The utility of travelling when destinations are heterogeneous: How much better is the next destination as one travels further?

In various studies (for example Golob et al., 1981, De Jong 1989), travel behaviour (for example, commuting or visiting a shop) is analysed on the basis of a utility function with the distance travelled (d) as one of the arguments. An example is U=U(d,Y-cd,T-td), (1) where Y and T are money and time budgets, and c and t are the money and time costs per unit distance. The partial derivatives of U with respect to its three arguments are assumed to be positive. As indicated by Small (1992) the theoretical foundation of this formulation is not entirely clear, however. One of the problems is that it ignores the derived character of transport: travelling kms is not an activity that gives utility per se, but only because these kms bring people to certain places they want to visit. One would have expected a formulation such as: U=U(v,Y-cd,T-td), (2) where v represents the gross utility of a visit to a certain destination at distance d. In this paper we develop a method that provides a justification for utility functions such as (1) by showing that these can be derived from formulations of type (2). The core element of our approach is that individuals compare potential destinations of their trips that are heterogeneous in terms of distance travelled and quality offered. Given the spatial distribution of destinations and the distribution of the quality of the jobs, one can derive the set of non-dominated alternatives that may serve as a destination. This non-dominated set is essentially a monotone relationship between distance travelled and utility of the trip. Examples of this curve are given under various assumptions concerning the spatial density of destinations and urban form. Implications of this approach are discussed for commuting distances of different types of jobs. Our approach gives an explanation for the paradox that highly educated workers tend to have long commuting distances. Given their high value of time one would expect short commuting distances, but the low spatial density of their jobs appears to dominate the outcome.