The Shortcut Tax
Every driver takes the quickest route.
Everyone can still arrive later.
One destination. Two ways there.
Width shows flow. Arrows show direction. Select a road to change its cost.
A shortcut has a season.
Change the crowd, and the same road can help, hurt, or stop being used.
Finding the interval…
Who shares the bottleneck?
Bring another neighbourhood onto the roads. A collective gain can hide who pays for it.
The second origin preset also makes A → D congestible. Both groups then change each other's quickest routes.
S → A
t(x) = 0 + 10x
Each road takes a fixed time plus extra minutes for every flow unit using it.
The time you take. The time you cause.
On a crowded road, one more driver delays everyone already there.
For t(x) = a + bx, the next driver feels a + bx minutes, but adds a + 2bx to total travel. The difference, bx, is the delay imposed on others.
Set each toll to that difference at the coordinated flow. Self-interested choices then reproduce the minimum total travel. Tolls below are expressed in equivalent minutes; money, revenue and affordability are outside this model.
| Road | Flow | Travel | Delay imposed marginal toll | Total marginal cost |
|---|
Inspect route flows and the equilibrium certificate
| Route | Flow | Travel minutes | Cost used to choose |
|---|