Urban Economics

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.title[
# Urban Economics
]
.subtitle[
## Urban Sprawl and Land-Use Controls
]
.author[
### Hussain Hadah (he/him)
]
.date[
### 16 November 2025
]

---

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<div style="position: absolute;left:20px;bottom:5px;color:black;font-size: 12px;">Hussain Hadah (he/him) (Tulane) | Urban Sprawl and Land-Use Controls | 16 November 2025</div>

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# .text-shadow[.white[Outline for Today]]

<ol>
    <li><h4 class="white"> Evidence on City Sprawl</h4></li>
    <li><h4 class="white"> Market Failures Leading to Sprawl</h4></li>
    <li><h4 class="white"> Land-Use Controls to Limit Sprawl</h4></li>
</ol>

---
## Next week <svg viewBox="0 0 448 512" style="height:1em;display:inline-block;position:fixed;top:10;right:10;" xmlns="http://www.w3.org/2000/svg">  <path d="M0 464c0 26.5 21.5 48 48 48h352c26.5 0 48-21.5 48-48V192H0v272zm64-192c0-8.8 7.2-16 16-16h288c8.8 0 16 7.2 16 16v64c0 8.8-7.2 16-16 16H80c-8.8 0-16-7.2-16-16v-64zM400 64h-48V16c0-8.8-7.2-16-16-16h-32c-8.8 0-16 7.2-16 16v48H160V16c0-8.8-7.2-16-16-16h-32c-8.8 0-16 7.2-16 16v48H48C21.5 64 0 85.5 0 112v48h448v-48c0-26.5-21.5-48-48-48z"></path></svg>

### Readings

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# Introduction

---
## Urban sprawl has been drawing strong feelings <svg viewBox="0 0 496 512" style="height:1em;display:inline-block;position:fixed;top:10;right:10;" xmlns="http://www.w3.org/2000/svg">  <path d="M248 8C111 8 0 119 0 256s111 248 248 248 248-111 248-248S385 8 248 8zm0 448c-110.3 0-200-89.7-200-200S137.7 56 248 56s200 89.7 200 200-89.7 200-200 200zm0-144c-33.6 0-65.2 14.8-86.8 40.6-8.5 10.2-7.1 25.3 3.1 33.8s25.3 7.2 33.8-3c24.8-29.7 75-29.7 99.8 0 8.1 9.7 23.2 11.9 33.8 3 10.2-8.5 11.5-23.6 3.1-33.8-21.6-25.8-53.2-40.6-86.8-40.6zm-48-72c10.3 0 19.9-6.7 23-17.1 3.8-12.7-3.4-26.1-16.1-29.9l-80-24c-12.8-3.9-26.1 3.4-29.9 16.1-3.8 12.7 3.4 26.1 16.1 29.9l28.2 8.5c-3.1 4.9-5.3 10.4-5.3 16.6 0 17.7 14.3 32 32 32s32-14.4 32-32.1zm199-54.9c-3.8-12.7-17.1-19.9-29.9-16.1l-80 24c-12.7 3.8-19.9 17.2-16.1 29.9 3.1 10.4 12.7 17.1 23 17.1 0 17.7 14.3 32 32 32s32-14.3 32-32c0-6.2-2.2-11.7-5.3-16.6l28.2-8.5c12.7-3.7 19.9-17.1 16.1-29.8z"></path></svg>

.pull-left[
### Critics say:

