Econ 330: Urban Economics

# Econ 330: Urban Economics
## Lecture 05
### Andrew Dickinson
### 21 October, 2021

---

# Lecture 05: Rents

---
class: inverse
name: schedule

# Schedule

- .hi-white[Reading] (Chapter 4)
  
  - .hi-white[PS01 due tonight at 12pm]
  
  - .hi-white[Be on the look out for PS02]
  ]
  
---

# Introduction: City shape

.pull-left[
  - What is a city?
- Why do cities exist?
  ]
.pull-right[
  - What determines city size?
- How do cities grow?
]

- What economic forces determine .hi-pink[city shape]?

- Why does the price of land change?
  
  - Why are buildings taller in city centers?

---

# Introduction: City shape

- .hi[Today:] How do these choices impact rental prices .hii[within] cities
  
--
  
  - .hi[Later:] How do these choices impact rental prices .hii[across] cities
  
    - Basic introduction into [discrete choice theory](https://en.wikipedia.org/wiki/Discrete_choice)*
    
---
class: inverse, middle, center
# Data

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# Data: NYC

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# Data: NYC

![](figures/ny.png)

source: [Oppurtunity Atlas](https://www.opportunityatlas.org/)

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# Data: US

---
# Data: OR, WA

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# Data: OR, WA

---

---
class: inverse, middle 
# Leaflet

[Data](https://ajdickinson.github.io/ec330-fall21/slides/005-rents/data.html)

---
name: bid-rent
class: inverse, middle, center
# Bid-Rent Curves

---
# The Bid-Rent Curve

A .hi[Bid - Rent Curve:] The relationship between rental prices and the distance of land from the city center .pink[†]

.footnote[
.pink[†] It actually does not have to be the city center -- can be a point of attraction. In this class we will always use the city center though.
]

- .hi-orange[Housing:] Accessibility to employment (low commuting costs)

- .hi-orange[Industrial Space:] Accessibility to consumers and suppliers

- .hi-orange[Tech/Office Space:] Accessibility to information

---
# Agricultural land rent model

- .hi[Land rent:] Periodic payment by a land consumer to a landowner

- .hi[Market value:] The amount paid to become the landowner

Rent on a plot of land is determined by how productive the plot is

- .hi[Agriculture:] Price of plot is determined by fertility
  
--

.hii[Consider a setting] where farmers grow corn on two types of land 
.pull-left[
  - High fertility (HF): Produces 4 units of corn]
.pull-right[
  - Low fertility (LF): Produces 2 unites of corn]
  
---
# Agricultural land rent model

.hi[Assumptions:]

.pull-left[
- .hi[(i).] Farmers rent from landowners
- .hi[(ii).] No barriers to the corn market
- .hi[(iii).] Perfect competition
]
.pull-right[
`$TC_{-r} = 15$` (excluding rent)

`$TC = 15 + r$` & `$P_{corn} = 10$`
]

.pull-left[
.hi-pink[Revenue:] `$TR = P_{corn} \cdot Q_{corn}$`
- HF: `$TR_{HF} = 10 \cdot 4 = 40$`
- LF: `$TR_{LF} = 10 \cdot 2 = 20$`
]

.pull-right[
.hi-pink[Profit:] `$\Pi = TR - TC$`
- `$\Pi_{HF} = TR_{HF} - TC = 40 - 15 - r$`
- `$\Pi_{LF} = TR_{LF} - TC = 20 - 15 - r$`
]

---
# Agricultural land rent model

The following table computes maximum WTP for rent:

![](./figures/table01.png)

Since there are no barriers to entry, more firms will enter

- `$\Pi \rightarrow 0$`

- `$\Pi_{HF} = TR_{HF} - TC = 40 - 15 - r = 0 \Rightarrow r = 15$`
- `$\Pi_{LF} = TR_{LF} - TC = 20 - 15 - r = 0 \Rightarrow r = 5$`

---
# (i) Housing prices model

Extend the bid-rent model to the housing sector within a city

In cities WTP for land depends on .hi[accessibility] rather than productivity

---
# (i) Housing prices model: Indifference

- Locational Eq

- IE: A marginal increase in rent just offsets the lower commuting costs
  
--

`\begin{align*}
\Delta P \cdot h + \Delta x \cdot t = 0
\end{align*}`

- `$P$`: .hi[Price] of housing (per `$ft^2$`)

- `$h$`: .hi[Housing quantity] ( `$ft^2$` )

]

- `$x$`: .hi[Distance] of commute (miles)

- `$t$`: .hi[Commuting costs] (per mile)

]