Econ 330: Urban Economics

# Econ 330: Urban Economics
## Lecture 02
### Andrew Dickinson
### 07 October, 2021

---

# Lecture 02: Review & The 5 Axioms of Urban Economics

---
class: inverse
name: schedule

# Schedule

- .hi-white[EC-201 Review Quiz on Canvas]
  
  - .hi-white[Letter of Intro on Canvas]
  
  - [Reading:](https://rawcdn.githack.com/ajdickinson/ec330-summer21/db71091164ea554b0bb7c7bb90528ece563e0bac/resources/Triumph-of-the-City-Edward-Glaeser.pdf) intro + chapter 1
]

---
class: inverse, middle
name: ec201_review
# Review

Resources for more EC-201 review: [Khan academy](https://www.khanacademy.org/economics-finance-domain/microeconomics/basic-economic-concepts-gen-micro#economics-introduction)

---
name:demand
# Review 011: Demand

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

- When prices increase, quantity demanded decreases

<br>

The key players are .hii[consumers]

]

<table class="table" style="font-size: 18px; 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;"> 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;color: #314f4f !important;background-color: white !important;"> 10 </td>
   <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> 0 </td>
  </tr>
</tbody>
</table>
]

--
  
  - .hi[Demand curves] are constructed from .hi[consumers] making optimal purchase decisions

---

# Review 011: Demand

Movement vs shift in demand

---

# Review 011: Demand

---

# Review 012: Supply

- When prices increase, the quantity supplied increases

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

<br>

The key players are .hi[firms]
]

.pull-right[
.hii[Example:] Supply schedule
<table class="table" style="font-size: 18px; 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;"> 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;color: #314f4f !important;background-color: white !important;"> 10 </td>
   <td style="text-align:center;color: #314f4f !important;background-color: white !important;"> 1250 </td>
  </tr>
</tbody>
</table>
]

---

# Review 012: Supply

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

Movement vs shift in demand

---

# Review 012: Supply

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

---
# Review 013: Equilibrium + surplus

- .hi[Equilibrium:] A pair of points `\((Q*,P*)\)` such that there is no excess supply or demand

- Supply = Demand
  
  - .ul[.blue[Fundamental Assumptions:]] Marginal value (utility) is decreasing and marginal cost is increasing
  
--
  
- .hi[Consumer Surplus:] The difference between a consumers .hi-gold[maximum] willingness to pay (WTP) and the market price

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

---
# Review 013: Market equilibrium

`\begin{align*}
Q = 1250 - 125*P \\
Q = 125*P
\end{align*}`

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

---
# Review 013: Market equilibrium shifts

---
# Example: Consumer surplus

![](./auffhammer_tweet.png)

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

---

# Example: Solve for the equilibrium

Suppose we are given the following:

- Supply: `\(\color{#e64173} {P(Q_s) = 10 + Q_s}\)`

- Demand: `\(\color{#6A5ACD} {P(Q_d)  = 20 - 4*Q_d}\)`

---
# Example: Solve for the equilibrium

- Supply: `\(\color{#e64173} {P(Q_s) = 10 + Q_s}\)`

- Demand: `\(\color{#6A5ACD} {P(Q_d)  = 20 - 4*Q_d}\)`

---
# Example: Solve for the equilibrium

- .hi[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*}`

- .hi[Consumer Surplus]:

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

- .hi[Producer Surplus]:

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

- .hii[in percentage terms]

- .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 014: Elasticities (examples)

Own price elasticity:

Cross price elasticity:

---
# Review 014: 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 014: Elasticities (questions)

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

- Substitutes, because 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, because an increase in the price of `\(y\)` .hi[decreases] demand for `\(x\)`
  
  - Lame example: Left and right shoes; pb and bananas
  
---
name:profit
# Review 015: 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 015: 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 015: 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 016: 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 [lecture 01](https://rawcdn.githack.com/ajdickinson/ec330-summer21/a75becc5e8f60e4d338d1a81d452b5fd09c2a905/slides/001-intro/01-intro.html), we are after some big questions in this course

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

- A 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 axioms of urban econ are 5 assumptions that we will take _as given_ throughout the class

- Almost everything moving forward 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

---
class: hide-count

# 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
  
--

`\(\implies\)` No incentive exists

- 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

---
class: hide-count
# 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_
  
--

- 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

---
class: hide-count
# 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
  
.footnote[.hi[†]: Highest total surplus]
  
--
  
  - .hi[Example:] In absence of quotas, do people fish too much or too little?
  
--
    - Too much. This harms future fisheries
--

Negative externalities are .hii[overprovided]

Positive externalities are .hi[underprovided]
  
  - So 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
  
--

<br>

---

# 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)

]
]