- Increases traffic congestion and pollution <svg viewBox="0 0 640 512" style="height:1em;position:relative;display:inline-block;top:.1em;" xmlns="http://www.w3.org/2000/svg">  <path d="M143.25 220.81l-12.42 46.37c-3.01 11.25-3.63 22.89-2.41 34.39l-35.2 28.98c-6.57 5.41-16.31-.43-14.62-8.77l15.44-76.68c1.06-5.26-2.66-10.28-8-10.79l-77.86-7.55c-8.47-.82-11.23-11.83-4.14-16.54l65.15-43.3c4.46-2.97 5.38-9.15 1.98-13.29L21.46 93.22c-5.41-6.57.43-16.3 8.78-14.62l76.68 15.44c5.26 1.06 10.28-2.66 10.8-8l7.55-77.86c.82-8.48 11.83-11.23 16.55-4.14l43.3 65.14c2.97 4.46 9.15 5.38 13.29 1.98l60.4-49.71c6.57-5.41 16.3.43 14.62 8.77L262.1 86.38c-2.71 3.05-5.43 6.09-7.91 9.4l-32.15 42.97-10.71 14.32c-32.73 8.76-59.18 34.53-68.08 67.74zm494.57 132.51l-12.42 46.36c-3.13 11.68-9.38 21.61-17.55 29.36a66.876 66.876 0 0 1-8.76 7l-13.99 52.23c-1.14 4.27-3.1 8.1-5.65 11.38-7.67 9.84-20.74 14.68-33.54 11.25L515 502.62c-17.07-4.57-27.2-22.12-22.63-39.19l8.28-30.91-247.28-66.26-8.28 30.91c-4.57 17.07-22.12 27.2-39.19 22.63l-30.91-8.28c-12.8-3.43-21.7-14.16-23.42-26.51-.57-4.12-.35-8.42.79-12.68l13.99-52.23a66.62 66.62 0 0 1-4.09-10.45c-3.2-10.79-3.65-22.52-.52-34.2l12.42-46.37c5.31-19.8 19.36-34.83 36.89-42.21a64.336 64.336 0 0 1 18.49-4.72l18.13-24.23 32.15-42.97c3.45-4.61 7.19-8.9 11.2-12.84 8-7.89 17.03-14.44 26.74-19.51 4.86-2.54 9.89-4.71 15.05-6.49 10.33-3.58 21.19-5.63 32.24-6.04 11.05-.41 22.31.82 33.43 3.8l122.68 32.87c11.12 2.98 21.48 7.54 30.85 13.43a111.11 111.11 0 0 1 34.69 34.5c8.82 13.88 14.64 29.84 16.68 46.99l6.36 53.29 3.59 30.05a64.49 64.49 0 0 1 22.74 29.93c4.39 11.88 5.29 25.19 1.75 38.39zM255.58 234.34c-18.55-4.97-34.21 4.04-39.17 22.53-4.96 18.49 4.11 34.12 22.65 39.09 18.55 4.97 45.54 15.51 50.49-2.98 4.96-18.49-15.43-53.67-33.97-58.64zm290.61 28.17l-6.36-53.29c-.58-4.87-1.89-9.53-3.82-13.86-5.8-12.99-17.2-23.01-31.42-26.82l-122.68-32.87a48.008 48.008 0 0 0-50.86 17.61l-32.15 42.97 172 46.08 75.29 20.18zm18.49 54.65c-18.55-4.97-53.8 15.31-58.75 33.79-4.95 18.49 23.69 22.86 42.24 27.83 18.55 4.97 34.21-4.04 39.17-22.53 4.95-18.48-4.11-34.12-22.66-39.09z"></path></svg>
- Consumes too much land <svg viewBox="0 0 384 512" style="height:1em;position:relative;display:inline-block;top:.1em;" xmlns="http://www.w3.org/2000/svg">  <path d="M378.31 378.49L298.42 288h30.63c9.01 0 16.98-5 20.78-13.06 3.8-8.04 2.55-17.26-3.28-24.05L268.42 160h28.89c9.1 0 17.3-5.35 20.86-13.61 3.52-8.13 1.86-17.59-4.24-24.08L203.66 4.83c-6.03-6.45-17.28-6.45-23.32 0L70.06 122.31c-6.1 6.49-7.75 15.95-4.24 24.08C69.38 154.65 77.59 160 86.69 160h28.89l-78.14 90.91c-5.81 6.78-7.06 15.99-3.27 24.04C37.97 283 45.93 288 54.95 288h30.63L5.69 378.49c-6 6.79-7.36 16.09-3.56 24.26 3.75 8.05 12 13.25 21.01 13.25H160v24.45l-30.29 48.4c-5.32 10.64 2.42 23.16 14.31 23.16h95.96c11.89 0 19.63-12.52 14.31-23.16L224 440.45V416h136.86c9.01 0 17.26-5.2 21.01-13.25 3.8-8.17 2.44-17.47-3.56-24.26z"></path></svg>
