Existence of Cities

.title[
# Existence of Cities
]
.subtitle[
## EC330, Set 03
]
.author[
### Andrew Dickinson
]
.date[
### Fall 2022
]

---

# Contents

### (i) Historical data

### (ii) Technological shifts

### (iii) _Why do cities exist?_

### (iv) Backyard  production model

---
# Housekeeping

.hi[PS01] will be posted later today
- Due on .hi[Wednesday, October 12th] on canvas by .hi[11:59p]
- Should be straight forward
- Though after today you won't be able to start question 5
- Must be submitted as a pdf

.hi[Note:]
- Use the space provided on the pdfs
- If you need more space, use scratch paper
- .hi-whites[Points will be deducted for messy work]

---
name: data
class: inverse, middle
# Historical data

---
# Historical data
More than .hi[4 billion] people living in urban area globally <sup>.hi[†]</sup>

<br>

.footnote[ <sup>.hi[†]</sup> Although the definition of an "urban area" is not exactly [well defined](https://blogs.worldbank.org/sustainablecities/what-does-urban-mean)]

Urban populations are now greater than rural populations
- Since .hi[2007]
- Only .hii[10%] of humans lived in urban areas in .hi[1800]
- Only .hii[1%] of land is categorize as urban area

<br>

By .hi[2050], .hii[66%] of global populations will live in urban areas

---
class: clear
# Historical data

---
class: clear
# Historical data

---
class: clear
# Historical data

---
class: inverse, middle
# Technological shifts

---
# Technological shifts

- .smallerer[.hii[1840s:] .hi[Rail] becomes ubiquitous
  - Transportation costs ⬇️]
  
---
class: clear
count: false
background-image: url("./figures/cronon.png")
background-position: center
background-size: contain

.footnote[ [Source: Atlas of Historical Geography of the United States](https://dsl.richmond.edu/historicalatlas/138/a/)]

---
count: false
# Technological shifts

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

---
class: hide-count

# Technological shifts

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

- Information costs ⬇️

]]

---
class: hide-count

# Technological shifts

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

- Information costs ⬇️]

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

- Information costs ⬇️
]
]

---
class: hide-count

# Technological shifts

- Transportation costs ⬇️]

- Information costs ⬇️]

- Information costs ⬇️]

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

- Transportation costs ⬇️
]]

---
class: hide-count

# Technological shifts

- Transportation costs ⬇️]

- Information costs ⬇️]

- Information costs ⬇️]
  
.ex[- 1908: Model T production starts

- Transportation costs ⬇️]

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

- Transportation costs ⬇️
  
]]

---
class: hide-count

# Technological shifts

- Transportation costs ⬇️]

- Information costs ⬇️]

- Information costs ⬇️]
  
.ex[- 1908: Model T production starts

- Transportation costs ⬇️]

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

- Transportation costs ⬇️

]]

---
class: hide-count

# Technological shifts

- Transportation costs ⬇️]

- Information costs ⬇️]

- Information costs ⬇️]
  
.ex[- 1908: Model T production starts

- Transportation costs ⬇️]

- .ex[1914: First commercial airline flight

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

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

- Information costs ⬇️

]]

---
class: hide-count

# Technological shifts

- Transportation costs ⬇️]

- Information costs ⬇️]

- Information costs ⬇️]
  
.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 ⬇️]
  
- .hii[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?

Urban population trends and technological innovations seem .hi[paradoxical]

The world is getting .hi[flatter], yet urban populations are .hi-red[booming]

This .hi[paradox] motivates the questions:

<br>

<br>

We will draw insights from economic models to answer these questions

---
# Paradox: Why do cities exist?

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

---
count: false
# Paradox: Why do cities exist?

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

<br>

Suppose there was .hi[no trade]
- _What would we need for this to be true?_
- _Would this lead to no cities?_
- _Even with trade, when is it the case that households just 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, .hi[A] & .hii[B], producing guns and oil
  
Each countries .hi[PPF] is described by:

- .hi[A:] `$\color{#4c566a} {Guns_A = 10 - 2*Oil_A}$`

- .hii[B:] `$\color{#b48ead} {Guns_B = 20 - 5*Oil_B}$`

<br>

---

# EC 201 Review 017: Trade - example

---

# EC 201 Review 017: Trade - example

???

Whomever _gives up less_ to produce the same amount extra has the comparative advantage

---

# PPF Heuristics

When looking at PPFs, to determine:

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

(ii) .hi[CA]: Check slopes
- A .hi[steeper slope] indicates CA on the vertical axis
- A .hii[shallower slope] indicates 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]

---
name: backyard
class: inverse, middle
# Backyard production model

---
# Backyard production model

A .hi[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]]

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 .hi-blue[exchange] and .hi-green[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

<br>

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

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

Locational equilibrium would be .hi[uniformly distributed] population

---

# Backyard production model: Relax A01

--
 
.hi[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
- Households are just as effective at trading as any firm

---
# 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)

<br>

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

<br>

These are represent the cities that .hi[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 .hi[A03]

With economies of scale factories can outproduce households by lowering average costs
- Use indivisible inputs (machines)
- Allow workers to specialize

In order to pay for labor, a factory must pay such that they are indifferent between working in a factory and a rural area (.hi[A1.])

However, land scarcity .hi[binds] and rents near the factory begin to increase
- Wages increase due to .hi[locational equilibrium]

---
# Factory area

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!

---

#Table of Contents

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

hello

###Existence
.smallest[

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

]
]

]
]