Econ 414 - Urban Economics

# Econ 414 - Urban Economics
## Local Government
### Marcelino Guerra
### March 30-April 1, 2021

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# Introduction

* In the U.S., most of the public goods and services that people consume are provided by local governments (e.g., police and fire protection, basic education, sanitation, among others)

* At the local level, various governments have their revenue and expenditure patterns more or less set, and consumer-voters can move to that community whose local government best satisfies their set of preferences
  * This freedom of choice is not easily available when it comes to public goods and services provided by the federal or state governments

* Moving from one local jurisdiction to another to get a different level of public goods and services is called **"voting with one's feet"**

* The voting process is likely to lead to a public goods' level that is not socially optimal - that is particularly true for federal expenditures. However, for local spending, fully mobile consumer-voters will move to that community where their preference patterns are best satisfied. Hence, each jurisdiction ends up providing the socially optimal level of public good for its population

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# Socially Optimal Level of a Public Good

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# An Illustration

<table class="table" style="margin-left: auto; margin-right: auto;">
<caption>Individual Preferences of consumers A, B, and C and Social Benefit</caption>
 <thead>
  <tr>
   <th style="text-align:right;"> Number of Officers </th>
   <th style="text-align:left;"> Marginal Benefit A </th>
   <th style="text-align:left;"> Marginal Benefit B </th>
   <th style="text-align:left;"> Marginal Benefit C </th>
   <th style="text-align:left;"> Marginal Social Benefit </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 1 </td>
   <td style="text-align:left;"> $19,000 </td>
   <td style="text-align:left;"> $16,000 </td>
   <td style="text-align:left;"> $13,000 </td>
   <td style="text-align:left;"> $48,000 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 2 </td>
   <td style="text-align:left;"> $17,000 </td>
   <td style="text-align:left;"> $14,000 </td>
   <td style="text-align:left;"> $11,000 </td>
   <td style="text-align:left;"> $42,000 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 3 </td>
   <td style="text-align:left;"> $15,000 </td>
   <td style="text-align:left;"> $12,000 </td>
   <td style="text-align:left;"> $9,000 </td>
   <td style="text-align:left;"> $36,000 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 4 </td>
   <td style="text-align:left;"> $13,000 </td>
   <td style="text-align:left;"> $10,000 </td>
   <td style="text-align:left;"> $7,000 </td>
   <td style="text-align:left;"> $30,000 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 5 </td>
   <td style="text-align:left;"> $11,000 </td>
   <td style="text-align:left;"> $8,000 </td>
   <td style="text-align:left;"> $5,000 </td>
   <td style="text-align:left;"> $24,000 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 6 </td>
   <td style="text-align:left;"> $9,000 </td>
   <td style="text-align:left;"> $6,000 </td>
   <td style="text-align:left;"> $3,000 </td>
   <td style="text-align:left;"> $18,000 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 7 </td>
   <td style="text-align:left;"> $7,000 </td>
   <td style="text-align:left;"> $4,000 </td>
   <td style="text-align:left;"> $1,000 </td>
   <td style="text-align:left;"> $12,000 </td>
  </tr>
</tbody>
</table>

<br/>

.center[**Suppose we know the individual preferences of consumers A, B, and C for the level of policing within a city. Assume that a policeman's salary is $24,000. What is the optimal level of the police force in that city?**]

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# An Illustration

* The marginal benefit numbers you saw on the table generate individual demand curves `$D_{A}$`, `$D_{B}$`, and `$D_{C}$` for the public good `$z$`

* `$D_{\Sigma}$` represents the marginal social benefit - the sum of the individual marginal benefits - generated by the public good

* The cost per unit of the public good is denoted by `$c$`

* Then, the socially optimal level of the public good - represented by `$z^{*}$` - corresponds to the intersection between the marginal social benefit `$D_{\Sigma}$` and the `$c$` line, where the marginal social benefit from an additional unit of `$z$` is just equal to its cost `$c$`