- Less incentives to develop downtown areas <svg viewBox="0 0 640 512" style="height:1em;position:relative;display:inline-block;top:.1em;" xmlns="http://www.w3.org/2000/svg">  <path d="M616 192H480V24c0-13.26-10.74-24-24-24H312c-13.26 0-24 10.74-24 24v72h-64V16c0-8.84-7.16-16-16-16h-16c-8.84 0-16 7.16-16 16v80h-64V16c0-8.84-7.16-16-16-16H80c-8.84 0-16 7.16-16 16v80H24c-13.26 0-24 10.74-24 24v360c0 17.67 14.33 32 32 32h576c17.67 0 32-14.33 32-32V216c0-13.26-10.75-24-24-24zM128 404c0 6.63-5.37 12-12 12H76c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm0-96c0 6.63-5.37 12-12 12H76c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm0-96c0 6.63-5.37 12-12 12H76c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm128 192c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm0-96c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm0-96c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm160 96c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm0-96c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm0-96c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12V76c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm160 288c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm0-96c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40z"></path></svg>
- Low density sprawl reduces social interaction <svg viewBox="0 0 576 512" style="height:1em;position:relative;display:inline-block;top:.1em;" xmlns="http://www.w3.org/2000/svg">  <path d="M96,128A64,64,0,1,0,32,64,64,64,0,0,0,96,128Zm0,176.08a44.11,44.11,0,0,1,13.64-32L181.77,204c1.65-1.55,3.77-2.31,5.61-3.57A63.91,63.91,0,0,0,128,160H64A64,64,0,0,0,0,224v96a32,32,0,0,0,32,32V480a32,32,0,0,0,32,32h64a32,32,0,0,0,32-32V383.61l-50.36-47.53A44.08,44.08,0,0,1,96,304.08ZM480,128a64,64,0,1,0-64-64A64,64,0,0,0,480,128Zm32,32H448a63.91,63.91,0,0,0-59.38,40.42c1.84,1.27,4,2,5.62,3.59l72.12,68.06a44.37,44.37,0,0,1,0,64L416,383.62V480a32,32,0,0,0,32,32h64a32,32,0,0,0,32-32V352a32,32,0,0,0,32-32V224A64,64,0,0,0,512,160ZM444.4,295.34l-72.12-68.06A12,12,0,0,0,352,236v36H224V236a12,12,0,0,0-20.28-8.73L131.6,295.34a12.4,12.4,0,0,0,0,17.47l72.12,68.07A12,12,0,0,0,224,372.14V336H352v36.14a12,12,0,0,0,20.28,8.74l72.12-68.07A12.4,12.4,0,0,0,444.4,295.34Z"></path></svg>
- Dependence on automobiles increases obesity rates
]

