Econ 414 - Urban Economics

# Econ 414 - Urban Economics
## Urban Transportation
### Marcelino Guerra
### March 16-18, 2021

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# Travel time to work in the US

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# Population Density and CTA Routes

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# Commuting Time in Metro Areas

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---

# Freeway Congestion

---

# Congestion Costs

---

# Congestion Costs

.pull-left[* We fix the residential location, and commuters respond to increases in commuting costs by changing either their route to work or choosing a different time of the day

* The freeway connects the suburb to downtown, and `\(T\)` is the number of cars on the freeway

* Speed is a function of the number of commuters using the freeway at the same time

* When the number of cars reaches the threshold `\(\bar{T}\)`, there is congestion, and the speed decreases sharply as T increases beyond `\(\bar{T}\)`

]

# Congestion Costs

**To derive the connection between commuting costs and `\(T\)`**, assume the existence of a monetary cost `\(m\)` and a time cost valued at the hourly wage `\(w\)`.

* The total commute trip cost is `\(g=m+w\frac{D}{s}\)`, where `\(D\)` is the distance in miles (freeway length), and `\(s\)` is the speed per hour. Hence, `\(\frac{D}{s}\)` is the duration of the trip

.pull-left[
* When the freeway is not congested (number of drivers less than or equal `\(\bar{T}\)`), an additional commuter does not increase the commute trip. However, when `\(T>\bar{T}\)`, those additional drivers slow down everybody else, increasing their time cost `\(w\frac{D}{s}\)`
]

---
# Congestion Externality

* One can write `\(g=g(T)\)` to represent the individual commuting cost - remember `\(s\)` depends on `\(T\)`. When the freeway is congested, `\(g(T)\)` is upward sloping

* The aggregate commuting cost is `\(Tg(T)\)` (the total number of cars times the cost per car)

* To see the externality, take the derivative of the aggregate cost with respect to `\(T\)`:

`\begin{equation}
\cfrac{d}{dT}\text{(aggregate commuting cost)}=MC=\underbrace{g(T)}_\text{Cost to the driver}+\underbrace{Tg^{'}(T)}_\text{Externality}  
\end{equation}`

* The formula shows the effect of one additional car in a congested freeway on the aggregate costs. In other words, the formula shows the marginal cost `\(MC\)` of an extra car

* The aggregate cost increases due to *i)* the individual cost of the added car and *ii)* the externality damage imposed by the added car on the others

---

# Private and Social Costs

* From the formula, we know that `\(MC=g(T)+Tg^{'}(T)\)`. The average cost `\(AC\)` is the total cost `\(Tg(T)\)` divided by the number of cars `\(T\)`. Hence, `\(AC=g(T)\)`

* Rewriting the formula:

`\begin{equation}
\underbrace{MC}_\text{Social cost}=\underbrace{AC}_\text{Private cost}+\underbrace{Tg^{'}(T)}_\text{Externality} 
\end{equation}`

* Both `\(MC\)` and `\(AC\)` depends on `\(T\)`. When there is no congestion, both curves coincide. However, when there is traffic congestion, the `\(MC\)` lies above `\(AC\)` and the vertical distance between the curves is equal to the externality damage resulting from an added car
]

---
# The Demand for Freeway Use

* To commute from the suburb to downtown, the drivers have three options: train, country road, and freeway

* For each commuter, there will be a preferred route, i.e., the one that has the lowest cost. On the other hand, the cost of the freeway is the same for everyone `\(g(T)\)`

* This idea can be used to derive the individual demands. The cost of the freeway needs to be measured relative to the next best alternative (say country road/train). Then, sort drivers on the basis of their willingness to pay to use the freeway (in other words, **the alternate cost**). 
]

![](figs/demand.gif)

**As you add more and more commuters, there you have the demand curve**]

---
# Traffic Allocations

* The height up to the demand curve at `\(T=j\)` represents the willingness to pay/cost of the alternative route of commuter `\(j\)`

* In the figure, you have two curves - `\(AC\)` and `\(MC\)` - and their intersections with the Demand curve

* The equilibrium is `\(T_{eq}\)`, where the private cost `\(AC\)` intersects `\(D\)`

* The social optimum is represented by the intersection of `\(D\)` and `\(MC\)`, and it has a traffic volume of `\(T_{opt}\)`

* As you can see, `\(T_{eq}>T_{opt}\)` and the freeway is overused

]

---

# The Equilibrium

* In equilibrium, commuters 1 through `\(T_{eq}\)` use the freeway, while commuters `\(T_{eq}+1\)` through n use alternate routes

* Equilibrium means no driver has an incentive to switch routes. In other words, no commuter would be better off switching to his alternate route, and no alternate-route user would be better off switching to the freeway

* Commuter `\(T_{eq}\)` is indifferent between the freeway and his alternate route. What about commuters `\(k\)` and `\(n\)`?

]

# The Social Optimum

* The commuters do not take into account the externality damage they impose to other drivers

* The socially optimal traffic allocation minimizes the **total cost of commuting**. In other words, the socially optimal allocation is one in which total commuting costs cannot be reduced by switching any commuter between routes

* Now, commuters 1 through `\(T_{opt}\)` use the freeway, while commuters `\(T_{opt}+1\)` through n use alternate routes

* Commuters `\(T_{opt}+1\)` throgh `\(T_{eq}\)` switch from the freeway to their alternate routes

]

# The Social Optimum - Another Approach

* A different way of thinking is the following. Assume that consumers with the highest willingness to pay/alternate costs will be assigned to the freeway.

