A new paper by Jeffrey Brinkman in the Journal of Urban Economics (working version here) analyzes two phenomena that are pervasive in urban economics—congestion costs and agglomeration economies. What’s interesting about this paper is that it formalizes the tradeoff that exists between the two. As stated in the abstract:

“Congestion costs in urban areas are significant and clearly represent a negative externality. Nonetheless, economists also recognize the production advantages of urban density in the form of positive agglomeration externalities.”

Agglomeration economies is a term used to describe the benefits that occur when firms and workers are in proximity to one another. This behavior results in firm clusters and cities. In regard to the existence of agglomeration economies, economist Ed Glaeser writes:

“The concentration of people and industries has long been seen by economists as evidence for the existence of agglomeration economies. After all, why would so many people suffer the inconvenience of crowding into the island of Manhattan if there weren’t also advantages from being close to so much economic activity?”

Since congestion is a result of the high population density that is also associated with agglomeration economies, there is tradeoff between the two. Decreasing congestion costs ultimately means spreading out people and firms so that both are more equally distributed across space. Using other modes of transportation such as buses, bikes and subways may alleviate some congestion without changing the location of firms, but the examples of London and New York City, which have robust public transportation systems and a large amount of congestion, show that such a strategy has its limits.

The typical congestion analysis correctly states that workers not only face a private cost from commuting into the city, but that they impose a cost on others in the form of more traffic that slows everyone down. Since they do not consider this cost when deciding whether or not to commute the result is too much traffic.

In economic jargon, the cost to society due to an additional commuter—the marginal social cost (MSC)—is greater than the private cost to the individual—the marginal private cost (MPC). The result is that too many people commute, traffic is too high and society experiences a deadweight loss (DWL). We can depict this analysis using the basic marginal benefit/cost framework.

In this diagram the MSC is higher than the MPC line, and so the traffic that results from equating the driver’s marginal benefit (MB) to her MPC, CH, is too high. The result is the red deadweight loss triangle which reduces society’s welfare. The correct amount is C*, which is the amount that results when the MB intersects the MSC.

The economist’s solution to this problem is to levy a tax equal to the difference between the MSC and the MPC. This difference is sometimes referred to as the marginal damage cost (MDC) and it’s equal to the external cost imposed on society from an additional commuter. The tax aligns the MPC with the MSC and induces the correct amount of traffic, C*. London is one of the few cities that has a congestion charge intended to alleviate inner-city congestion.

But this analysis gets more complicated if an activity has external benefits along with external costs. In that case the diagram would look like this:

Now there is a marginal social benefit associated with traffic—agglomeration economies—that causes the marginal benefit of traffic to diverge from the benefits to society. In this case the efficient amount of traffic is C**, which is where the MSC line intersects the MSB line. Imposing a congestion tax equal to the MDC still eliminates the red DWL, but it creates the smaller blue DWL since it reduces too much traffic. This occurs because the congestion tax does not take into account the positive effects of agglomeration economies.

One solution would be to impose a congestion tax equal to the MDC and then pay a subsidy equal to the distance between the MSB and the MB lines. This would align the private benefits and costs with the social benefits and costs and lead to C**. Alternatively, since in this example the cost gap is greater than the benefit gap, the government could levy a smaller tax. This is shown below.

In this case the tax is decreased to the gap between the dotted red line and the MPC curve, and this tax leads to the correct amount of traffic since it raises the private cost just enough to get the traffic level down from CH to C**, which is the efficient amount (associated with the point where the MSB intersects the MSC).

If city officials ignore the positive effect of agglomeration economies on productivity when calculating their congestion taxes they may set the tax too high. Overall welfare may improve even if the tax is too high (it depends on the size of the DWL when no tax is implemented) but society will not be as well off as it would be if the positive agglomeration effects were taken into account. Alternatively, if the gap between the MSB and the MB is greater than the cost gap, any positive tax would reduce welfare since the correct policy would be a subsidy.

This paper reminds me that the world is complicated. While taxing activities that generate negative externalities and subsidizing activities that generate positive externalities is economically sound, calculating the appropriate tax or subsidy is often difficult in practice. And, as the preceding analysis demonstrated, sometimes both need to be calculated in order to implement the appropriate policy.