.pull-right[
### The data shows:
- Spatial growth was really high---from 1.3% to 1.9% of land area got developed from 1976 to 1992 (Burchfield et al., 2006) <svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;" xmlns="http://www.w3.org/2000/svg">  <path d="M496 384H64V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-32c0-8.84-7.16-16-16-16zM464 96H345.94c-21.38 0-32.09 25.85-16.97 40.97l32.4 32.4L288 242.75l-73.37-73.37c-12.5-12.5-32.76-12.5-45.25 0l-68.69 68.69c-6.25 6.25-6.25 16.38 0 22.63l22.62 22.62c6.25 6.25 16.38 6.25 22.63 0L192 237.25l73.37 73.37c12.5 12.5 32.76 12.5 45.25 0l96-96 32.4 32.4c15.12 15.12 40.97 4.41 40.97-16.97V112c.01-8.84-7.15-16-15.99-16z"></path></svg>
- Other sources show that the rate is even higher
]

As a result, many cities have implemented land-use controls to limit sprawl

---
## Growth management policies to control urban sprawl <svg viewBox="0 0 640 512" style="height:1em;display:inline-block;position:fixed;top:10;right:10;" xmlns="http://www.w3.org/2000/svg">  <path d="M616 192H480V24c0-13.26-10.74-24-24-24H312c-13.26 0-24 10.74-24 24v72h-64V16c0-8.84-7.16-16-16-16h-16c-8.84 0-16 7.16-16 16v80h-64V16c0-8.84-7.16-16-16-16H80c-8.84 0-16 7.16-16 16v80H24c-13.26 0-24 10.74-24 24v360c0 17.67 14.33 32 32 32h576c17.67 0 32-14.33 32-32V216c0-13.26-10.75-24-24-24zM128 404c0 6.63-5.37 12-12 12H76c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm0-96c0 6.63-5.37 12-12 12H76c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm0-96c0 6.63-5.37 12-12 12H76c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm128 192c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm0-96c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm0-96c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm160 96c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm0-96c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm0-96c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12V76c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm160 288c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40zm0-96c0 6.63-5.37 12-12 12h-40c-6.63 0-12-5.37-12-12v-40c0-6.63 5.37-12 12-12h40c6.63 0 12 5.37 12 12v40z"></path></svg>

### At least 12 states have growth management policies

### New Jersey committed in 1998 to spend $1 billion to purchase vacant land to limit

---
## Do the critics have a point? <svg viewBox="0 0 384 512" style="height:1em;display:inline-block;position:fixed;top:10;right:10;" xmlns="http://www.w3.org/2000/svg">  <path d="M202.021 0C122.202 0 70.503 32.703 29.914 91.026c-7.363 10.58-5.093 25.086 5.178 32.874l43.138 32.709c10.373 7.865 25.132 6.026 33.253-4.148 25.049-31.381 43.63-49.449 82.757-49.449 30.764 0 68.816 19.799 68.816 49.631 0 22.552-18.617 34.134-48.993 51.164-35.423 19.86-82.299 44.576-82.299 106.405V320c0 13.255 10.745 24 24 24h72.471c13.255 0 24-10.745 24-24v-5.773c0-42.86 125.268-44.645 125.268-160.627C377.504 66.256 286.902 0 202.021 0zM192 373.459c-38.196 0-69.271 31.075-69.271 69.271 0 38.195 31.075 69.27 69.271 69.27s69.271-31.075 69.271-69.271-31.075-69.27-69.271-69.27z"></path></svg>

<br>

### Do cities take up too much space?

<br>

### Should they implement land-use controls to limit sprawl?

---
class: segue-yellow
background-image: url("assets/TulaneLogo.svg")
background-size: 20%
background-position: 95% 95%

# The Empirical Evidence

---
## This table shows the results from two papers

#### The results tells us if X increases by 1 percent, Y increases by how much percent?

#### Both studies show that higher population leads to more land use

- 1 percent increase in population leads to 1.1 and 0.76 percent increase in land use

#### Income effects are large: 1 percent increase in income leads to 1.5 and 0.3 percent increase in land use

#### Higher agricultural rent leads to less land use, mixed evidence on the effect of commuting costs

---
## It is easy to see why urban sprawl happens in the US

<br>

### So, if we are growing in population and getting richer, is it bad that we are sprawling out?

<br>

### Well, it depends

### If this sprawl is being driven by consumer preferences, then it is .brand-mardigras[not a problem]

### However, if sprawl is being driven by market failures, then it is a .brand-crawfest[problem]

---
## Market failures related present in economic process that determines size of cities

<br>

### 1. The amenity value of open space

<br>

- Assume each acre of open space provides `$\mathbf{b}$` dollars above and beyond its agricultural value
- This benefit is not captured when land is converted from agricultural to urban use
- A landowner can either rent the land to a developer `$\mathbf{r}$` rent it out to a farmer `$\mathbf{r_a}$`
- If `$\mathbf{r}$` > `$\mathbf{r_a}$`, the land will be developed
- Society would ideally want the landowner to take into account the amenity value `$\mathbf{b}$`
- So society would want the land developed only if `$\mathbf{r} + \mathbf{b}$` > `$\mathbf{r_a}$` `$\Rightarrow$` city boundary rent should be `$\mathbf{r} = \mathbf{r_a} - \mathbf{b}$`

---
## Socially optimal effect agricultural rent

<br>

### 1. The amenity value of open space

<br>

- So a optimal city size would emerge if the rent is `$\mathbf{r} = \mathbf{r_a} - \mathbf{b}$`, which includes the amenity value of open space

