# Paying for Roads

This is an attempt to place a lower-bound on the optimal gasoline tax. There are several reasons motorists should be taxed:

- Those who use a service should pay for it. Otherwise, the government is effectively subsidizing the service, which means it will be overprovided and an economically inefficient allocation of resources.
- Congestion is an externality road use imposes on others and should therefore be taxed. A gasoline tax reduces road use, which reduces congestion.
- Most cars burn gasoline, which release carbon dioxide, which contributes to climate change. This imposes a social cost, which should be internalized via a tax.
- Government spending on public transportation reduces congestion, which benefits drivers, meaning they should pay for part of the costs to internalize the positive externality. I'm going to ignore this, because it's hard to estimate the size of this externality.
- Traffic causes health problems Traffic Congestion and Infant Health: Evidence from E-ZPass, which I'm going to ignore owing to large uncertainty over how large these effects are.

A sharp-eyed reader will object that most of these points don't suggest taxing gasoline per-se, but rather road usage measured in hours or miles.

However, realistically, tolls are expensive Sample Tolling Scenario for Iowa US 20 in Western Iowa and widely hated, while odometer taxes are easily avoided. So we're kind of stuck taxing gasoline as an imprecise proxy for road usage. This makes it difficult to figure out the optimal amount to tax gasoline vs. to raise with tolls. However, I've mostly solve this problem from a mathematical perspective.

You can treat taxing gasoline instead of road usage as imposing a tax of $k_i \cdot t$ on each mile traveled, where $k_i$ is that person's inverse gas mileage (e.g. gallons-per-mile) and $t$ is the gasoline tax.

For some elasticity of demand for roads ($e$), value from road usage ($A$) and cost of road maintenance ($c$), we can model social welfare as
$$U = A \cdot x^{1 - 1/e} - c \cdot x $$
and the $i^{th}$ person's welfare as
$$ u_i = A \cdot x^{1 - 1/e} - k_i \cdot t \cdot x $$
From this, some calculus and algebra shows the optimal tax rate is given by
$$ t^* = c \frac{\sum_{i=1}^n{k_i^{-e}}}{\sum_{i=1}^n{k_i^{1-e}}} $$
Some friends and I have come up with an elegant proof that this implies that if we've made the decision to tax gasoline rather than use tolls, the optimal amount of gasoline tax raises should raise *more* revenue than the optimal toll would have. This makes this entire post an exercise in estimating a *lower-bound* on the optimal gasoline tax.

## Roads Costs

In 2010, state and local governments raised just \$49 billion in gasoline taxes and tolls, while they spent \$155 billion on just highways. Nationally, just 32.0% of the \$155 billion state and local governments spent on road infrastructure came from taxes and fees levied on drivers Gasoline Taxes and Tolls Pay. Once you include federal spending, that increases to 50.7% of \$183 billion. No state covers all road costs by taxing drivers Road Spending by State. So, we should raise about \$90 billion more.

## Congestion

Americans spend 4.8 billion hours in traffic each year Negative Externalities: Who Causes Traffic Congestion?. The Department of Transportation's puts the value of a human life at \$9.1 million. Since the average American has 43.4 years of life left, this suggests a year of human life should be valued at \$210,000, or \$36 per waking human hour. This implies a total cost from traffic at \$173 billion per year times $q$, where $q$ is a number between 0 and 1 measuring how bad an hour of traffic is compared to dying an hour earlier (0 = traffic is fine, 1 = traffic is death). We'll let $q=0$ for the rest of this post in keeping with trying to estimate a lower bound.

## Climate Change

CO_{2} emission has a social cost of roughly \$12 per ton Nordhaus, W., D. , and a gallon of gasoline emits 19.6 pounds of CO_{2} when burned How much carbon dioxide is produced from burning gasoline and diesel fuel?, which means that each gallon of gas should be taxed 11.8¢ to internalize that externality.

Diesel fuel emitts 22.4 pounds of CO_{2} per gallon How much carbon dioxide is produced from burning gasoline and diesel fuel?, which justifies a 13.4¢ tax per gallon.

Extrapolating from current tax policy Fuel taxes in the United States, we can estimate the total revenue from such taxes at \$8.4 billion.

## Overview

Adding this up, we find we should increase gasoline taxes by \$90 billion + \$0 billion + \$8 billion = between \$98 billion.

The US federal government taxes gasoline at 18.4¢ per gallon [24.4¢ for diesel], but state gasoline taxes increase the average tax to 49.4¢ per gallon [55.4¢ for diesel]. The taxes on gasoline and diesel raise \$35.2 billion for the federal government Fuel taxes in the United States. Since we should to raise \$98 billion more, we should increase the tax rate on gasoline by \$1.87 [that is (35.2/18.4)*98].

Of course, this assumes no change in behavior. Realistically, gasoline taxes would reduce gasoline consumption and road use, which reduces the externality of congestion and the demand for roads. However, the elasticity of gasoline is between -0.02 and -0.04 Gasoline prices tend to have little effect on demand for car travel, so this would have only affect our estimate by a tiny amount. Given current gasoline prices Weekly Retail Gasoline and Diesel Prices, we're effectively proposing increasing the price by 67%, which suggests usage would drop between 1% and 2%.

This suggests our estimate may be a little steep, but this doesn't really change the ultimate conclusion: gasoline taxes are far, far too low and we should be taxing motorists at least four times what we are now.

And keep in mind that this lower bound could be several times lower than the optimal level since we're effectively ignoring the externalities from congestion, public transit externalities, and health costs.