Review + The 5 Axioms of Urban Economics

.title[
# Review + The 5 Axioms of Urban Economics
]
.subtitle[
## EC 330, Set 02
]
.author[
### Andrew Dickinson
]
.date[
### Fall 2022
]

---

# Schedule

.hi-white[(i) Reading: intro + chapter 1] [(link)](https://rawcdn.githack.com/ajdickinson/ec330-summer21/db71091164ea554b0bb7c7bb90528ece563e0bac/resources/Triumph-of-the-City-Edward-Glaeser.pdf)
  
.hi-white[(ii) PS01 (posted later this week)]
]

---
class: inverse, middle
# Road map

---
class: inverse, middle
name: demand
# Review: Demand

---
name:demand
# Review 01: Demand

.hi[Demand:] Quantity of a good that a .hi-blue[consumers] are willing/able to purchase at a given price

.hi[Demand Curve:] A [function](https://linkshortner.net/RspsX) that describes the relationship between prices and quantities demanded ([ceteris paribus](https://en.wikipedia.org/wiki/Ceteris_paribus))

- `\(P \uparrow \longrightarrow Q_d \downarrow\)`

- When prices increase, quantity demanded decreases

]

<table class="table" style="font-size: 16px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;"> Price </th>
   <th style="text-align:center;"> Quantity </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> 0 </td>
   <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> 1250 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> 2 </td>
   <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> 1000 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> 4 </td>
   <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> 750 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> 6 </td>
   <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> 500 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> 8 </td>
   <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> 250 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 10 </td>
   <td style="text-align:center;"> 0 </td>
  </tr>
</tbody>
</table>
]

--
  
.smallerer[.hi[Demand curves] are constructed by optimal consumption decisions by .hi[consumers]]

---
# Review 01: Demand

---
count: false -->
# Review 01: Demand

Difference between a .hi-blue[movement] vs a .hi-green[shift] in demand

.hi[(i)] A .hi-blue[movement] along the demand curve
- A change in price causes a movement along a demand curve

.hi[(ii)] A .hi-green[shift] in the demand curve
- A shift occurs when the whole curve (function) changes
- Either left or right .hi-red[NOT] up or down
- Examples of demand shifts
  - Price of a substitute/compliment good changes
  - Rise of incomes (pandemic checks)
  - Seasonal factors 
  - Change in tastes/popularity ([chicken]( https://www.westonaprice.org/wp-content/uploads/win2017moody1.jpg))

---
# Review 01: Demand

---
class: inverse, middle
name: demand
# Review: Supply

---
# Review 02: Supply

.hi[Supply Curve:] A function that describes the relationship between prices and quantities supplied ([ceteris paribus](https://en.wikipedia.org/wiki/Ceteris_paribus))

- When prices increase, the quantity supplied increases

- `\(P \uparrow \longrightarrow Q_s \uparrow\)`

]

.pull-right[
.hii[Example:] Supply schedule
<table class="table" style="font-size: 16px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;"> Price </th>
   <th style="text-align:center;"> Quantity </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> 0 </td>
   <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> 2 </td>
   <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> 250 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> 4 </td>
   <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> 500 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> 6 </td>
   <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> 750 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #314f4f !important;background-color: white !important;"> 8 </td>
   <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> 1000 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 10 </td>
   <td style="text-align:center;"> 1250 </td>
  </tr>
</tbody>
</table>
]

---

# Review 02: Supply

.center[
<img src="02-review_files/figure-html/plot02a-1.png" style="display: block; margin: auto;" />
]

---
count: false -->
# Review 02: Supply

Difference between a .hi-blue[movement] vs a .hi-green[shift] in supply

.hi[(i)] A .hi-blue[movement] along the supply curve
- A change in price causes a movement along a supply curve

.hi[(ii)] A .hi-green[shift] in the supply curve
- A shift occurs when the whole curve (function) changes
- Either left or right .hi-red[NOT] up or down
- Examples of supply shifts
  - Changes in production costs (steel increases `\(\rightarrow\)` car market)
  - Natural conditions (drought)
  - New technology (conveyor belt)
  - Government policies (.hi-red[taxes], .hi-blue[subsidies], regulations)

