Econ 330: Urban Economics

# Econ 330: Urban Economics
## Lecture 04
### Andrew Dickinson
### 19 October, 2021

---

# Lecture 04: Clustering, City Size, and Growth

---
class: inverse
name: schedule

# Schedule

- .hi-white[Reading] (Chapter 3 & 4)
  
  - .hi-white[Problem set 01 due on Tuesday, October 19th]
  ]

---
# Last Time

We discussed some .hi[fundamentals] that lead to the existence of cities

Need some reason for the higher land prices within a city to be justified 
- Economies of scale
  
--

.hi-blue[Questions]:
 .center[Why do cities grow beyond one factory?]
 
--
 
.center[Why are there differences in size across cities?]

---
# Clustering

So we explained .hi-blue[why] cities exist..

Can we explain why there might be more than one firm?

Where to start?

Suppose a firm makes a positive economic profit.

`\(\Rightarrow\)` additional firms enter the market

`\(\Rightarrow \Pi \rightarrow 0\)`

---

How many firms are in the cluster?

---
class: inverse, middle 
# Data: Firm clustering

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# Clustering

![](./figures/table01.png)

---
name: cluster
# Clustering

![](./figures/map01.png)

---
name: cluster
# Clustering

![](./figures/cluster_graph02.png)

Which axiom do these data relate to?

---

Why might profit increase ( `\(\Pi \uparrow\)` ) initially as more firms .hi-orange[cluster]?

- .hi-orange[(i).] Sharing intermediate inputs

- .hi-orange[(ii).] Labor matching

- .hi-orange[(iii).] Knowledge spillovers

- .hi-orange[(iv).] Labor pool sharing

<br>

---

# (i). Sharing inputs

Similar firms .hi-blue[share inputs] to benefit from economies of scale

- Rapidly changing goods that require sophisticated intermediate inputs

- Electronic components and testing facilities
    
--

- Firms will share intermediate input suppliers to help reduce costs
  
--

- Costs `\(\downarrow \quad \Rightarrow \quad \Pi \uparrow\)`
    
--

<br>

---
# (ii). Labor matching

In models of labor markets, we typically assume that firms and workers match perfectly

In the real world this is rarely the case
- Firms and workers are .blue[not always perfectly matched]
- Mismatches .hii[require training] to eliminate skill gap. .hi[Training is costly]
- Think of the training you may need for your first job

A large city will reduce these costs

---
# (ii). Labor matching

Consider a labor pool of software programmers

The skill sets of these programmers vary greatly

- Coding languages: C, Javascript, Python, Rust, etc.
  
  - Programming tasks: graphics, AI/ML, OS development etc.

Clustering .hi[attracts] more of the kind of workers they want

Better for firm if they can find a worker to fill role immediately

- Firms have higher probability in a cluster

---
# (ii). Labor matching: HS model

.smallererer[.hi[(i). Variation in worker skills:] Workers have a unique skill set described by an "address" on a circle]

.smallererer[.hi[(ii). Firm entry:] Firms enter the market and pick a good with an associated skill requirement]

.smallererer[.hi[(iii). Training costs:] Workers incur the cost associated with closing the gap on the circle between their own skill and the skill requirement to produce the good]

.smallererer[.hi[(iv). Competition for workers:] Each firm offers a wage to anyone who meets the skill requirement; workers accept the highest net wage
- Net wage `\(=\)` gross wage - training costs]

- .smallererer[.hi[A4: Production is subject to economies of scale] to ensure firms hire more than one worker]

- .smallererer[.hi[A5: Competition generates zero economic profit] to ensure perfect competition]

---
# (ii). Labor matching: HS model

---
# (iii). Knowledge spillovers

- One of most important external benefit of a college campus (classroom) is the .hii[peer effects]
  
--

.hi-blue[Examples:]
.pull-left[
- Graduate school
- Jam sessions
]
.pull-right[
- Attending seminars, workshops, and conferences
]

Knowledge spillovers increase with more people and more knowledge

`\(\Rightarrow\)` Knowledge Spillovers `\(\uparrow\)` `\(\longrightarrow\)` Productivity `\(\uparrow\)`

---

# Agglomeration economies

- Benefits that come when firms and people locate near one another together in cities and industrial clusters

> Agglomeration economies are the benefits that come when firms and people locate near one another together in cities and industrial clusters. These benefits all ultimately come from transport costs savings: the only real difference between a nearby firm and one across the continent is that it is easier to connect with a neighbor. Of course, transportation costs must be interpreted broadly, and they include the difficulties in exchanging goods, people, and ideas

Source: [Ed. Glaeser](https://www.nber.org/chapters/c7977.pdf)

---

Let's refine our language with definitions:

i. _.hi[Localization economies]_

- The economic forces that cause clustering that act on firms .blue[_within the same_] industry
- Local to a particular industry
- Example: Firms in the software industry cluster in Silicon Valley