]

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# Majority Voting

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# Majority Voting

* Democratic societies choose `$z$` through a voting process

* Suppose consumer-voters pay a uniform tax to cover the costs of the public good. In our example, there are three households in the jurisdiction. Hence, the total cost of a public good `$cz$` - remember, `$c$` is the cost per unit and `$z$` is the level of public good provision

* This yields a tax of `$\frac{cz}{3}$` for each consumer

* The cost per unit `$z$` is then `$c/3$`

* Optimal individual levels are denoted by `$z_{A}^{*}$`, `$z_{B}^{*}$`,  `$z_{C}^{*}$`. The socially optimal level is `$z^{*}$`

]

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# Majority Voting

* When consumers prefer different levels of `$z$`, a voting process is needed to reduce this disparity of views

* Since consumers vote for the candidate promising the `$z$` level closest to his preferred level, a candidate can attract more votes by moving to the "center", proposing a level `$z$` in the middle of the range of preferences

* The **"median voter model"** then predicts that `$z_{B}^{*}$` is going to be the level of the public good provision. To judge the performance of the voting process, one must compare this median value with the socially optimal level `$z^{*}$`. In this example, the two levels happen to be the same, and the voting outcome is socially optimal

]

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# Majority Voting

* **That outcome `$z=z^{*}$`, however, is just an accident**. Suppose that consumer's A demand is actually `$D_{A^{+}}$`. Then, the marginal social benefit curve is now `$D_{\Sigma^{+}}$`, and that leads to a new socially optimal level `$z^{*+}$` of the public good

* Since the "median voter model" still predicts that `$z_{B}^{*}$` is going to be the level of the public good provision, that result leads to underprovision (i.e., `$z=z_{B}^{*}<z^{*+}$`)

* The voting process's problem is that it fails to register the intensity of preferences for non-median voters. In reality, the pattern of preferences is asymmetric, and the most likely result is either underprovision or overprovision of public goods 
]

# Voting with One's Feet

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# Voting with One's Feet

* We just saw that, under the voting outcome, consumer-voter C gets more public good than he wants, and consumer-voter A gets less than she wants

* Assuming a large number of communities, consumer-voters fully mobile and with full knowledge about the differences among revenue and expenditure patterns of those local governments will move to that community where their preference patterns are best satisfied

* To illustrate this point, consider a situation with only two types of consumers - A (high-demand) and C (low-demand) - and two jurisdictions, each one with a population of 100. Hence, the per capita cost per unit of `$z$` is equal to `$\frac{c}{100}$` in each jurisdiction

* Jurisdiction I has 10 A-types and 90 C-types, and Jurisdiction II has 10 C-types and 90 A-types. Hence, the median voter in Jurisdiction I is a C-type, and in Jurisdiction II is an A-type

* From the A-type perspective, in Jurisdiction I, the public good is underprovided. On the other hand, in Jurisdiction II, from a C-type standpoint, the public good is excessively provided

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# Voting with One's Feet

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# Voting with One's Feet

* In this situation, type-A voters in the jurisdiction I have the incentive to move to jurisdiction II and get higher levels of public good's consumption: their consumer surplus level rises from `$J+K$` to `$J+K+L$`

* The C-type in jurisdiction II can reduce their consumption level by moving to jurisdiction I and increasing their consumer surplus level from `$J-M$` to `$J$`

* With consumer-voters shopping around for the desired public-good level, the two places will end up completely homogeneous, with jurisdiction I containing 100 C-types and jurisdiction II having 100 A-types. In this case, everybody agrees on the level of `$z$`. Therefore, the level of public good provision is socially optimal.

* If demand differences are, for instance, due to income differences, then the model predicts that jurisdictions should be homogeneous by income. However, this prediction does not match reality: cities contain people with different levels of income. The model leaves out other relevant factors related to locational choices, such as employment opportunities, family ties, preferences for amenities, etc.

