Econ 330: Urban Economics

class: center, middle, inverse, title-slide

# Econ 330: Urban Economics
## Lecture 07
### Andrew Dickinson
### 29 July, 2021

---

class: inverse, center, middle
# Lecture 07: Urban Labor Markets

---
class: inverse, middle
# Schedule

.pull-left[
.ul[.bigger[.hi-gold[Today:]]]

.hi-white[(i). Urban labor markets]

- .hi-white[Urban labor demand]

- .hi-white[Urban labor supply]

- .hi-white[Urban labor EQ]

]

--

.pull-right[
.ul[.bigger[.hi-gold[Upcoming:]]]

- .hi-white[Reading] (Chapter 5)
  
  - .hi-white[Problem set 01 due on Sunday at Midnight]
  
.ul[.bigger[.hi-gold[After MT:]]]

- .hi-white[(ii). Monopsony]
  ]

---
# Housekeeping

---
class: inverse, middle, center
# Urban labor markets

---
# Urban labor Markets

.hi[Why care about labor markets in urban economics?]

David Card: 
> A city _is_ a labor market

--

Cities provide incentives for firms and workers to locate close to each other

Density of a city is generated entirely by incentives in the labor market

--

<br>

.qa[Q:] Modeling .hii[individual] location decisions, what should we consider?

---
# Urban labor Markets

.hi[What are the most important features in location decisions?]

--
.pull-left[
- Wages
- Rents
- Amenities (catch all)]

--
.pull-right[
- Birthplace
- Distance to birthplace]

--

.hii[Wages] are significant factor of individual/household location choices

.hi[Imagine] if Amazon/Google/Microsoft opens a campus in Portland
  
--

- What would happen to rents? Gentrification? Commute times?
  
--

<br>

.hi[Introducing large amounts of high paying jobs + capital changes a city]

---
# Urban labor Markets

.hi[A labor market consists of:]

.hi[(i).] Firms that buy labor. Generate labor demand

.hi[(ii).] HH's who sell labor. Generate labor supply

--

Labor and urban economist model labor markets (supply) differently

--

.hi-gold[Labor:] Discuss labor supply as being generated from labor-leisure tradeoff

- Model: Rational agents making optimal choices over leisure/education

--

.hii[Urban:] Discuss labor supply as being generated from _location choices_
  
  - Assume people work fixed hours but choose where to work

---
class: inverse, middle
# Urban labor Markets: Labor demand

---
# Urban labor Markets: Labor demand

What do both fields have (somewhat) in common?

--

.center[.hi[Labor demand]]

--

.ul[.hi[Definition:] Labor Demand]

- Set of quantities of labor demanded corresponding to a _set_ of wages
  
--
 
.qa[Q:] What's the difference between changes in:
.pull-left[
- _labor demand_]
.pull-right[
- _quantity of labor demanded_]

--

`\(\Delta\)` Labor demand: Shift in the demand curve

`\(\Delta\)` Quantity of labor demanded: Movement along a demand curve

---
# Urban labor Markets: Labor demand

We will start with the .hi[competitive] model:

--

.ul[.hi[Assumptions:]]

.hii[(i).] Firms seek to maximize profits

--

.hii[(ii).] Markets are perfectly competitive (in .orange[both] inputs and output)

--

`\(\Rightarrow\)` No individual firm can influence the price of labor (or other inputs)
  
`\(\Rightarrow\)` No individual firm can influence the output price

--

Are these assumptions reasonable? Discuss

--

---
# Urban labor Markets: Labor demand

Derive a condition for EQ labor the firm will hire in the competitive model?

`\begin{align*}
\pi &= P*Q - TC
\end{align*}`

---
# Urban labor Markets: Labor demand

Derive a condition for EQ labor the firm will hire in the competitive model?

