Econ 330: Urban Economics

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# Econ 330: Urban Economics
## Lecture 09
### Andrew Dickinson
### 30 November, 2021

---

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# Lecture 09: Place Based Policies

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# Schedule

.pull-left[
.ul[.bigger[.hi-gold[Today:]]]

.hi-white[(i). Place-based policies]

- .white[General utility framework]

]

.pull-right[
.ul[.bigger[.hi-gold[Upcoming:]]]

- .hi-white[Reading] (Chapter 8)
  
  - .hi-white[PS03 will be posted later today]
  
]

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# Place-based polcies

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# Place-based polcies

.hi[.ul[Definition:] Place-based policies] - Location specific policies/laws

- What are some examples?

.pull-left[
  - State and Local Taxes
- State/City minimum wage
- Abortion restrictions
- Air quality monitoring]
.pull-right[
  - Zoning & Land Use Restrictions
- Enterprise Zones
- Medicinal and recreational marijuana laws]

.hi[Federal policies] that are .hii[uniform across all states] _are not_ place-based

- Harder to migrate across .hii[international borders] than state borders

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# Place-based polcies: Examples

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# Pb polcies: Minimum wage

.center[
![:scale 60%](figures/min_wage.png)
]

Federal Minimum Wage: `\(7.25\)` (not a place based policy)

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# Pb polcies: Enterpise zones

.hi[.ul[Definition:] Enterprise zone]:

> A geographic area that has been granted .pink[tax breaks, regulatory exemptions, or other public assistance] in order to encourage private economic development and job creation

Examples:

- Jersey City, NJ since 1983
  
  - China: Shanghai and Shenzen (Special Economic Zones (SEZ))
  
---
# Pb polcies: Brownfield remediation

.hi[.ul[Definition:] Brownfield]:

> A geographic area that has previously been developed land that is not currently in use due to industrial and/or commerical pollution

Examples include abandoned business such as:
.pull-left[
- Gas stations
- Dry cleaning
- Factories]
.pull-right[
- Mills
- Foundries
]

There are several Brownfields in the [Eugene/Springfield area](https://ofmpub.epa.gov/apex/cimc/f?p=CIMC:73::::73:P71_WELSEARCH:97405%7CZipcode%7C%7C%7C%7Ctrue%7Cfalse%7Cfalse%7Cfalse%7Cfalse%7Cfalse%7C(BF_ASSESS_IND%3D%27Y%27)

- [Ninkasi over took a brownfield to expand brewing operations in 2012](https://youtu.be/D4RcUacsW3U?t=97)

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# Pb polcies: Brownfields remediation
.center[
![:scale 80%](figures/us_brownfields.png)
]

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# Pb polcies: Brownfields remediation

Brownfields lower the amenity value of neighborhoods
- [High health costs associated with living near a brownfield](https://michellemmarcus.files.wordpress.com/2019/09/marcus_lust_092319.pdf)
  - Petroleum leaks from underground storage tanks lead to increases in the probability of low birth weights and preterm birth by .hi[7-8 percent]
- Tremendously expensive to clean up

Land is not used it is not contributing to local economies- opportunity cost

Cleaning these up raises .hi[amenity value] of the neighborhood

Property values around brownfields are far lower than comparable land
  - What happens to property values? Go up
    - .hii[Gentrification]

---
# Pb policies: Air quality

_December 2, 1970_: Environmental Protection Agency  (EPA) is Established

- Included the Clean Air Act
    - Regulates county level air quality with a system of air monitors
  
--

.hi[Following years]: amendments to the CAA

.pull-left[

- .hi[1990:] Additional power granted to state/local authorities to enforce air quality standards
- .hi[1997:] PM 2.5 (particulate matter of 2.5 micrograms or less) standards placed

]

.pull-right[
- .hi[2005:] PM2.5 standards enforced
- .hi[2011:] Standards for greenhouse gases]

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# Pb polcies: Air quality

Particulate Matter (.hi.orange[PM]) in the US is regulated at the .hi.green[county level].pink[†]

.footnote[
.pink[†] For more details, look [here](https://www.epa.gov/pm-pollution)
]

If a county exceeds certain threshold for .hi.orange[PM] , all firms over a certain size need to pay a pretty big fine
  - Exceptions for fires, other natural events

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# Pb polcies: Air quality

![](figures/aq_2.png)

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# Pb polcies: Air quality

![:scale 90%](./figures/di.png)

- [Di et al. (2016)](https://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC5761665&blobtype=pdf)

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# Pb polcies: Air quality

Does air quality monitoring make sense at a local level? Why or why not?

.center[
![:scale 55%](./figures/morehouse-rubin.png)
]

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# Pb polcies: Discussion

.hi[Why do we care about place-based policies?]

.center[.hii[People are mobile and respond to changes in incentives]]

Place-based policies influence .hi[location decisions]
- TotC give really good intuition in the chapter about Detroit.

.hi[Question:] Why do federal policies impact cities differently?

Min wage: might be .hi[binding] in some states, others not
  
- Some labor markets might be competitive. Others not
    
--
  
- Federal Income Tax: Cost of Living varies by state.