* The area below the `\(MC\)` curve represents the `\(T\)` freeway users aggregate cost. The area below the demand curve represents the alternate cost of the commuters

* Suppose `\(T=k<\bar{T}\)`, i.e., only the drivers up to `\(k\)` will use the freeway. The other drivers (from `\(k+1\)` to `\(n\)`) will use the alternative routes. Therefore, the cost of using the freeway is **E**. The cost of using the alternative routes is **Q+G+V+H**

* In this case, the total cost is **E+Q+G+V+H**
]

---
# The Social Optimum - Another Approach

.pull-left[* What are the respective areas when the cutoff is `\(T_{opt}\)`?
  * The cost of using the freeway is **E+G**
  * The alternate costs are equal to everything to the left of `\(T_{opt}\)` and under the demand curve: **V+H**
  * The total cost is **E+G+V+H**

* What are the respective areas when the cutoff is `\(T_{eq}\)`?
  * Cost of using the freeway: **E+G+V+Z**
  * Alternate cost: **H**
  * Total costs: **E+G+V+Z+H**
]

# Optimal Freeway Capacity

* When the demand curve intersects the `\(MC\)` curve, the total commuting cost is minimized, and the optimal number of drivers is `\(T_{opt}\)`

* As you can see, the optimal `\(T\)` is greater than `\(\bar{T}\)`, and there will be congestion. Therefore, forcing the `\(T\)` to be equal or lower than `\(\bar{T}\)` is not in society's interest

.pull-left[* What happens when they increase the capacity of the freeway? The curves slide over to the right, reaching a higher threshold `\(\bar{T}\)`

* Should the freeway be so large that the demand curve intersects `\(MC\)` at a point lower than `\(\bar{T}\)`? **No**, go back two slides

* The optimal-size freeway should be congested
]

---
# Optimal Freeway Capacity

.pull-left[
 
* Remember, the goal of expanding a freeway is to reduce the total commuting cost. Since it is a high investment, there must be a benefit of doing it

* Consider the slight freeway widening from `\(MC_{0}\)` to `\(MC_{1}\)`. The total commuting cost before the expansion was **G+H+I+J**

* After the expansion, the total commuting cost is **G+J**

* One needs to compare the benefits **H+I** with the cost of building new lanes

* [What if new lanes increase the demand for driving in the freeway?](https://www.resources.org/common-resources/the-fundamental-law-of-road-congestion-and-its-implications-for-transportation-policy/)
]

---

# Congestion Pricing

---
# Congestion Tolls

* The market equilibrium has too many freeway commuters since no individual has an incentive to consider the social cost of using the freeway

* The consumers only look at private costs `\(AC\)` in making decisions, and to get the optimal amount of drivers using the freeway, one needs to get the prices right

* The optimal outcome can be achieved by charging congestion tolls: **this will raise commuter's private cost `\(AC\)` until it coincides with the `\(MC\)` curve**, internalizing the externality

]

`\(\Rightarrow\)` To generate this coincidence, the toll charged needs to be equal to the height `\(e\)`, i.e., the vertical distance between `\(AC\)` and `\(MC\)` at the optimal point `\(T_{opt}\)`

]

---
# The London Congestion charge

* Concerns about London's traffic congestion in the 1990s led the Department of Transport to start research about the effects of a potential congestion charge

* The first study proposed a £4.00 toll on each trip entering Central London

* The 2000 report focused instead on an "area license": a day pass that allows vehicles to travel into and around the zone as frequently as desired for a fixed charge

* On February 17, 2003, London imposed a £5.00 daily charge for driving or parking a vehicle on public roads within the congestion charge zone between the hours of 7:00 a.m. to 6:30 p.m., Monday to Friday

* The charge was based on extensive modeling of household behavior and the resulting traffic patterns instead of a measure of the marginal cost of congestion. Other scenarios were evaluated, with charges at £2.50 and £10.00

* That charge was assumed to be accompanied by both reduced congestion and improvements in public transportation

---
# Congestion charge boundaries
<iframe src="https://www.google.com/maps/d/embed?mid=1sVykjrC54hdZ9ccqrabPliIlDaI" width="1100" height="500"></iframe>

---
# Costs and Benefits
.pull-left[
* The charge reduced traffic by 15%

* The time spent in traffic jams dropped sharply - around 30%

* Traffic level in the bordering areas fell in almost all areas after the scheme's second year. Besides, there was also an increase in the journey time reliability

* One of the congestion charges' goals was to reallocate road space from private cars to public transportation, and the number of individuals entering central London by bus rose by 38%.

]

**Source:** Jonathan Leape, JEP 2006
] 
---
# Costs and Benefits
.pull-left[ 
* The total estimated annual costs of the congestion charging scheme are £163 million, while the total annual benefits are £230 million

* The costs are a substantial fraction of the benefits
  * These high costs have raised questions about the operational efficiency of the London scheme. That also suggests the need for careful analysis before extrapolating the benefits of the congestion pricing to other cities
  
* Overall, the London congestion charge has been a success

]

]