`\begin{align*}
\pi &= P*Q - TC\\
\pi &= \underbrace{P*F(L,K)}_\text{TR} - \underbrace{w*L-r*K}_{\text{TC}}
\end{align*}`

where:

--

- `\(P\)`: Output price
 
 - `\(F(L,K) = Q\)`: Quantity produced (function of labor and capital)
 
  - `\(Q = F(L,K)\)`
  
--

- `\(w\)`: Wage rate; `\(L\)`: total labor employed `\(\Rightarrow w*L =\)` cost of labor
 - `\(r\)`: rental rate; `\(K\)`: capital `\(\Rightarrow r*K =\)` cost of capital

---
# Urban labor Markets: Labor demand

.hi[Claim]: Firm hires labor iff the _marginal profit_ w.r.t to labor is positive.

--

.hi[.ul[Definition:] Marginal Profit w.r.t to labor] ( `\(\frac{\Delta \pi}{\Delta L}\)` )

- The change in profit from hiring an additional unit of labor

--

.hi["Proof":] (Too many cooks)

- If `\(\frac{\Delta \pi}{\Delta L} <0\)`, added profit from an additional unit of labor is negative (ie. a loss), so the firm _should not_ hire the next unit

--

- If `\(\frac{\Delta \pi}{\Delta L} > 0\)`, added profit from an additional unit of labor is positive (ie. a gain), so the firm _should_ hire the next unit

--

- If `\(\frac{\Delta \pi}{\Delta L} = 0\)` Optimal allocation for the firm. Can't do better

--

---
# Urban labor Markets: Labor demand

.ul[.hi[Definitions:]]

- .hi[Marginal Product of Labor]: Change in output from an additional unit of labor employed

--

- `\(MP_L = \frac{\Delta F(L,K)}{\Delta L}\)`

--

- .hi[Marginal Revenue Product of Labor]: Value of the change in output from an additional unit of labor employed

--

-  `\(MRP_L = P*\frac{\Delta F(L,K)}{\Delta L}\)`

---
# Urban labor Markets: Labor demand

So what is `\(\frac{\Delta \pi}{\Delta L}\)`?

--

`\begin{align*}
\frac{\Delta \pi}{\Delta L} = P*\frac{\Delta F(L,K)}{\Delta L} - w*\frac{\Delta L}{\Delta L}  
\end{align*}`

---
# Urban labor Markets: Labor demand

So what is `\(\frac{\Delta \pi}{\Delta L}\)`?

`\begin{align*}
\frac{\Delta \pi}{\Delta L} &= P*\frac{\Delta F(L,K)}{\Delta L} - w*\frac{\Delta L}{\Delta L} \\
&= P*MP_L - w\\
& = MRP_L - w
\end{align*}`

--

Now, set `\(\frac{\Delta \pi}{\Delta L}=0\)` to get the labor demand curve:

`\begin{align*}
 MRP_L - w =0 \implies MRP_L = w
\end{align*}`

--

.center[.hi[What does this mean in words?]]

--

.center[.hii[A firm will hire labor until labor costs (wage) exactly ofsets the marginal revenue product of labor]]

---
# Urban labor Markets: Labor demand

<img src="07-labor_files/figure-html/supply_demand-1.svg" style="display: block; margin: auto;" />

---
# Urban labor Markets: Labor demand

Why might .hi[labor demand] curves vary across cities?

--

.hi[(i).] Differences in productivity across cities (agglomeration)

--

.hi[(ii).] Variation in (business) taxes across cities

--

.hi[(iii).] Industrial public service infastructure (electricity, water, gas pipelines)

--

.hi[(iv).] Land use policies
  - stricter zoning `\(\implies\)` higher land price `\(\implies\)` less money for other inputs

--

.hi[(v).] Demand for a city's exported goods

---
# Urban labor Markets: Labor demand

.qa[Q]: What would two cities where everything is equal except one has a higher productivity of labor look like?

--

<img src="07-labor_files/figure-html/supply_demand2-1.svg" style="display: block; margin: auto;" />

---
# Urban labor Markets: Labor demand

.qa[Q]: What about a city with lower export demand?

--

<img src="07-labor_files/figure-html/supply_demand3-1.svg" style="display: block; margin: auto;" />

---
class: inverse, middle, center
# Urban labor markets: Supply

---
#Labor Supply

Labor supply is driven from location decisions of individuals. What generates location choices?