---
# Review 02: Supply

.center[
<img src="02-review_files/figure-html/plot02b-1.png" style="display: block; margin: auto;" />
]

---
class: inverse, middle
# Review: Equilibrium

---
# Review 03: Equilibrium + surplus

.hi[Equilibrium:] Pair of points `\((Q^*,P^*)\)` such that no excess supply or demand remains
- Perfect market (Supply = Demand)

.hi[Implicit assumptions] 
- .hii[(i)] marginal values (utilities) decrease
- .hii[(ii)] marginal costs increase

.hi[Shortage:] Situation in which current demand for a product exceeds supply (excess demand)
- Food shortages
- Toilet paper during COVID

---
count: false
# Review 03: Equilibrium + surplus

.hi[Equilibrium:] Pair of points `\((Q^*,P^*)\)` such that no excess supply or demand remains
- Perfect market (Supply = Demand)

.hi[Implicit assumptions] 
- .hii[(i)] marginal values (utilities) decrease
- .hii[(ii)] marginal costs increase

.hi[Surplus:] Situation in which current supply for a product exceeds demand (excess supply)
- Unemployment
- Oil price war during COVID

---
class: clear
count: false

---
count: false
# Note: Drawing

Your grade will depend on the .hi[clarity] of your drawings on both problem sets and .hi-red[exams]

To get .hi[full points], your graphs must includes the following
- label your axis
- label your curves ( `\(D\)`, `\(D'\)`, `\(S\)`, `\(S'\)` )
- label your eqs ( `\(E\)`, `\(F\)` )
- _dashed_ lines from eqs to axis

---
# Review 03: Equilibrium

`\begin{align*}
Q_d = 1250 - 125*P_d \\
Q_s = 125*P_s
\end{align*}`

.center[
<img src="02-review_files/figure-html/plot03-1.png" style="display: block; margin: auto;" />
]

---
class: inverse, middle
# Review: Surplus

---
# Example: Consumer surplus

.hi[Consumer Surplus:] The difference between a consumers .hi-blue[maximum] willingness to pay (WTP) and the market price

.hi[Producer Surplus:] The difference between the price producers .hi-red[minimum] willingness to sell and the market price

.center[
<img src="02-review_files/figure-html/plot04-1.png" style="display: block; margin: auto;" />
]

---
# Example: Consumer surplus

![](./auffhammer_tweet.png)

Source: [@auffhammer](https://twitter.com/auffhammer)

---

# Example: Solve for the equilibrium

Suppose we are given the following:

Supply: `\(\color{#4c566a} {P(Q_s) = 10 + Q_s}\)`

Demand: `\(\color{#b48ead} {P(Q_d)  = 20 - 4*Q_d}\)`

---
# Example: Solve for the equilibrium

Suppose we are given the following:

Supply: `\(\color{#4c566a} {P(Q_s) = 10 + Q_s}\)`

Demand: `\(\color{#b48ead} {P(Q_d)  = 20 - 4*Q_d}\)`

---
# Example: Solve for the equilibrium

`\begin{align*}
10 + Q^\star &= 20 - 4*Q^\star\\
5Q^\star &= 10\\
Q^\star &= 2
\end{align*}`

Plug this into either supply or demand equation to get:

`\begin{align*}
P^\star = 10 + 2 = 12
\end{align*}`

- `\(CS= \frac{1}{2}*(20-12)*(2-0) = 8\)`
  
--

- `\(PS = \frac{1}{2}*(12-10)(2-0) = 2\)`
  
---
# Example:

Using the follow supply + demand functions

Determine:

- (i) Graph each curve and label carefully
- (ii). Equilibrium prices ( `\(p^*\)` ) and quantities ( `\(q^*\)` )
- (iii). Consumer surplus
- (iv). Producer surplus

---
name: elasticites
# Review 04: Elasticities

- .hi[Own price elasticity (good x)]: Measures how much quantity demanded for .hi[x] will respond to a one percent change in the price of good .hi[x]
  
    - Formula: `\(\varepsilon_{x, P_x} = \frac{\%\Delta Q_x}{\%\Delta P_x}\)`
--

- .hi[Cross price elasticity (goods x,y)]: Measures how much quantity demanded for .hi[x] will respond to a one percent change in the price of .hii[y]
    
    - Formula: `\(\varepsilon_{x,P_y} = \frac{\%\Delta Q_x}{\%\Delta P_y}\)`
    
---
# Review 04: Elasticities

Suppose `\(\varepsilon_{x, P_x}= -0.5\)`. What does this mean in words?

