Tag Archives: DWL

Congestion taxes can make society worse off

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.

congestion diagram 1

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:

congestion diagram 2

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.

congestion diagram 3

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.

Ex-Im’s Deadweight Loss

To hear defenders of Ex-Im talk, you’d think that export subsidies are ALL upside and no downside. Economic theory suggests otherwise.

Clearly, some benefit from export subsidies. The most-obvious beneficiaries are the 10 or so U.S. manufacturers whose products capture the bulk of Ex-Im’s privileges (if they didn’t benefit, their “all hands on deck” public relations campaign to save the bank wouldn’t make a lot of sense).

Foreign purchasers who receive loans and loan guarantees from the bank in exchange for buying these products also clearly benefit.

The least-conspicuous beneficiaries are the private banks who finance these deals and get to offload up to 85 percent of the risk on to U.S. taxpayers. But they too clearly benefit.

Those are the upsides. But as economists are wont to say, “there is no such thing as a free lunch.”

Behind each of these beneficiaries is someone left holding the bag: there are taxpayers who bear risks that private lenders are unable or unwilling to bear. There are consumers who must pay higher prices for products that are made artificially expensive by Ex-Im subsidies. And there are other borrowers who lose out on capital because they aren’t lucky enough to have the full faith and credit of the U.S. taxpayer standing behind them.

One might be tempted to think that gains of the winners roughly offset the losses of the losers. But basic economic analysis suggests that the losses exceed the gains.

A few simple diagrams illustrate this point.

First consider any subsidy of a private (that is, excludable and rivalrous) good. Perhaps the most relevant example is a subsidy to private lenders. This is shown in the familiar supply and demand diagram shown below. The quantity of loanable funds is displayed along the horizontal axis and the price of a loan—the interest rate—is shown on the vertical axis.

People want loans to invest in their projects. We call this the “Demand for Investment.” It is shown as the blue, downward-sloping line. It is downward sloping because there are diminishing marginal returns to investment and because if you have to pay a higher interest rate, you will borrow less.

Other people have money to lend. We call this the “Supply of Savings.” It is depicted below as the solid red, upward-sloping line. It is upward sloping because there are increasing opportunity costs to lending out money and lenders must be enticed with higher and higher interest rates to lend more and more money.

The key to understanding this diagram—and this is a point that non-economists tend to find unintuitive—is that there is an optimal quantity of loans and it is not infinity. There is some point beyond which the marginal opportunity cost of further lending exceeds the marginal expected benefit from these investments.

Now consider what happens when the government guarantees the loans. Knowing that taxpayers will cover up to 85 percent of their losses, rational lenders will be willing to supply any given quantity of loans at a lower interest rate. Thus, the supply of savings shifts to the lower, dashed red line. But just because loan guarantees shield lenders from the true opportunity cost of these funds, it does not mean that the true opportunity cost goes away. In this case, taxpayers wear the risk. (For a dated but lucid explanation of the true opportunity cost associated with Ex-Im, see this Minneapolis Fed paper).

Society as a whole is made poorer because scarce resources are redirected from higher-valued uses toward lower-valued uses. In other words, those who lose end up losing more than the winners win. Economists call this “dead weight loss” (DWL). It is represented by the red triangle in the diagram below (click to enlarge).

DWL of a Subsidy

So far, this is the basic economic theory of a subsidy. But economists have developed more-specific models to understand subsidies in the context of international trade.

To get a handle on this, check out some videos by Professor Michael Moore of George Washington University. If international trade diagrams are new to you, I’d recommend looking at these diagrams before watching his videos. Then watch Professor Moore’s excellent illustration of an export subsidy in a small country, followed by the slightly more-complicated—but more relevant—case of export subsidies in a large country.

Small country case:

Large country case:

This is the basic case for free trade and it is widely accepted by economists. Some astute readers may know that there are some interesting theoretical exceptions to this rule. These exceptions derive from what are known as “strategic trade” models. They posit that in some situations—such as oligopolistic industries—governments can theoretically manage to use subsidies to make domestic firms win more than domestic consumers lose. The world is still poorer, but domestic winnings outweigh domestic losses.

These models are worth understanding. But the truth is they have not—and should not—undermine the basic economic case for free trade. The best exposition of this point is a classic piece by Paul Krugman called “Is Free Trade Passe?” In it, Krugman carefully walks the reader through the logic of these models. He then notes, quite rightly, that:

The normative conclusion that this justifies a greater degree of government intervention in trade, however, has met with sharp criticism and opposition—not least from some of the creators of the new theory themselves.

Krugman then ticks through the reasons why free trade should still be the reasonable rule of thumb. For one thing, since the strategic trade models seem to only work in oligopolistic industries, policy makers would need to know exactly how oligopolists will respond to these subsidies and the fact is “economists do not have reliable models of how oligopolists behave.” Then there is the problem of entry. Even if a government does solve the empirical problem of anticipating and accurately responding to oligopolists, it “may still not be able to raise national income if the benefits of its intervention are dissipated by entry of additional firms.”

Krugman’s final two critiques are fascinating because they are precisely the sorts of concerns a George Mason economist might raise. First, there is what Hayek might call the information problem:

[T]o pursue a strategic trade policy successfully, a government must not only understand the effects of its policy on the targeted industry, which is difficult enough, but must also understand all the industries in the economy well enough that it can judge that an advantage gained here is worth advantage lost elsewhere. Therefore, the information burden is increased even further.

And finally, there is the public choice problem. At the international level, “In many (though not all) cases, a trade war between two interventionist governments will leave both countries worse off than if a hands-off approach were adopted by both.” And at the domestic level:

Governments do not necessarily act in the national interest, especially when making detailed microeconomic interventions. Instead, they are influenced by interest group pressures. The kinds of interventions that new trade theory suggests can raise national income will typically raise the welfare of small, fortunate groups by large amounts, while imposing costs on larger, more diffuse groups. The result, as with any microeconomic policy, can easily be that excessive or misguided intervention takes place because the beneficiaries have more knowledge and influence than the losers.

To this, one could add a host of problems that arise when governments privilege particular firms or industries.

Which (finally) brings me to the bottom line: the economic case remains strong that export subsidies to domestic firms like Boeing and GE end up costing American consumers, borrowers, and taxpayers more than they end up benefiting the privileged firms.