, and this provokes some challenges in translating the conventional integrability conditions. The definitive contribution in this regard is McFadden (1981), who considers the applicability of the integrability conditions to a random utility maximisation (RUM) framework. This study seeks to promote deeper understanding of McFaddens analysis by repeating his derivation from first principles, and annotating this derivation with commentary throughout. It then extends the analysis beyond the scope of McFaddens and reports on thefindings. For the covering abstract see ITRD E145999
Samenvatting