178DAVID A. HENSHER(Deaton & Muellbauer, 1980, p. 69; Blundell, 1988; Theil, 1975, p. 197) and prevails most clearly between close substitutes. Such aggregate studies do not account for the range of prices across a service and across individuals. An aggregate demand model for bus travel does not usually differentiate between the services available within the mode by ticket type, location of travel and time of the day. Furthermore, it is often assumed that the representative service has a unique price applying to every individual riding on that mode. In reality, there is an array of services to meet individual needs and choices and each of these services has its own price. Discrete choice models take advantage of the variety of trip attributes faced by consumers. Even with the coarsely graduated fares of public transit, there are many options. Added to this is the truly individual cost of service by the private car. To keep the experiment and sample to a manageable size, the public transport ticket categories have been collapsed to those most frequently used, while private vehicles have been modelled as one service. For each service, respondents faced personalised costs, which varied across the sample. However, as with aggregate studies, demand and revenue evaluation of pricing policies must still be based on a representative price for each service. In the case of discrete choice estimates made with either the HEV or multinomial logit (MNL) models, the probabilities of individual q choosing modes i and j with respect to the utility of fares or costs of i and j are symmetric @Piq @Pjp @V jq @V iq (11.6)The aggregate share elasticity is equal to the ordinary elasticity where no generation effect is assumed and is deed as the probability weighted average of individual elasticities (Ben-Akiva & Lerman, 1985, p. 112; Hensher & Johnson, 1981, p. 59). The partial derivative of the individual probability is written with respect to the systematic component of the individual utility P bc Piq @Piq @V jq cjq Piq q P ij mij (11.7) PiqqLetci ciq 8q be a uniform cost of using service i:(11.8)