A 1% change in the .hi[price of good x] will lead to a .5% change in the _opposite_ direction in the .hi[quantity demanded for good x]

The equation can be helpful. If `\(\varepsilon_{x, P_x}= -0.5\)`, then:

`\begin{align*}
\frac{\%\Delta Q_x}{\%\Delta P_x}&= -0.5\\
\%\Delta Q_x &= -0.5 * \%\Delta P_x
\end{align*}`

---
exclude: false
# Review 04: Elasticities (questions)

- If `\(\varepsilon_{x,y}>0\)`, are these goods complements or substitutes?

- Substitutes, an increase in the price of `\(y\)` .hi[increases] demand for `\(x\)`
  
  - Lame example: cheerios and other cereal
  
--

-  If `\(\varepsilon_{x,y}<0\)`, are these goods complements or substitutes?

- Complements, an increase in the price of `\(y\)` .hi[decreases] demand for `\(x\)`
  
  - Lame example: Left and right shoes; pb and bananas
  
---
name:profit
# Review 05: Cost functions

- .hi[Total Revenue (TR)]: Total money firm brings in from selling `\(Q\)` units. 
  
  - `\(TR = P*Q\)`
  
--

- .hi[Total Cost (TC)]: The cost of producing `\(Q\)` units units

- .hi[Average Cost (AC)] = `\(\frac{TC}{Q}\)`

- .hi[Profit] (denoted as `\(\Pi\)`):

`\begin{equation}
\Pi = TR-TC
\end{equation}`
  
---
# Review 05: Cost functions

Suppose the price of the output good is `\(3\)` dollars per unit. Suppose a firm's cost function is `\(TC(Q) = 1+Q\)`. If the firm produces 8 units of the good, calculate:

- `\(TR\)`

- `\(TC\)`

- `\(AC\)`

- `\(\Pi\)` (profit)

---

# Review 05: Cost functions

Suppose the price of the output good is `\(3\)` dollars per unit. Suppose a firm's cost function is `\(TC(Q) = 1+Q\)`. If the firm produces 8 units of the good, calculate:

- `\(TR = 3*8 = 24\)`

- `\(TC = 1 + 8 = 9\)`

- `\(AC = \frac{9}{8}\)`

- `\(\Pi = 24 - 9 = 15\)`

---
name:utility

# Review 06: Utility

- .hi[Utility:] Satisfaction one receives from consuming a good or a service

- Ordinal not cardinal; only know order of preference not how much
  
--

- .hi[Utility function:] `\(U(x)\)` A function that describes utility given from `\(x\)`
  
--
  
- .hi[Marginal Utility:] Additional utility received from one additional good

- .hi[The Law of Diminishing Marginal Utility:] Marginal utility decreases as one consumes more and more goods or services

---

---

# The five axioms of urban economics

As discussed in .hii[set 01], we are after some big questions in this course

- Agree upon a few basics before moving onto more complex problems

.hi[Axiom:] Statement which is regarded as being established or evidently true
- Long agreed upon assumptions

Axioms are the building blocks upon which theory is built

The 5 assumptions that we will take _as given_ throughout the class

- Almost everything will be tied to one of these assumptions

---

# The five axioms of urban economics

Some lectures will focus on refining our understanding of these axioms

Almost everything we learn ties back to one of the 5 axioms

---
count: false

# The five axioms of urban economics

Some lectures will focus on refining our understanding of these axioms

Almost everything we learn ties back to one of the 5 axioms

---

name:axiom_1
#Axiom 1

.hi[Locational EQ:] The balance that exists when there is no incentive for firms or households to move
- .hi[Prices] must adjust s.t. there is indifference between locations
- no incentive exists to move

- Rents .hi[near] downtown > rents .hii[far] from downtown
- Home prices .hi[near] good schools > home prices .hii[near] bad schools
- Wages in .hi[high-cost] cities > wages in .hii[low-cost] cities
- Amenities in .hi[high-cost] cities > amenities in .hii[low-cost] cities