--

1) .hi[Wages]

2) Rents

3) Amenities

4) Other, individual specific stuff (like birth location)

--

---
# Labor Supply

A _set_ of quantities of labor supplied corresponding to a _set_ of wages.

.qa[Q1]: What causes _movement along_ the labor supply curve?

--

- A change in wages. That's it!

--

.qa[Q2]: What causes a _shift_ of the labor supply curve?

--

1) Changes in amenities (building of a nicer school, eroding of air quality)

2) Changes in residential government expenditures (increase in taxes drives people away, increases in govt spending brings people in)

--

---
# Labor Supply

Knowing how responsive workers are to changes in wages is key for vast swaths of policies

- Estimates for labor supply elasticities are pretty big

- If `\(\varepsilon_{\text{workforce},\text{wage}} = 2\)`, what does this mean?

--

.hi.orange[In general] estimated labor supply elasticities are higher for workers with a college degree than without a college degree. What does this mean?

--

- College educated individuals are more responsive to changes in wages w.r.t to their location decisions

--

--

---
# Labor Supply Example

<img src="07-labor_files/figure-html/labor_supply-1.svg" style="display: block; margin: auto;" />

---
# Labor Supply

.qa[Question]: What happens when a city improves its school quality?

--

<img src="07-labor_files/figure-html/labor_supply2-1.svg" style="display: block; margin: auto;" />

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

---
#Equilibrium

__Defn__

- A .hi[labor market equilibrium] is a pair of points `\((L^*, W^*)\)` such that:
  
    - labor supply = labor demand

- In other words: a labor market eq is where there is no excess supply or demand
  
--

We usually think of cities as being "seperate" labor markets, so the eqs can be different across cities

--

---
# Equilibrium: Example

<img src="07-labor_files/figure-html/eq1-1.svg" style="display: block; margin: auto;" />

---
# Quiz 04

[link](https://raw.githubusercontent.com/ajdickinson/ec330-summer21/main/problem-sets/quizzes/quiz04.pdf)

---
class: inverse, center, middle
# End of MT material

---
# Min Wage Refresher

Recall from EC201: minimum wages are a form of .hi[price controls]. Specifically, a minimum wage is a:

--

- Price floor: dictates the _minimum_ allowed price for transactions in a marketplace

--

We say that a price floor is .hi.purple[effective] if it has an impact on the market equilibrium

--

- Price floors that are below the market price are ineffective

---
# Min Wage Refresher

Is the following effective/ineffective?:

<img src="07-labor_files/figure-html/min1-1.svg" style="display: block; margin: auto;" />

---
# Min Wage Refresher

The following is .hi[ineffective]

<img src="07-labor_files/figure-html/min1.5-1.svg" style="display: block; margin: auto;" />

---
# Min Wage Refresher

Is the following effective/ineffective?:

<img src="07-labor_files/figure-html/min2-1.svg" style="display: block; margin: auto;" />

---
# Min Wage Refresher

The following is .hi[effective]

<img src="07-labor_files/figure-html/min3-1.svg" style="display: block; margin: auto;" />

---
# Min Wage Refresher

<img src="07-labor_files/figure-html/min4-1.svg" style="display: block; margin: auto;" />

---
# Example: Two Cities

If we treat cities as two _seperate_ labor markets, have:

.pull-left[

<img src="07-labor_files/figure-html/city_1-1.svg" style="display: block; margin: auto;" />

]

.pull-right[

<img src="07-labor_files/figure-html/city_2-1.svg" style="display: block; margin: auto;" />

]

---
#Significance?

__2 Questions__

- Why do we care so much about modeling cities as different labor markets? .hi.purple[Discuss]
  
--

- Do you think all labor markets across cities and industries are competitive? .hi.purple[Discuss]

---
# Some Notes

- All else equal, low tax cities grow faster than high tax cities

- Elasticity (business activity, taxes)
  
--

- Across cities: -0.1 to -0.6
  
  -  Within cities: -1.0 to -3.0

--

- Manufacturers are more sensitive to tax differences
 
---

# Competitive Model

We built up labor .hi[supply] and .hi[demand]. Where do these come from?