.pull-left[
<img src="01-class_files/figure-html/unnamed-chunk-3-1.png" width="70%" style="display: block; margin: auto;" />
]

.pull-right[
  - How do we get from `$x_0$` to `$x_1$`?
  - By implementing land-use controls that limit development
  - Imposing a development tax
]

---
## This model assumes that people value open space and the government knows the value

<br>

### Is this realistic?

#### It is not hard to imagine that the person designing anti-sprawl policies might reach a value that is larger than that of the average person

#### This could lead to reducing dwelling sizes and make living in the city more costly (people do not value the open space that is saved)

#### So land-use controls could lead to a loss in welfare if the value of open space is overestimated

---
## Market failures related present in economic process that determines size of cities

<br>

### 2. The market failure related to traffic congestion <svg viewBox="0 0 512 512" style="height:1em;display:inline-block;position:fixed;top:10;right:10;" xmlns="http://www.w3.org/2000/svg">  <path d="M499.99 176h-59.87l-16.64-41.6C406.38 91.63 365.57 64 319.5 64h-127c-46.06 0-86.88 27.63-103.99 70.4L71.87 176H12.01C4.2 176-1.53 183.34.37 190.91l6 24C7.7 220.25 12.5 224 18.01 224h20.07C24.65 235.73 16 252.78 16 272v48c0 16.12 6.16 30.67 16 41.93V416c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32v-32h256v32c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32v-54.07c9.84-11.25 16-25.8 16-41.93v-48c0-19.22-8.65-36.27-22.07-48H494c5.51 0 10.31-3.75 11.64-9.09l6-24c1.89-7.57-3.84-14.91-11.65-14.91zm-352.06-17.83c7.29-18.22 24.94-30.17 44.57-30.17h127c19.63 0 37.28 11.95 44.57 30.17L384 208H128l19.93-49.83zM96 319.8c-19.2 0-32-12.76-32-31.9S76.8 256 96 256s48 28.71 48 47.85-28.8 15.95-48 15.95zm320 0c-19.2 0-48 3.19-48-15.95S396.8 256 416 256s32 12.76 32 31.9-12.8 31.9-32 31.9z"></path></svg>

<br>

### Why congestion is a market failure

- Each additional car on a congested road **slows down all other drivers**  
- Drivers bear only their **private commuting cost**, not the **external delay** they cause
- Result: The **private cost < social cost**, leading to **too much driving** and **excessively large cities**

---
## The Congestion Externality

- The *externality* arises because a single extra car increases travel time for all others
- Each driver’s additional time loss is small, but **summed across all drivers**, the total cost is **non-negligible**
- No individual driver has the incentive to account for this social cost
- Thus:
  - Commuting decisions are distorted  
  - City size is **too large** in the free-market equilibrium

---
## The Effect on Urban Spatial Structure

.pull-left[
### Without congestion tolls:
- Commuting is **too cheap**
- Residents are willing to live farther away
- The equilibrium city radius would be **larger than optimal**
]

.pull-right[
### With congestion tolls:
- Higher commuting cost → shorter optimal commutes
- Population locates **closer to the center**
- The city becomes **more compact**
]

---
## Congestion Tolls as a Policy Tool

### What the toll should equal:

- A congestion toll must equal the **external cost** a driver imposes on others  
- When this toll is charged:
  - Commuters internalize the full social cost  
  - Traffic volumes fall  
  - The **city shrinks to the efficient size**

### Key insight:
**Tolls make the market mimic the social optimum.**

---
## Evidence from Real-World Congestion Pricing

### Cities implementing congestion pricing:

- **Singapore** (one of the earliest and most comprehensive systems)  
- **London** (central-city cordon charge)  
- **Stockholm** (peak-hour bridge tolls)
- **New York City** just did this!

