## Welfare Analysis in Transport Networks

### Authors

P Besseling, M van 't Riet, CPB Netherlands Bureau for Economic Policy Analysis, NL

### Description

User benefits in a network can be calculated on the basis of the changes in journeys or in the use of links of the network. We believe the link approach deserves rehabilitation and illustrate this with examples from actual cost-benefit analyses.

### Abstract

Should one calculate user benefits on the basis of the change in door-to-door journeys or derive them from the change in the use of each and every separate link of the networks affected? Economists mostly favour the first approach since consumers think in terms of door-to-door journeys. However, since policy measures typically involve a change in the user costs of parts of the networks, one is tempted to use the second approach.

To investigate this question we first develop a concise general equilibrium model elaborating on Kidokoro (2004, 2006). His model consists of consumers, producers, a government, a network and a congestion externality. We extend his model in two directions. First, we replace his elementary network of two routes between two nodes by a full-fledged network consisting of an undetermined number of links between an undetermined number of nodes for an undetermined number of modalities. Second, we replace his representative consumers living at a particular node by heterogeneous consumers living ?somewhere?.

In this model, the ?door-to-door journeys? are called routes, the separate parts of the networks are called links. Utility is defined as a function of the consumption of routes, not links, as it should be. Nevertheless, it turns out that in equilibrium both the demand for routes and the demand for links and the costs of using the routes and the costs of using the links all plays a role. For measuring welfare we follow the standard procedure of first deriving the expression for indirect utility. We show that indirect utility might be either cast in terms of equilibrium prices for the use of routes or cast in terms of equilibrium prices for the use of links. Then we proceed by deriving the rule-of-a-half (ROH) as an approximation for the change in the user benefits. We show that the ROH can both be evaluated in terms of the use of routes and in terms of the use of links. The two approaches yield exactly the same outcome.

This result implies that the choice for either approach does not depend on theory but on practical considerations. The link approach might give less precise outcomes in case of a new link. In that case, we propose a step-by-step approach for the new link and the most affected competing links. The routes approach lacks precision as well. Since the number of routes is sheer endless, routes always have to be aggregated into origin-destination-matrices. However, the conditions that allow for aggregation are hardly ever being met. From a real-life case, a cost-benefit analysis for a high-speed rail link between Amsterdam and Brussels, we showed that aggregation of journeys which are not perfect substitutes does indeed yield considerable measurement errors. Hence, we recommend the links approach as a complement, or even as a substitute, for the OD-matrix approach.

#### Publisher

Association for European Transport