--

- Demand: Firms
  
  - Supply: Workers

--

What did we assume about the market structure?

--

- .hi[Perfect Competition]

--

---
count: false
# Competitive Model

We built up labor .hi[supply] and .hi[demand]. Where do these come from?

- Demand: Firms
  
  - Supply: Workers

What did we assume about the market structure?

- .hi[Perfect Competition]

- Firms pay workers their MV of labor (max WTP)
  
  
--

Probably not super reasonable

--

---
# Monopsony

Let's consider a different labor market structure:

--

<center>
<font size="15"> Monopsony </font>
</center>

--

- We say a firm is a .hi[monopsonist] if they are .hi.purple[the only employer] of labor in the area (city)

- We say a firm has .hi[monopsony power] if they have the ability to influence the market wage

--

- Not to be confused with __monopoly__ (in which there is only one .hi.purple[seller] of a good)
  
  - __Monopsony__ has to do with one .hi.purple[buyer] of a good 
  
--

---
# Examples of Monopsonys

Can you think of any?

--

- Universities (go GTFF!)

- Coal Towns

- Amazon / Walmart Towns?

--

---
# Monopsony

So what do you think the main consequence(s) of .hi[monopsony] are?

<center>
<font size="15"> Monopsonists have the ability to pay a wage below the marginal value </font>
</center>

The consequences?

--

- .pink[Higher profit] for the firms

- Deadweight loss (inefficient outcome)

--

We will formalize this in a few slides, but first lets go over some evidence of local monopsonys

---
# Monopsony: Formalizing the Result

In the competive model, the firm pays the worker `\(w = MRP_l\)`.

--

- Is this what the monopsonist would do?

- Where is this?

--

---
# Recall: The competitive model

Remember: in the competitve model, the firm seeks to maximize profits (but does not influence prices).

- The competitive firm hires labor until the marginal profit w.r.t to labor is zero
  
`\begin{align*}
\pi &= TR - TC\\
\pi &= TR - wL - rK
\end{align*}`

Profit maxing cond: `\(\frac{\Delta \pi}{\Delta L} = 0 \implies MRP_L -w = 0 \implies w = MRP_L\)`

---
# Monopsony: Formalizing the Result

With a monopsonist, the amount of labor they hire influences the wage. That is, now

--
`\begin{align*}
\pi &= TR - w(L)L - rK
\end{align*}`
--

where `\(w(L)\)` is an .pink[increasing function] of the .pink[amount of labor hired]

--

- The firm should hire labor until marginal cost is equalized to marginal benefit (.hi.purple[same as before])
  
  - or: _.pink[marginal profit] wrt labor_ is equal to zero
  
`\begin{align*}
\frac{\Delta \pi}{\Delta L} =0 
\end{align*}`

---
# Monopsony: Formalizing the Result

Notation: `\(TC(L) =w(L)*L\)` is the TC from labor in monopsony (__note__: `\(w(L)\)` wage is a function of labor)

`\begin{align*}
\pi &= TR - TC(L) - rK
\end{align*}`

--

Profit Maximization:

`\begin{align*}
\frac{\Delta \pi}{\Delta L} &=0
\end{align*}`

---
count: false
# Monopsony: Formalizing the Result

Notation: `\(TC(L) =w(L)*L\)` is the TC from labor in monopsony (__note__: `\(w(L)\)` wage is a function of labor)

`\begin{align*}
\pi &= TR - TC(L) - rK
\end{align*}`

Profit Maximization:

`\begin{align*}
\frac{\Delta \pi}{\Delta L} &=0\\
MRP_L - \frac{\Delta TC(L)}{\Delta L} &= 0\\
\end{align*}`

---
count: false
# Monopsony: Formalizing the Result

Notation: `\(TC(L) =w(L)*L\)` is the TC from labor in monopsony (__note__: `\(w(L)\)` wage is a function of labor)

`\begin{align*}
\pi &= TR - TC(L) - rK
\end{align*}`

Profit Maximization:

`\begin{align*}
\frac{\Delta \pi}{\Delta L} &=0\\
MRP_L - \frac{\Delta TC(L)}{\Delta L} &= 0\\
MRP_L &= \frac{\Delta TC(L)}{\Delta L}\\
MRP_L & = MC_L
\end{align*}`

---
count: false
# Monopsony: Formalizing the Result

So the monoposonist hires until:

`\begin{align*}
MRP_L & = MC_L
\end{align*}`

Compared to the competitve outcome:

`\begin{align*}
MRP_L & = W
\end{align*}`

.hi[Important:] Note that in the competitive model, marginal cost of labor was constant (and equal to wage).