### What studies find:
- After toll adoption, cities become **more compact**
- Residents choose **shorter commuting distances**
- Urban models correctly predict **declines in city size** when tolls are introduced

---
## From the News

---
## Welfare Effects of Correcting Congestion Externalities

- By increasing the cost of commuting, tolls:
  - Reduce excessive driving  
  - Align **private** and **social** commuting costs  
  - Lead to **higher welfare** than the no-toll equilibrium

- Since congestion makes free-market cities **too large**,  
  **charging congestion tolls moves the city toward the socially optimal spatial size.**

---
class: segue-yellow
background-image: url("assets/TulaneLogo.svg")
background-size: 20%
background-position: 95% 95%

# Land-Use Controls: Policies

---
## Using Land-Use Controls to Attack Sprawl <svg viewBox="0 0 576 512" style="height:1em;display:inline-block;position:fixed;top:10;right:10;" xmlns="http://www.w3.org/2000/svg">  <path d="M560.02 32c-1.96 0-3.98.37-5.96 1.16L384.01 96H384L212 35.28A64.252 64.252 0 0 0 191.76 32c-6.69 0-13.37 1.05-19.81 3.14L20.12 87.95A32.006 32.006 0 0 0 0 117.66v346.32C0 473.17 7.53 480 15.99 480c1.96 0 3.97-.37 5.96-1.16L192 416l172 60.71a63.98 63.98 0 0 0 40.05.15l151.83-52.81A31.996 31.996 0 0 0 576 394.34V48.02c0-9.19-7.53-16.02-15.98-16.02zM224 90.42l128 45.19v285.97l-128-45.19V90.42zM48 418.05V129.07l128-44.53v286.2l-.64.23L48 418.05zm480-35.13l-128 44.53V141.26l.64-.24L528 93.95v288.97z"></path></svg>

### Two main anti-sprawl policies discussed:

1. **Development tax**  
   - Price-based instrument  
   - Internalizes the open-space externality (amenity benefits)

2. **Congestion toll**  
   - Corrects the congestion externality  
   - Shrinks the city by raising effective commuting costs

---

## Urban Growth Boundary (UGB)

### What is a UGB?

- A **quantity-based** anti-sprawl instrument  
- Government sets a maximum city radius `$\bar{x}_1$`  
- Development outside this boundary is prohibited

### Key point:
> A UGB can replicate the **same effect** as a development tax *if set at the optimal radius `$\bar{x}_1$`.

- In the model, restricting development at `$\bar{x}_1$`  produces the same land-rent curve shift as imposing a per-acre development tax `$b$`.

---

## Why UGBs Can Be Problematic

- A UGB limits **land area**, not commuting decisions
- Thus, it corrects the symptom (too much land consumption), not the cause (externality)
- When the externality is **traffic congestion**, a UGB **cannot substitute** for a congestion toll

### Important distinction:
- A development tax fixes the underlying externality  
- A UGB **mimics the outcome** only in the open-space amenity case  
- But it **fails** in the congestion case because it does not change commuting incentives

---

## UGBs and Consumer Welfare

### When UGBs can reduce welfare:

- If average consumers do **not** value preserved open space highly
- Limiting housing supply increases:
  - **Land rents**
  - **Housing prices**
  - **Density**
  - **Living costs**

### Policy implication:
> UGBs should be used with caution because the welfare costs may exceed the benefits.

---
## Let's plot this out

.pull-left[
- Assume landowners act as a group, so all they care about is rent

- The government restricts land use at `$\bar{x}_1 < \bar{x}_0$`

- Land between `$\bar{x}_1$` and `$\bar{x}_0$` earns rent `$r_a$`  instead of `$r_0$` and they lose area `$V$`
- Land inside `$\bar{x}_1$` earns rent `$r_1$` instead of `$r_0$` and they gain area `$S$`
- If `$S > V$`, land rent rises and landowners benefit
- Similar models that apply to homeowners would show that they benefit as well by increasing their property values
]

.pull-right[

<img src="assets/image06.jpg" width="100%" style="display: block; margin: auto;" />
]

---

## A Motive for UGBs: Landowner Gain

### Political economy explanation

- Landowners **gain** when UGB raises land rents inside boundary
  - Restricting city size shifts the rent curve up  
  - Generates rent gains represented by area **S**  
  - These gains accrue to landowners

- As long as the rent gain **S > V** (the loss outside the boundary), landowners push for tighter UGBs

### Result:
UGBs may be adopted **not** for efficiency reasons, but because landowners benefit financially.

## Additional Motives for UGBs

- Some motivations are **not** about market failures:
  - Desire to boost housing capital gains  
  - Local political pressure to preserve aesthetics or neighborhood character  
  - Resistance to density and “undesirable” growth