--
  
ii. _.hi.orange[Urbanization economies]_

- The economic forces that cause clustering that act on firms .blue[_across different_] industries
- The presence of one firm attracts firms from different industries
- Example: Universities; corporate headquarters
  
---

# Localization Economies

A _.hi[localization economy]_ occurs when an increase in the size of an industry leads to an increase in productivity of production

Evidence of higher .hi[labor productivity]

- Higher output `\(\rightarrow\)` more productive workers (Henderson, 1986)
  
- Tech workers benefit more from .orange[knowledge spillovers] than manufacturing (Mun & Huchinson, 1995)

Evidence of higher .hi[rates of entry]

- More firms are born where .hii[output is higher]; that is, where the industry is clustered (Carlton, 1986)

---
# Urbanization Economies

_.hii[Urbanization Economies]_- the size of a city increases in productivity

--
  
.hi[Matching]: common skills across sectors (excel, for example)

<br>

Urbanization Economies result in .hi[large, diverse cities]

---
# Examples

Two major examples of .hi[localization] & .hi.orange[urbanization] economies:

1) .hi-blue[Silicon Valley]

- .hi[Localization]: firms locate close to each other to share .orange[high-skilled labor pool] despite very high rents

2) .hi-blue[Los Angeles]

- .hii[Urbanization]: No super dominant industries, yet it continues to grow

---
class: inverse, middle, center
# City Size

---
# City Size

We've seen why agglomeration economies explain why .hi[firms] cluster.

But how to agglomeration economies explain why .hii[people] cluster?

- Agglomeration economies increase productivity and lead to higher wages in larger cities

<br>

---
# City Size in the US

There seems to be a functional relationship within city sizes and rank within a single country

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# What Function? f(x) = 1/x

---
# What Function? Zipf's law

---
name: zipf
# Size: Zipf's Law

`\begin{align*}
rank = \frac{C}{N}
\end{align*}`

- C represents a constant for a country/region

- N represents the population level

We can use the function described by Zipf's law to approximate city size based on rank

---
# Zipf's Law: Example

Assume the .hi[third] ( _rank_ ) largest city in a region has .hii[200,000 people] ( `\(N\)` )

- Use Zipf's law to figure out how many people are in the _fifth-largest_ city

1) Calculate the constant `\(C\)`:

`\begin{align*}
3 &= \frac{C}{200,000}\\
C &=  600,000
\end{align*}`

2) Use that info to calculate the population of the 5th largest city:

`\begin{align*}
5 &= \frac{600,000}{Pop_5}
\end{align*}`

---

# Zipf's Law: Example

Assume the .hi[third] ( _rank_ ) largest city in a region has .hii[200,000 people] ( `\(N\)` )

- Use Zipf's law to figure out how many people are in the _fifth-largest_ city

1) Calculate the constant `\(C\)`:

`\begin{align*}
3 &= \frac{C}{200,000}\\
C &=  600,000
\end{align*}`

2) Use that info to calculate the population of the 5th largest city:

`\begin{align*}
5 &= \frac{600,000}{Pop_5} \implies Pop_5 = 120,000
\end{align*}`

---

# Zipf's Law: Intuition

.qa[Q]: In words, what does .hii[Zipf's law] tell us about the relationship between .hi[rank] and .hi[city size]?

- .hi[A few] cities will be big

- There is a .hi[big drop] in population as rank increases
  
  - Most low rank (high number) cities are .hi[pretty similar] in size

---
# Example: Zipf's Law

.hi[(i).] Assume that the Zipf's Law for cities is exactly true. If the .hi[fourth-largest] city in a region has .hii[2.5 million] people, how many people live in the region's .hi[largest] city? Show your work.

<br>

---
# Primate Cities

> A major city that works as the .hi[financial, political, and population center of a country] and is not rivaled in any of these aspects by any other city in that country.

> "_at least twice as large as the next largest city and more than twice as significant."_

.hi[Examples]:
.smallerer[
.pull-left[
.hi[City]
- Seoul, South Korea
- Santiago, Chile 
- Buenos Aires, Argentina
- Lima, Peru
]
]
.smallerer[
.pull-right[
.hi[Percent of Total Population]
- 45.8%
- 35.5%
- 33.7%
- 31.7%
]
]

---

# Why Primate Cities?

What might generate primate cities?

- Large .hi[economies of scale] in exchange

- Inadequate .hii[transportation infrastructure] elsewhere

- .hi[Political factors]?

- Easier for dictators to bribe, surveil populations of a primary city (?)
  