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# Utility framework

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# Utility framework

This next section of the class will add another layer of complexity

Set up a .hi[utility framework] to understand how policies impact welfare
-- Only scratches the surface of how one may model impacts of pb policy

Some of these examples are based on [Mark Colas'](https://sites.google.com/site/markyaucolas/home?authuser=0) notes
  - Learn more about this in his 400 urban economics class

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# Utility framework

.hi[Utility:] Abstract notions of people's preferences. .hii[Why does it matter?]

Location based policies impact individual .hi[location decisions]
- Model decision through the lens of an individual's utility (welfare)
- Higher utility is better
  - `\(U(\text{City A}) > U(\text{City B})\)` `\(\implies\)` Moving to City A

Suppose City B makes a policy change that raises wages
- Now `\(U(\text{City A}) < U(\text{City B})\)` `\(\implies\)` Moving to City B

Changes in a location based policy are going to change .hi[incentives]
- eg. San Diego has extremely strict zoning restrictions

Zoning restrictions `\(\implies\)` limited housing supply `\(\implies\)` high rents `\(\implies\)` "why do i live here.." `\(\implies\)` move to Oregon

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# Utility framework

.hi[Example]: Preferences over left-shoes and right-shoes may be expressed with the following utility function:

`\begin{align*}
U(\text{left shoes},\text{right shoes}) = \min\left\{ \text{left shoes}, \text{right shoes}   \right\}
\end{align*}`

.qa[Q:] In words, what does this say?

.qa[A:] Another right shoe does nothing for me unless I get another left shoe

--

.qa[Q:] Give the above utility function, which bundle would I rather consume?

`\begin{align*}
\text{bundle 1}: (10000,1) \hspace{2in}
\text{bundle 2}: (2,2)
\end{align*}`

.qa[A:] `\(U(10000,1) = 1 < U(2,2) = 2\)`, so I would rather consume bundle 2

---
# Utility framework

.hi[Main point:] Utility is used to rank outcomes

.hi[Remember:] Utility is .hii[ordinal] _not_ .hi-gold[cardinal]

This means: we can only speak to the ordering of outcomes, not the levels

- Many utility functions give equivalent preference rankings

.hi[What if utility over shoes was:]

`\begin{align*}
U_2(\text{left shoes},\text{right shoes}) = 10*\min\left\{ \text{left shoes}, \text{right shoes}   \right\}
\end{align*}`

.qa[Q:] Does this represent the same underlying preferences as before?

.qa[A:] Yes, because `\(U_2(10000,1) = 10*1 = 10 < U_2(2,2) = 10*2 = 20\)` 
 
- So the bundle `\((2,2)\)` is still preferred to `\((10000,1)\)`

---
# Utility framework: Locations

.center[.hi[Could we write a utility function over locations?]]

.center[.hii[Yes!]]

What would a locational utility function take as .hi[inputs?]

What do people make location decisions on?

For now, assume people only care about 3 features of locations:

--
  
.center[.hi[wages], .hii[rents], .hi-gold[amenites]]

These all vary across locations, right? (first part of this class)

Let `\(w_j\)`, `\(r_j\)`, and `\(a_j\)` denote wages, rents, and amenities in location `\(j\)`

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# Utility framework: Locations

Let `\(w_j\)`, `\(r_j\)`, and `\(a_j\)` denote wages, rents, and amenities in location `\(j\)`

- `\(j = SF\)`, for example

.hi[General form]: `\(U(w_j, r_j,a_j) = U_j\)`

- This says utility in location `\(j\)` is a function of wages, rents, and amenities, in location `\(j\)`

In practice, could write down an infinite number of functions for `\(U(\cdot)\)`

.hi[Usual assumptions:]
.pull-left[
- Higher wages are better
- Lower rents are better]
.pull-right[
- More amenities are better]

.center[.hii[Is this reasonable?]]

---
# Utility framework: Locations

.hi[Example:] Assume linear utility functions and everyone is identical:

`\begin{align*}
U(w_j, r_j, a_j) = w_j - .5*r_j + a_j
\end{align*}`

Suppose our two locations are SF and OAK again. If:

-  `\(w_{SF} = 10, r_{SF} = 8, a_{SF} = 4\)`
  
-  `\(w_{OAK} = 8, r_{OAK} = 3, a_{OAK} = 1\)`

.qa[Q] How do workers sort across the cities?

- `\(U(w_{SF}, r_{SF}, a_{SF}) = 10 - .5*8 + 4 = 10\)`

- `\(U(w_{OAK}, r_{OAK}, a_{OAK}) = 8 - .5*3 + 1 = 7.5\)`

.center[Well 10 > 7.5 so... everyone moves to SF]

---
# Utility framework: Locations

.center[.hi[Is it reasonable that everyone would move to SF? What are we missing?]]

.center[.hi[Was that last example an example in locational equilibrium?]]

.center[.hii[No!]]

