A note on Sydney toll relief

It is excellent that the government plans to assist people affected by the growing cost of tolls in Sydney. The proposed mechanism offers toll users a maximum of $60 per week. Beyond this $60 cap toll, users will not pay anything every week when they use the Sydney toll system.

The toll relief is proposed for two years with a budget of around half a billion dollars. The maximum benefit per user is capped at $400 per week, which means a $340 benefit per week. The expected number of users who benefit from the scheme is approximately 700,000. Therefore, given the budget, the average benefit per user would be around $750 for the entire life of the scheme. This $750 ($375 per year) is negligible compared to the claimed aim of $340 per week. It is then unclear how the scheme can assist the users with objective cost assistance.

Beyond the scheme's financial feasibility, some unpleasant travel behaviour consequences will likely emerge, defeating the scheme's purposes. I use a simple transport network example to illustrate these consequences.

This example is a highly simplified example for demonstration purposes. Consider a network from an origin (e.g., Paramatta) with a demand of 11 (people, trips, or vehicles) to a destination (e.g., Sydney). There are three parallel paths between the two nodes. One is public transport with a fixed cost of $1 and travel time equal to Flow+6. Therefore, travel time increases by one unit for every user using the service. There is a fast toll road with a travel time of flow plus 2 and a cost of 4 dollars. There is a local road that is free and slow, with the travel time being equal to two times the flow plus one. The following diagram shows the network.

Once the demand of 11 is assigned to the network, we end up having 3 trips for the toll road, 4 trips on the local road, and 2 trips on the public transport. The generalised cost on all used paths between the origin and the destination is $9. There is a link between the origin and the destination, representing trips that are not generated but could be induced had the travel cost reduced, given a potential utility of $9 at the destination. Most likely, these trips are leisure trips and not mandatory.   

If we decide to reduce the toll cost to $3, an interesting situation occurs. The following diagram presents the new equilibrium conditions under which no one can unilaterally change their selected path.

By reducing the cost of the toll system, we see that one of those trips that were not made is now induced. An unpleasant but exciting finding is that all paths still have the generalised cost of $9. However, the toll road is more congested, with increased flow and consequent travel time.

In the next scenario, we make the network a bit complicated by introducing two classes of toll users. Some users are normal users as before. A new class is defined as those who benefit from a toll relief mechanism. The diagram representing the situation is presented below.

The results of this scenario are similar to the previous scenario, with one point to be highlighted: the total flow on the toll road is the sum of both classes of toll users. Therefore, travel time is the total flow of the toll road plus 2.  In this scenario, we end up having no toll user who is willing to pay $4 to use the toll, which means everybody will try to join the discounted scheme. Therefore, all used paths still have the generalised cost of 9$.

Now, if we make the discounted toll system cheaper by $1, another trip is induced, making the toll system more congested. The total travel time of the toll system is 7, while the generalised cost of all paths is still $9. In this scenario, nobody is still using the normal toll scheme.

Now, let's significantly discount the cost of the toll system to $1. The results are shown in the following diagram.  

In this scenario, the discounted toll system attracts some flow from the non-toll and also from the public transport system. In the real world, if this scenario is kept in place for an extended period (2 years is already long enough), some people not living at the origin may feel that the generalised cost of residing at the origin and working at the destination is low and decide to relocate their home to the origin zone. If this phenomenon occurs, it will be extremely hard to reverse it because housing relocation shapes land use with complicated implications for other choices of people, such as school location. We may end up having higher demand at the origin, causing more congestion on roads connecting the two zones. Further, people switching to auto from public transport for the period of the discount scheme might develop the habit of using auto, which might make it hard again to shift them to public transport, causing long-term impacts on externalities of congestion in the transport system.

The last scenario is an attempt to make our notoriously simplified example more similar to one in which some people receive discounted toll relief and are the ones inducing demand. In this scenario, only those inducing demand are considered toll road users with a discounted rate of $1. The following diagram shows the results of this scenario.

In this scenario, the two induced trips belong to those who have reached the toll cap and now pay a discounted toll amount (we could consider $0, but we kept it as $1 to make it similar to the previous example).

Interestingly, the generalised cost of toll users with a discount is $6.8, significantly lower than the other used paths. In this scenario, due to the high cost of the toll system ($4), we still have 3.8 trips on the toll system, making the toll road more congested than in the first scenario (3 trips). Please note that two of these trips are induced by people who might have capped their toll to benefit from the discount scheme. The local road and bus system are now more congested. Nonetheless, some of these users may need to start not doing their activity because the hyper path of staying home (cost of 9+) is now better than making the trip. In other words, a potential leisure activity giving the utility of 9 units may discourage people from making a trip at the cost of 9.8 unless they have to. In other words, in the last scenario, some people induce trips that are not essential, forcing others to pay more for what they used to use or give up travelling.