---
count: false
# The five axioms of urban economics

Some lectures will focus on refining our understanding of these axioms

Almost everything we learn ties back to one of the 5 axioms

---
name:axiom_2
#Axiom 2

- AKA _positive feedback loop_
  
--

> Consider a city where the sellers of new automobiles are initially spread evenly throughout the city. If one seller relocates next to another seller on Auto Road, what happens next? Auto consumers compare brands before buying, and the pair of sellers on Auto Road will facilitate comparison shopping and thus attract buyers. The increased consumer traffic on Auto Road will make it an attractive site for other auto sellers, so they will move too. The ultimate result is an “autorow,” a cluster of firms that compete against one another, yet locate nearby.

---
count:false 
#Axiom 2

- AKA _positive feedback loop_

- Tech firms in the Silicon Valley

- Artists in Santa Fe, NM

- Hippies in Eugene, OR

Explains common pattern of clustering of similar people and firms

---
count: false
# The five axioms of urban economics

Some lectures will focus on refining our understanding of these axioms

Almost everything we learn ties back to one of the 5 axioms

---
name:axiom_3
# Axiom 3

.hi[Externality]: A .hii[cost] or .hi[benefit] of a transaction experienced by somebody who is not involved in the transaction

.hii[Negative Externalities] (costs)
.pull-left[
- Pollution
- [Car noise](https://www.youtube.com/watch?v=Wy4ZK4qBUrI)]
.pull-right[
- Dilapidated housing
- Second-hand smoke]

.hi[Positive Externalities] (benefits)
.pull-left[
- Vaccines
- Public schools]
.pull-right[
- Remodeling housing
- Beekeepers]

---
# Axiom 3: Externalities

What do these have to do with .hi[efficiency]?<sup>.hi[†]</sup>

Private incentives are not aligned with social costs or benefits
- .hi[Example:] In absence of quotas, do people fish too much or too little?
- Too much. This harms future fisheries

<br>

Negative externalities are .hii[overprovided]

Positive externalities are .hi[underprovided]
  
A market with an externality is .hi[inefficient]

---

# The five axioms of urban economics

Some lectures will focus on refining our understanding of these axioms

Almost everything we learn ties back to one of the 5 axioms

---

name:axiom_4
#Axiom 4

- .hii["Lumpy" inputs:] Capital inputs may be indivisible; cannot scale down
  
  - .hii[Factor specialization:] Larger operations have more employees who then can specialize

--
.pull-left[
- Transportation of goods
- Pizza ovens]
.pull-right[
- Education
- Building CPU]

---

# The five axioms of urban economics

Some lectures will focus on refining our understanding of these axioms

Almost everything we learn ties back to one of the 5 axioms

---

name:axiom_5
#Axiom 5

Degree of competition dictates .hi[number of firms] in the market
- Firms enter (drives price down) until .hi[economic profit] `\(\rightarrow\)` zero
- Enough firms earn enough to stay in business but no more

- Different from accounting profit; hear on the news/balance sheets
  
--

.hi[Examples:] 
- breweries in the [post-homebrew era](https://beerandbrewing.com/the-day-homebrewing-was-legalized/)
- marijuana dispensaries after legalization

---

# List of the 5 Axioms

---
class: inverse, middle
# Schedule
.pull-left[
.hi-white[Next Class]:

- Determinants of city size]

- [Reading:](https://rawcdn.githack.com/ajdickinson/ec330-summer21/db71091164ea554b0bb7c7bb90528ece563e0bac/resources/Triumph-of-the-City-Edward-Glaeser.pdf) intro + chapter 1]

---

#Table of Contents

.col-left[
###Econ 201 Review
.smallest[
1. [Supply & Demand](#supply_demand)
1. [Elasticities](#elasticities)
1. [Profit, Revenue, & Cost](#profit)
]
]

1. [Axiom 1: Prices adjust to acheive locational equilibrium](#axiom_1)
1. [Axiom 2: Self-reinforcing effects generate extreme outcomes](#axiom_2)
1. [Axiom 3: Externalities are Inefficient](#axiom_3)
1. [Axiom 4: Production is subject to economies of scale](#axiom_4)
1. [Axiom 5: Competition generates zero economic profit](#axiom_5)

]
]