Econ 330: Urban Economics

# Econ 330: Urban Economics
## Lecture 03
### Andrew Dickinson
### 12 October, 2021

---

# Lecture 03: Existence of Cities

---
class: inverse
name: schedule

# Schedule

- .hi-white[Problem set 01 due next Thursday]
  
  - .hi-white[Reading:] intro + ch. 1, 2
]

---
# Housekeeping:

PS01 was posted

- Due on .hii[Tuesday, October 19th] on canvas

PS01 is going to be the easiest of the quarter

- Some questions you may not be able to start yet

- Use the space provided on the pdfs

- Use scratch paper! .hi[Points will be deducted for messy work]

- Submit on Canvas by .hi[midnight]

---
class: inverse, center, middle
# Why do cities exist? Some data

---
name: data
# Data: Global urban trends (1960-2017)

---
# Data: Global urban trends (1960-2017)

---
# Data: Global urban trends (1960-2017)

---
name: history

# Technological shifts

- .hii[1840s:] .hi[Rail freight] becomes ubiquitous
 
  - Transportation costs ⬇️

.footnote[Source: [Cronon's _Natures Metropolis:  Chicago and the Great West_](https://www.amazon.com/Natures-Metropolis-Chicago-Great-West/dp/0393308731)
]

---
class: hide-count

# Technological shifts

- Transportation costs ⬇️]
  
-  .hi-orange[1840s:] .hi[Telegraph] is invented

- Informational distance ⬇️

]]

---
class: hide-count

# Technological shifts

- Transportation costs ⬇️]
  
.ex[- 1840s: Telegraph is invented

- Informational distance ⬇️]

- .hi-orange[1870's:] .hi[Telephone] is invented

- Informational distance ⬇️
]
]

---
class: hide-count

# Technological shifts

- Transportation costs ⬇️]

- Informational distance ⬇️]

- Informational distance ⬇️]

- .hi-orange[1908:] .hi[Model T] production starts

- Transportation costs ⬇️
]]

---
class: hide-count

# Technological shifts

- Transportation costs ⬇️]

- Informational distance ⬇️]

- Informational distance ⬇️]
  
.ex[- 1908: Model T production starts

- Transportation costs ⬇️]

- .hi-orange[1914:] First commercial .hi[airline flight]

- Transportation costs ⬇️
  
]]

---
class: hide-count

# Technological shifts

- Transportation costs ⬇️]

- Informational distance ⬇️]

- Informational distance ⬇️]
  
.ex[- 1908: Model T production starts

- Transportation costs ⬇️]

- Transportation costs ⬇️]
  
]
.pull-right[
- .hi-orange[1980s:] Airline [deregulation](https://en.wikipedia.org/wiki/Alfred_E._Kahn)

- Transportation costs ⬇️

]]

---
class: hide-count

# Technological shifts

- Transportation costs ⬇️]

- Informational distance ⬇️]

- Informational distance ⬇️]
  
.ex[- 1908: Model T production starts

- Transportation costs ⬇️]

- .ex[1914: First commercial airline flight

- Transportation costs ⬇️]
  
]
.pull-right[
.ex[- 1980s: Airline deregulation

- Transportation costs ⬇️]
  
- .hi-orange[1990's:] The internet

- Information costs ⬇️

]]

---
class: hide-count

# Technological shifts

- Transportation costs ⬇️]

- Informational distance ⬇️]

- Informational distance ⬇️]
  
.ex[- 1908: Model T production starts

- Transportation costs ⬇️]

- .ex[1914: First commercial airline flight

- Transportation costs ⬇️]]

- Transportation costs ⬇️]
  
.ex[- 1990's: The internet

- Information costs ⬇️]
  
- .hi-orange[2020s:] Post COVID
  
  - Transportation costs ⬇️
  
  - Information costs ⬇️

- Among many other technological changes

]]

---
class: inverse, middle, center
# Why do cities exist?

---
name: paradox
# Paradox: Why do cities exist?

Considering the urban population trends and technological shifts, .hi[there seems to be a paradox]

This paradox motivates the question:

Let's use insights from economic models to answer these questions from an economic perspective

---

# Paradox: Why do cities exist?

What do you think?

There is a pretty simple, one-word answer. .hi-pink[Any guesses?]

First, suppose there was .hi[no trade]

- What would we need for this to be true? 
  
--

- _Would this lead to no cities?_

- Even with trade, _possible_ that households trade amongst themselves

---

# EC 201 Review 017: Trade

- .hi[Absolute Advantage] (AA): An economic agent or entity has .hi-slate[AA] in exchange if they can produce more of the good in the same amount of time 
  
--
 
  - .hi[Comparative Advantage] (CA) : An economic agent or entity has .hi-slate[CA] in exchange if they can produce the good at a lower _oppurtunity cost_

- .hi[Production Possibilities Frontier] (PPF): All possible combinations of goods that an economic agent or entity can produce

---

# EC 201 Review 017: Trade - example

.hi[Example]: Suppose we have two countries A & B- producing guns and oil
  
Each counties PPF is .note[given] by:

- .hi[Country A]: `$\color{#e64173} {Guns_A = 10 - 2*Oil_A}$`

- .hi[Country B]: `$\color{#6A5ACD} {Guns_B = 20 - 5*Oil_B}$`

1) Graph each countries PPF

2) Determine who has the AA in each good and who has the CA in each good

---

# EC 201 Review 017: Trade - example

---

# EC 201 Review 017: Trade - example

---

# EC 201 Review 017: Trade - example

.hi[Idea] Whomever _gives up less_ to produce the same amount extra has the comparative advantage. Check: 
<img src="03-size_files/figure-html/ppf3-1.svg" style="display: block; margin: auto;" />

---

# PPF Heuristics

When looking at PPFs, to determine:

1) .hi[AA]: Check .hii[intercepts]
  
  - Whoever has higher valued .hii[intercept] has the .hi[AA] in production

2) .hi[CA]: Check .hi-gold[slopes]

- A .hi-gold[steeper slope] indicates .hi[CA] on the vertical axis
  
  - A .hi-gold[shallower slope] indicates .hi[CA] on the horizontal axis

---
# Why do cities exist?