### Key point:
> Policies may be driven by politics, not economics.

---

## Building-Height and Density Restrictions <svg viewBox="0 0 448 512" style="height:1em;display:inline-block;position:fixed;top:10;right:10;" xmlns="http://www.w3.org/2000/svg">  <path d="M128 148v-40c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40c0 6.6-5.4 12-12 12h-40c-6.6 0-12-5.4-12-12zm140 12h40c6.6 0 12-5.4 12-12v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12zm-128 96h40c6.6 0 12-5.4 12-12v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12zm128 0h40c6.6 0 12-5.4 12-12v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12zm-76 84v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm76 12h40c6.6 0 12-5.4 12-12v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12zm180 124v36H0v-36c0-6.6 5.4-12 12-12h19.5V24c0-13.3 10.7-24 24-24h337c13.3 0 24 10.7 24 24v440H436c6.6 0 12 5.4 12 12zM79.5 463H192v-67c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v67h112.5V49L80 48l-.5 415z"></path></svg>

.pull-left[
### Height limits:

- Many cities impose max building heights or Floor Area Ratio (FAR) limits  
- Examples:
  - Washington, DC  
  - Paris  
  - Barcelona
  - Huntsville, AL
]

.pull-right[

### Effect in the urban model:

- Lower allowed FAR leads to:
  - Smaller buildings in the city center  
  - Housing becomes more expensive  
  - Residents consume smaller dwellings  
  - City expands spatially → **more sprawl**

]

### Takeaway:
Building-height limits **increase** sprawl by reducing density where people most want to live.

---

## FAR Restrictions: Model Implications

- When FAR is restricted:
  - It restricts the height of buildings in the city where otherwise they would be tallest
  - Housing prices `$p$` increase  
  - Land rents `$r$` increase  
  - The city’s boundary `$\bar{x}$` expands  
  - Dwellings get smaller  
  - Outer areas see **taller buildings** (nonbinding FAR)

### Irony:
Policies intended to reduce density at the core **increase overall sprawl**.

---

---

## Zoning Laws

.pull-left[
### Most pervasive land-use control in U.S.

- Separate land uses into zones:
  - Residential  
  - Commercial  
  - Industrial  
  - High/low density classifications

]

.pull-right[

### Purpose:
> Prevent negative externalities (noise, pollution, traffic)

### Example:
- Factories generate noise/dirt → lower nearby housing prices  
- Zoning places factories at city’s edge to minimize externalities
]

---

## Zoning and Land Rents

- Without zoning:
  - Factories locating near residential areas lower `$p$` nearby  
  - Land rents fall across large neighborhoods
- With zoning:
  - Factories are consolidated in one area  
  - Negative externality footprint reduced by ~75%  
  - Landowner income loss decreases proportionally

### Takeaway:
Zoning can improve welfare by **reducing negative externalities**.

---

## Is Zoning Necessary?

- Some cities impose **no zoning at all** (e.g., Houston)
- Houston’s development patterns don’t look dramatically different from zoned cities
- Argument:
  - Externalities sometimes manage themselves  
  - Market forces may naturally separate incompatible land uses

### But:
- Houston’s growth was unusual (large-scale single-ownership developments)  
- These internal arrangements acted *like* zoning substitutes

---

## Empirical Evidence on Land-Use Controls (cont'd)

.pull-left[
<img src="assets/image08.jpg" width="100%" style="display: block; margin: auto;" />
]

.pull-right[
<img src="assets/image09.jpg" width="100%" style="display: block; margin: auto;" />
]

---

## Empirical Evidence on Land-Use Controls <svg viewBox="0 0 512 512" style="height:1em;display:inline-block;position:fixed;top:10;right:10;" xmlns="http://www.w3.org/2000/svg">  <path d="M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z"></path></svg>

### Findings from the literature:

- UGBs  
- Height restrictions  
- Density restrictions  
- Impact fees

➡ **All tend to raise housing prices**.

### Why?
- They restrict supply  
- They increase scarcity of developable land  
- They reduce the elasticity of housing production