In .hi[locational equilibrium], utility is .hii[equalized across locations]

Can't have: `\(U(w_{SF}, r_{SF}, a_{SF}) > U(w_{OAK}, r_{OAK}, a_{OAK})\)`

.center[.hi[How can we use locational eq to "fix up" our last example?]]

We can .hii[allow rents] (or wages or both) .hii[to adjust] such that utility is equivalent across the two cities

---
# Utility framework: Locations

.hi[Another Problem:] People move and utility is equal across all locations

.hi[Thus far], we assume .hii[wages] and .hi-gold[rents] are exogenous
- Fall from the sky, do not change with location decisions

.center[This is a .hi[bad assumption] right?]

Let rents, but not wages, adjust to individual location decisions

- Make rents .hii[endogenous] to the model

---
# Utility framework: Rents

Rents in every city given by:

`\begin{align*}
r_j(L_j) = 2\times L_j
\end{align*}`

- `\(r_j(L_j)\)`: rents _are a function_ of the population (not multiplied)

- `\(L_j\)` is the pop in city `\(j\)`; choosing 2 was arbitrary

Suppose we have two cities `\(1\)` and `\(2\)`, with 7 people total: `\(L_1 + L_2 = 7\)`

.hi[Utility:] `\(U(w_{j}, r_{j}(L_j), a_{j}) = w_j - .5\times r_j(L_j) + a_j\)`

.hii[Wages:] `\(w_1 = 12\)`, `\(w_2 = 7\)`

.hi-gold[Rents:] `\(r_j(L_j) = 2*L_j\)`

.hi-pink[Amenities:] `\(a_1 = a_2 = 0\)`

---
# Utility framework: Rents example

Suppose we have two cities `\(1\)` and `\(2\)`, with 7 people total: `\(L_1 + L_2 = 7\)`

.hi[Utility:] `\(U(w_{j}, r_{j}(L_j), a_{j}) = w_j - .5\times r_j(L_j) + a_j\)`

.hii[Wages:] `\(w_1 = 12\)`, `\(w_2 = 7\)`

.hi-gold[Rents:] `\(r_j(L_j) = 2*L_j\)`

.hi-pink[Amenities:] `\(a_1 = a_2 = 0\)`

.qa[Qs:] How many people live in each city? What are rents in each city?

.hi[Note:] You have .hi[two equations] and .hi[two unknowns] (namely, `\(L_1\)` and `\(L_2\)`)
  
  - `\(U(w_{1}, r_{1}(L_1), a_{1}) = U(w_{2}, r_{2}(L_1), a_{2})\)` (from locational eq) 
    
  - `\(L_1 + L_2 = 7\)` you know the total population

---
# Utility framework: Rents example

Locational eq gives:

`\begin{align*}
w_1 - .5*r_1(L_1) &= w_2 - .5*r_1(L_2)\\
12 - .5*(2*L_1) &= 7 - .5*(2*L_2)\\
-L_1 &= -5 - L_2\\
L_1 &= 5 + L_2
\end{align*}`

Population must sum to 7. Thus:

`\begin{align*}
L_1 + L_2 &= 7\\
5+ L_2 + L_2 &= 7\\
2*L_2 &= 2\\
L_2 = 1 \implies L_1 = 6
\end{align*}`

---
# Utility framework: Place based policies

Ok, how do we tie this back into .hi[place-based] policies?

.hi[Example]

Initial equilibrium: `\(U(w_{j}, r_{j}(L_j),a_{j}) = k\)` for all cities `\(j\)`

Suppose `\(SF\)` implements a 30%, flat, income tax

- Post-tax wage in city `\(SF\)` is now `\(w^{tax}_{SF} = 0.7*w_{SF}\)` 
  
  - Assume .hi[wages are fixed], but .hii[rents adjust to population]

Utility in city `\(j\)` is:

`\begin{align*}
U(w^{tax}_{SF}, r_{SF}(L_{SF}),a_{SF}) < U(w_{SF}, r_{SF}(L_{SF}),a_{SF})
\end{align*}`

If utility is .hi[increasing in wages], then an income-tax lowers utility.

---
# Utility framework: Equilibrium

.center[Can it be an equilibrium if:]

`\begin{align*}
U(w^{tax}_{SF}, r_{SF}(L_{SF}),a_{SF}) < U(w_{SF}, r_{SF}(L_{SF}),a_{SF})
\end{align*}`

.center[.hii[No!]]

Because `\(U(w_{SF}, r_{SF}(L_{SF}),a_{SF}) = k\)`

So `\(U(w^{tax}_{SF}, r_{SF}(L_{SF}),a_{SF}) \neq k\)`

Thus people move .hi[away from SF] and rents fall

So utility goes up in SF until `\(U(w^{tax}_{SF}, r_{SF}(L_{SF}),a_{SF}) = k\)`

---

# Extensions

This flexible way of modeling gives us many options for modeling place based policies

- Other kind of subsidies/taxes: goes into `\(w_j\)`

- Rent subsidies or property taxes: impacts `\(r_j\)`

- .qa[Q]: How would you model an increase in public school quality?

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# Fin