We need land to produce food and resources; dense cities don't provide

Cities exist because of human .hi[technology] has created systems of production and trade that defy the natural order

Three conditions must be satisfied:

.hi[(i).] .hii[Agricultural surplus:] People outside cities must produce enough food to feed themselves and city dwellers

.hi[(ii).] .hii[Urban production:] City dwellers must produce goods or services to exchange for food grown by rural workers

.hi[(iii).] .hii[Transportation for exchange:] Efficient transportation system to facilitate the exchange of food and urban products must exist

The technology in this case is what we call .hi[trade]

---

A simple economic model to understand the economic incentives of cities

Consider a region that produces and consumers two products:

- .hi[Bread]

- .hii[Shirts]

.center[.hi[Let's make three assumptions that would eliminate any incentives for households to geographically cluster]]

- .smallerer[Relaxing each assumption will give us .hii[intuition] about the formation of cities]

---
# Backyard production model

- No comparative advantages
  
--
  
.hi[A02:] Constant Returns to Scale (CRS) in .hii[exchange] and .hii[transportation]

- Per unit price to .hi[trade] goods _is the same_ no matter how much is traded 
  
  - No need for middle man firms to help with distribution
  
--

- The per unit price of production is constant
  
  - No economies of scale `$\rightarrow$` households productivity = firm productivity

---
# Backyard production model

.center[.hi[These three assumptions would eliminate exchange and ensure each household is self sufficient:]]

- There is no incentive to specialization due to transaction costs<sup>.hi[†]</sup>

- Locational equilibrium would be uniformly distributed population

.footnote[<sup>.hi[†]</sup>transaction cost is the opportunity cost of the time required to exchange products
<sup>.hi[††]</sup> Axiom 5 of urban economics]

---

# Backyard production model: Relax A01

--
 
.qa[A]: Nope. Let's relax that assumption
.hii[Ex:]
- Soil may be more productive in certain regions; better climate
- One region specializes in bread while the other in shirts

Relaxing A01 will lead to differences in productivity across cities:

`$\implies$` .hi[comparative advantages]

`$\implies$` specialization + trade

However, specialization and trade will not alone lead to urban growth
- HH trade directly with one another

---

# Relax A02

In absence of scale economies, households trade directly<sup>.hi[†]</sup>

]

- .hi[CRS in Exchange]: `$\implies$` households are just as efficient at executing trades as firms (no cost benefits to scaling)

- No reason to pay a firm to do so (and thus no reason to pay for density)

A trading firm will use productive inputs such as:

- Large truck for transportation

- Specialized workers

---

# Relax A02

To take full advantage advantage of scale economies firms locate s.t. they minimize costs of distribution

--
  
`$\implies$` higher prices of land `$\implies$` density

- .hi[The growth of trading cities is implied by A04]

These are represent the cities that existed before the industrial revolution

- Most city workers did not produce goods but distributed them

- Trade was risky; insurance, credit, banking and legal services sprouted

---

Now relax the final assumption A03

Suppose factory workers can produce at a cheaper per-unit cost than HH

Consider the shirt making factory:

- .hi[Home] production: `$20$`  p shirt
  - .hi[Factory]:  `$12$` p shirt (economies of scale)
  
--

The factory locates in a town with 50 miles to east and west of villages
  
   - 50 cents/mile to ship west.
   - 20 cents/mile to ship east
   
---
# Factory Towns

Under what condition will a consumer purchase the shirt from a factory?

`\begin{align*}
\underbrace{p_f}_\text{factory price} + \underbrace{t \times d}_\text{transit cost = cost p mile$\times$miles} \leq \underbrace{p_h}_\text{Home Price}
\end{align*}`

1. Graph the cost of shirts throughout the entire region

2. Find the .hi[market area] of the town

- Find the sum of the .hii[maximum distances] to the east and west that consumers will purchase the shirt from the factory

---

#Regional Costs

---
#Market Area Calculation

Market area depends on which side we are looking at. Let `$m$` denote miles

--
  
  `$12 + .5*m_{west} \leq 20 \implies m_{west} \leq 16$`
  
--

.hi[East:] Consumers buy from factory if 
  
  `$12 + .2*m_{east} \leq 20 \implies m_{east} \leq 40$`
  
--

`$40+16 = 56$`

---

# Factory Towns

1. Would workers rather live .hi.orange[closer] or .hi[further] from the factory?
  
--
  
  - .hi[Closer!]
    
--

2. What happens to land-prices .hi[close] to the factory?

--
  
  - They .hi[increase]
  
--

3. What happens to .hi[density]?

- It will .hi[increase] 
 
--

__Result:__ Factory town!

---
class: inverse, middle, center
# Introduction to Clustering

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# Clustering

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

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

Where to start? .hi[Axoim 5]

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?

---

#Table of Contents

.pull-left[
###Data & History
.smallest[
1. [Urban Populations](#data)
1. [History](#history)
1. [Paradox](#paradox)
]

###Existence
.smallest[

1. [Why do Cities Exist?](#exist)
1. [Trade Basics](#trade)
1. [Factory Towns](#factory_towns)

]
]

]
]