  -  Capital cities with dictatorships are _45%_ larger than capital cities of other countries
    
   - Is this relationship .hi.orange[causal]? <sup>.orange[†]</sup>

.footnote[
.orange[†] Maybe somebody does. But you definitely can't say from the 45% number. Much of modern econ is about figuring out when relationships _are_ causal. For a completely unrelated, but informative and entertaining example, see [this video](https://www.youtube.com/watch?v=6YrIDhaUQOE&t=133s). 
]

---
# Why Zipf's Law?

- "Winner take all" situations from policies, agglomeration, knowledge spillovers, etc.

- Wages grow, workers in, firms enter, `\(\rightarrow\)` labor demand `\(\uparrow\)` `\(\rightarrow\)` wages grow . 🔁
  
--

---
# Size

Why do costs increase as workers move in? (Diseconomies of scale?)

(i). .hi[Commute costs increase]

- More people `\(\implies\)` more congestion (all else equal)
  
--

(ii). .hi.green[Pollution] increases

- More workers `\(\implies\)` more production `\(\implies\)` more .green[pollution]?

(iii). .hii[Disease]

--
  - Early 1900's (US), living in a city `\(\rightarrow\)` life expectancy `\(\downarrow\)` 5 years
  
  - Now, the US's largest cities life expectancy exceeds the national average

- Life expectancy in cities is lower than rural areas in developing economies. .hi[Why?]

---
name: utility
# Utility

What we use to model the values individuals place on different city attributes

.hi[(i).] Higher levels of utility are .hii[preferred] to lower levels. And more consumption is better than less

.center[.hi[Similar to the assumption that firms maximize profits, we also assume that individuals maximize utility]]

---
# Modeling City Size

---

# Modeling City Size

---

# Modeling City Size

---
name: eq
# Locational Equilibrium

.hi[Locational Equilibrium] occurs when utility levels (valuations) across cities are the same for all workers

In a system of cities, .hi[migration] has a .hii[self-correcting] effect
- Locational Eq is stable when the utility curve is downward sloping
  - `\(\implies\)` Cities tend to be too large rather than too small

In practice, we usually do this by .hii[worker type] (demographic, income level, education, etc)
  
- For now, we will just consider the case when .hi[all workers are equivalent] (_but not cities_)

- This assumption is mostly for accounting purposes. Best to start simple.

---
# Locational Eq Graph

---

# Locational Eq: Implications

Back to the .hi.orange[real world]: _Why is this framework useful?_

- If utility really has this shape, what does this mean for policy?
  
--

_Policies that impact the .hi[spatial distribution] of the population can have far flung effects on individuals it was not designed to impact, .hii[via migration]_

- Local school quality improvements `\(\rightarrow\)` increased prices. Higher utility from school quality, lower from higher prices. Some people may be displaced? (Gentrification)
  
--

- Net effect could be positive, but there will be winners and losers
    
--

More on this later in the term (.hii[place-based] policies).

---

---
name:growth_factors
# Growth

---
name:example
# Example: Innovation

.pull-left[
<img src="04-growth_files/figure-html/u_innov-1.svg" style="display: block; margin: auto;" />
]

Population each city: .orange[800k] (total pop, 1.6 m)]

---
# Example: Innovation

.pull-left[
<img src="04-growth_files/figure-html/u_innov2-1.svg" style="display: block; margin: auto;" />
]

In the absence of migration, utility is now higher in the higher productivity city]

---
# Example: Innovation

.pull-left[
<img src="04-growth_files/figure-html/u_innov3-1.svg" style="display: block; margin: auto;" />

]
.pull-right[
.hi[Migration] induces workers toward the more productive city and away from the less productive city

- .hi.orange[New locational eq] ( `\(u^*\)` ): utility is equalized (higher than before). populations change 
]

- People are identical and perfectly mobile

In real life high skilled workers are generally far more mobile than low skilled

---
# Example Recap

<div style="text-align: left"> Consider two cities: each with an equilibrium population of 800k and the same utility per worker curve</div>

- .hi[Innovation] (tech progress) in one city .blue[shifts utility per worker] curve up

- Workers in the innovative city enjoy a higher level of utility

- Workers migrate from the city that failed to innovate

Eventually, a new equilibrium is reached where .hi[utility per worker] is the .hi[same across both cities]
  
- Innovative city is larger

---
name:economy_wide
# Economy - Wide Growth

.hi[Note]: If there is an .hii[innovation for the entire economy], then .hi[both cities] experience upward shift of utility curve
  
  - Since there is no utility gap, there is .hi[no migration]

- Still economic growth, but city sizes stay the same

---
# Table of Contents

1. [Urbanizations vs Localization](#urban)
]

### City Size
.smallest[

1. [Zipf's Law](#zipf)

1. [Utility](#utility)

1. [Locational Eq](#eq)
]
]

1. [Growth factors](#growth_factors)

1. [Example](#example)

1. [Economy Wide Growth](#economy_wide)

]
]

---

exclude:true