Econ 330: Urban Economics

# Econ 330: Urban Economics
## Lecture 2
### John Morehouse
### January 8th, 2020

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

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# Schedule

## Today

1) .hi.purple[EC201 Review]

2) .hi.purple[5 Axioms of Urban Economics]

## Upcoming

- .hi.slate[EC201 Review Quiz on Canvas]
  
  - .hi.slate[Letter of Intro on Canvas]
  
  - .hi.slate[Reading] (intro & chapter I of _ToTC_)

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- The quiz will open .hi[tonight at 8PM] and is due .hi[Monday the 13th] @ Midnight

- __90 Minute__ Time limit, and __one__ attempt. It should take you _well_ under 90 minutes

- Worth 4% of your final grade

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#EC201 Quiz

##.hi.orange[Format]

- .hi[5 Questions] worth .hi.purple[4 points each]

- 2 Multiple Choice

- 3 Calculations

## .hi.orange[Topics]:

- Graph Supply and Demand. Compute Equilibrium
  
  - Compute Consumer and Producer Surplus
  
  - Elasticities (interpretation)
  
  - Profit, cost, revenue

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name:supply_demand
# Supply & Demand

We will start with .hi.purple[supply] & .hi[demand]:

- .hi.slate[Supply curves] are constructed from .hi.purple[firms] making the best production decisions they can

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

The key players in *the* market are:

- .hi.purple[firms] (generating supply)
  
  - .hi[consumers] (generating demand)
  
  
--

.hi.slate[Fundamental Assumptions]: Marginal value (utility) is decreasing and marginal cost is increasing

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#EC201: Supply & Demand

##Related Definitions

- .hi.slate[Equilibrium]: A pair of points `\((Q^\star, P^\star)\)` such that there is no excess supply or demand
  
  - In other words, equilibrium is when Supply = Demand
  
--
 
--

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

- .hi.slate[Producer Surplus]: The .hi.purple[difference] between the producers __minimum__ willingness to sell and the market price

--
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# An Example

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

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#EC201: Market Equilibrium Computation

.hi.slate[Example]

Suppose we are given the following:

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

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

##Tasks

1. Carefully graph and label both curves

1. Compute the Equilibrium

1. Compute Consumer and Producer Surplus

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#EC201: Example

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#Calculation

- .hi.slate[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.slate[Consumer Surplus]:

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

- .hi.slate[Producer Surplus]:

- `\(PS = \frac{1}{2}*(12-2)(2-0) = 2\)`

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name:elasticites
#EC201: Elasticities

In general, elasticities measure responsiveness of one variable to another, __in percentage terms__

.hi.slate[Common elasticities]

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

---

#Elasticities: Interpretations

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

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*}`

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__Review Questions__:

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

- Substitutes, because an increase in the price of `\(y\)` __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 `\(y\)` __decreases__ demand for `\(x\)`
  
---

name:profit
#EC201: Cost & Production

##Definitions

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

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

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

- .hi.slate[Profit] (often denoted as `\(\pi\)`): `\(\pi = TR-TC\)`

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#EC201: Cost & Production Ex

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:

- `\(TR\)`

- `\(TC\)`

- `\(AC\)`

- Profit

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#EC201: Cost & Production Ex

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:

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

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

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

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

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1. .hi[EC201 Review]: ✅

- Supply & Demand
  
  - Elasticities
  
  - Production & Cost

2. .hi.purple[5 Axioms of Urban Economics]

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#Foundations

As discussed in [lecture 1](https://rawcdn.githack.com/johnmorehouse/EC330_UrbanEcon/7a8c47a98871c1b0777d7af3a2cd490cf1fd6c23/Slides/001-intro/lecture_one.pdf), we are after some big questions in this course

- It is useful to agree upon a few basics before moving onto more complicated problems

## The 5 Axioms

- 5 .hi[assumptions] that we will _take as given_ throughout the class

- Some lectures will be focused on refining our understanding of these axioms

- Almost everything we learn here ties back to one or multiple of the 5 axioms

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name:axiom_1
#Axiom 1

__Axiom 1__: _Prices adjust to acheive .hi[locational equilibrium]_ <sup>.hi[†]</sup>

- .hi[Locational Equilibrium]: The balance that exists when there is no incentive for firms or households to move

.hi.slate[Examples]

- Rents .hi.orange[near] campus > rents .hi.purple[far] from campus

- Home prices .hi.orange[near] good schools > home prices .hi.purple[near] bad schools

- Wages (and or) Amenities in .hi.orange[high] cost cities > Wages (and or) Amenities in .hi.purple[low] cost cities

---

name:axiom_2
#Axiom 2

__Axiom 2__: _.hi[Self-reinforcing effects] generate extreme outcomes_

- Also called a _positive feedback loop_

.hi.slate[Examples]

- Tech firms in the Silicon Valley

- Artists in Santa Fe, NM

Useful for explaining why it is common to have clustering of people and firms of similar types

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name:axiom_3
#Axiom 3

__Axiom 3__ _.hi[Externalities] are Inefficient_

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

.hi.purple[Negative Externalities] (costs)

- Pollution
  
  - Noise 
  
  - Dilapidated housing

.hi.orange[Positive Externalities] (benefits)

- Vaccines
  
  - Education

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#Externalities part II

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

- With any externality, private incentives are not aligned with social costs or benefits
  
--
  
  - .hi.slate[Example]: In the absence of quotas do people fish too much or too little?
  
--
    
--

- Too much. This harms future fisheries
--

- Negative externalities are .hi.purple[overprovided] and positive externalities are .hi.orange[underprovided]
  
  - So a market with an externality is .hi[inefficient]

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name:axiom_4
#Axiom 4

__Axiom 4__: _Production is subject to .hi[economies of scale]_

- .hi[Economies of Scale]: When the average cost of production decreases as quantity produced increases
  
--

.hi.slate[Examples]

- __Transportation__ of good & people
  
  - Trains shipping to small towns .hi.orange[vs] big cities
  
--

- __Education__
  
  - 20 person class .hi.orange[vs] 80 person class
  
--

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name:axiom_5
#Axiom 5

__Axiom 5__: _Competition generates zero .hi[economic profit]_

- Degree of competition dictates .hi.purple[number of firms] in the market

- Firms enter (drives price down) until .hi[economic profit] is zero. That is, enough firms earn enough to stay in business but no more

- .hi[Economic Profit]: inclusive of .hi.purple[oppurtunity cost]

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# List of the 5 Axioms

1. Prices adjust to acheive .hi[locational equilibrium]

2. .hi[Self-reinforcing effects] generate extreme outcomes

3. .hi[Externalities] are Inefficient

4. Production is subject to .hi[economies of scale]

5. Competition generates zero .hi[economic profit]

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# Checklist
1. .hi[EC201 Review]: ✅

- Supply & Demand
  
  - Elasticities
  
  - Production & Cost

2. .hi[5 Axioms of Urban Economics]: ✅

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#Planning

- City Size

- Review Quiz (.hi.purple[Monday the 13th] @ Midnight)

- Letter of Intro (.hi.purple[Tuesday the 14th] @ Midnight)

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#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)

]
]

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