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# The Role of the Property-tax System

* So far, we assumed that all the consumer-voters pay the same tax `$\frac{cz}{n}$`. In case the funding for local government expenditure comes from property tax, the taxation would ultimately depend on the income levels of those households. Therefore, rich and poor consumer-voters would have different tax burdens. How does the model change?

* When rich and poor live in the same jurisdiction that provides public goods at level `$z_{R}$` - the preferred level from the high-income people - and pay the same tax `$\frac{c}{100}$`, this tax burden is too high and the consumer surplus for low-income households is `$Q-T-S$`. Therefore, they would be better off moving to a homogenous jurisdiction where the public-good provision is at level `$z_{P}$`, where their consumer surplus is `$Q$`

]

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# The Role of the Property-tax System

* Now, assume that a single poor household moves to the rich jurisdiction. Also, suppose the tax burden depends on the size of the houses. Since the low-income household lives in a smaller dwelling, he only pays a fraction `$\frac{\alpha c}{100}$`

* Having this lower tax burden and enjoying `$z_{R}$` as public-good provision, the low-income household consumer surplus is `$Q+R-S$`. Assuming `$R-S>0$`, he is better off now compared to the situation where he lives in a homogeneous low-income community with `$z_{P}$` as the level of public good provision

* Hence, under a property-tax system, voting with the feet may no longer lead to the formation of homogeneous jurisdictions
]

# Other issues
<br/>

* High-income jurisdictions may enforce segregation with minimum lot size requirements. By forcing poor consumer-voters to live in bigger houses that they can't afford, fiscal zoning eliminates the incentive for entry

* Although homogeneous communities are efficient - they enjoy the socially optimal public good level - that outcome may seem inequitable. To correct that, the government can redistribute tax revenues to low-income jurisdictions to even out differences in public good provision (differences in school quality, for instance)

* Under the voting with the feet model, an existing central city with poor and rich consumer-voters will lose its wealthy residents, who will move to a homogeneous rich jurisdiction - most likely a new suburban community. That would contribute to urban sprawl and create financial distress in the central city

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class: inverse,center, middle

# Public Good Congestion and Jurisdiction Sizes

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# Congestion vs Cost Sharing

* Until now, we assumed that `$z$` was pure public good, completely ignoring congestion. This assumption is unrealistic since spending usually increases as the jurisdiction's population grows to keep the same per capita level of public-good provision

* To represent the cost of providing a congested public good, let `$n$` denote the jurisdiction's population size. We replace `$c$` by `$c(n)$` because the cost parameter now depends on the number of residents `$n$`

* An optimal jurisdiction size `$n^{*}$` would minimize the per capita cost of the public good `$\frac{c(n)}{n}$`

* Hence, when the jurisdiction has the optimal population `$n^{*}$`, consumer-voters gets the public good as cheaply as possible

]

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# Jurisdiction's Optimal Size

* At the optimal jurisdiction size `$n^{*}$`, two forces balance each other: congestion and cost-sharing
  * As `$n$` increases, congestion causes `$c$` to rise. However, when more and more people share the cost of the public good, it gets cheaper, and that benefit is captured by the denominator of the ratio `$\frac{c(n)}{n}$`

.pull-left[ 
* For the earlier portrayal of voting with the feet to be robust, all jurisdictions must be kept at optimal size: 
  * Communities below the optimum size seek to attract new residents to lower average costs
  * Communities above optimum size does the opposite
  * Communities at the optimal level try to keep their populations constant

]

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# Multiple Public Goods

* The existing patterns of overlapping local governments can be explained by the concept of optimal jurisdiction size

* Consider the case where the local government offers two public goods: sewage/sanitation and police protection. The optimal jurisdiction size for police is `$n_{P}^{*}$`, which is different than the size that gives the jurisdiction the lowest average cost for sanitation services `$n_{SS}^{**}$`

.pull-left[ * Hence, the police protection would be provided by cities, and a large "sanitation district" would provide sewage/sanitation services

]