The driver has allowed for the delay. He leaves early, takes coffee into the car, and submits his morning to the narrow interval in which a thousand other people must reach much the same place. The cost is visible to him in minutes. What he has not allowed for is the small addition his own arrival makes to all the other journeys. His car occupies road that cannot at that moment carry theirs; a little of their morning passes into his decision without entering his reckoning. Everyone in the queue can therefore have chosen sensibly for himself while helping to produce a journey that costs the company of travellers more than it is worth. The road charges in time. It sends each person only part of the bill.
The distinction is between delay experienced and delay imposed. A congestion toll is meant to supply the latter, not to charge again for the former. William Vickrey made that distinction central to his argument for road pricing: a traveller choosing a route should face the added cost his trip places on others as well as the cost he bears himself. An empty road may have virtually no congestion charge on this reasoning, even though its construction was expensive. A delivery blocking a narrow street may create a considerable charge without moving very far. The relevant scarcity is the passage denied to others at that place and time, rather than a uniform number of pennies attached to every mile.
Put the missing minutes into a deliberately simple road. Let q measure traffic over a specified period, and let c(q) be the money value of operating cost and travel time per journey. Suppose every traveller faces that same cost and each is small enough to treat the prevailing flow as given. Total travel cost is then q c(q). Another small increment adds its own cost, c(q), and raises the cost of the traffic already there by q c′(q). The second term is the congestion toll. It is not the whole cost of the new trip, nor all the delay on the road divided by its users. It is the additional burden this increment puts upon the other journeys. If flow does not raise their cost, this component of the toll is zero.
The earlier Highway gave this road numbers worth retaining because the accounts can all be followed. In its invented units, willingness to pay for the marginal trip is twenty minus the flow, while private travel cost is two plus the flow. With no toll, the two meet at nine: a trip at the margin is worth eleven and costs its traveller eleven. Yet it adds nine more to everyone else's costs. The marginal social cost is twenty, against a benefit of eleven. That last trip is privately defensible and collectively wasteful under the example's measure. Some earlier trips have the same defect in smaller degree. The problem lies in the missing term of the choice, not in a peculiar taste for sitting in traffic.
A toll of six brings the flow to six. Private travel cost is then eight, the toll is six, and the marginal trip's value is fourteen. Each of the remaining travellers faces the full incremental cost at that flow. The road remains crowded: a measure of delay is worth bearing for the journeys it makes possible. Total benefit less total resource cost rises from forty and a half to fifty-four, a gain of thirteen and a half. Driving the last car off the road would throw away beneficial journeys along with the congestion. The efficient flow here is found where another trip's worth meets the additional cost it creates, not where the road becomes empty or the authority's receipts reach their maximum.
The toll collector receives thirty-six, but thirty-six is not the gain the road has created. It is money transferred from travellers to the recipient. The real gain is the thirteen and a half produced by the changed journeys and travel costs. Indeed, before the receipts are used, travellers as a group have lost: their surplus falls from forty and a half to eighteen. Each retained traveller saves three in travel cost and pays six at the gate. The policy can therefore improve total surplus while worsening the users' position before any return of revenue. Calling the road efficient does not answer who should receive the money, which alternative service should be improved, or whether a person with little choice should bear the same charge as one with several convenient routes.
The road charges in time. The toll gives the driver the part of the bill his arrival sends to others.
A city requires the same accounting across a web of alternatives. Charge one crossing while leaving a parallel crowded street free, and the displaced traffic can impose a new cost elsewhere. A charge set by the hour can move departures, rather than merely remove trips; a departure can burden people who join the queue later as well as those already in it. The static road has suppressed these connections to make one omission visible. It does not settle the right charge for a network with a bottleneck, several modes and changing arrival times. The institution must follow the effects far enough to discover whether it has relieved the crowd or moved it beyond the charging boundary. Collection also uses resources, and a method that makes every car stop can help manufacture the delay it proposes to price.
Nor does the charge for using the road decide whether another lane should be built. Capacity has a cost in construction, maintenance and land, and the people whose houses or businesses occupy that land have claims of their own. A toll may reveal intense demand for a scarce passage; it does not establish that widening it is cheaper than improving another mode or changing the pattern of access. The inherited Club asks a related question about sharing a facility until crowding erodes the gain. A public road adds the obligations of a city: access to work, care and ordinary participation cannot be valued solely by the ease with which someone can produce money at a gate. The monetary calculation informs those obligations by showing a cost that otherwise goes unacknowledged.
The question's thousand delayed drivers need not each send an invoice. A public rule can gather their dispersed cost into the decision that produces it. In the simple road, the answer is exact: charge the added traveller for the increase in the others' travel costs, while leaving his own time in his own account. In practice the rule also needs a boundary, a clock, a collection method and a decision about the receipts. Those choices determine whether the toll is a charge for scarce passage, a device for raising money, or an expensive way of relocating a queue. The larger atmosphere has no tollgate at which its users can be counted so conveniently. The next plate follows the cost into a common space from which the person who emits cannot see where his addition will arrive.