---
count: false
# Monopsony: Formalizing the Result

So the monoposonist hires until:

`\begin{align*}
MRP_L & = MC_L
\end{align*}`

Compared to the competitve outcome:

`\begin{align*}
MRP_L & = W
\end{align*}`

.hi[Important:] Note that in the competitive model, marginal cost of labor was constant (and equal to wage).

- Now: marginal cost is increasing because monopsonist is _only_ buyer of labor

---
# An Example:
.center[**Monopsonist Wage Schedule**]
<table class="table table-striped" style="margin-left: auto; margin-right: auto;">
<caption></caption>
 <thead>
  <tr>
   <th style="text-align:center;"> .pink[Wage] </th>
   <th style="text-align:center;"> .purple[Labor] </th>
   <th style="text-align:center;"> TC </th>
   <th style="text-align:center;"> .hi[MC] </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;line-height: 110%;"> 1 </td>
   <td style="text-align:center;line-height: 110%;"> 1 </td>
   <td style="text-align:center;line-height: 110%;">  </td>
   <td style="text-align:center;line-height: 110%;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;line-height: 110%;"> 2 </td>
   <td style="text-align:center;line-height: 110%;"> 2 </td>
   <td style="text-align:center;line-height: 110%;">  </td>
   <td style="text-align:center;line-height: 110%;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;">  </td>
  </tr>
</tbody>
</table>

Let's fill in the table. What do you notice?

---
count: false
# An Example:
.center[**Monopsonist Wage Schedule**]
<table class="table table-striped" style="margin-left: auto; margin-right: auto;">
<caption></caption>
 <thead>
  <tr>
   <th style="text-align:center;"> .pink[Wage] </th>
   <th style="text-align:center;"> .purple[Labor] </th>
   <th style="text-align:center;"> TC </th>
   <th style="text-align:center;"> .hi[MC] </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;line-height: 110%;"> 1 </td>
   <td style="text-align:center;line-height: 110%;"> 1 </td>
   <td style="text-align:center;line-height: 110%;"> 1 </td>
   <td style="text-align:center;line-height: 110%;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;line-height: 110%;"> 2 </td>
   <td style="text-align:center;line-height: 110%;"> 2 </td>
   <td style="text-align:center;line-height: 110%;"> 4 </td>
   <td style="text-align:center;line-height: 110%;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 9 </td>
   <td style="text-align:center;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 16 </td>
   <td style="text-align:center;">  </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 25 </td>
   <td style="text-align:center;">  </td>
  </tr>
</tbody>
</table>

Let's fill in the table. What do you notice?

---
count: false
# An Example:
.center[**Monopsonist Wage Schedule**]
<table class="table table-striped" style="margin-left: auto; margin-right: auto;">
<caption></caption>
 <thead>
  <tr>
   <th style="text-align:center;"> .pink[Wage] </th>
   <th style="text-align:center;"> .purple[Labor] </th>
   <th style="text-align:center;"> TC </th>
   <th style="text-align:center;"> .hi[MC] </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;line-height: 110%;"> 1 </td>
   <td style="text-align:center;line-height: 110%;"> 1 </td>
   <td style="text-align:center;line-height: 110%;"> 1 </td>
   <td style="text-align:center;line-height: 110%;"> 1 </td>
  </tr>
  <tr>
   <td style="text-align:center;line-height: 110%;"> 2 </td>
   <td style="text-align:center;line-height: 110%;"> 2 </td>
   <td style="text-align:center;line-height: 110%;"> 4 </td>
   <td style="text-align:center;line-height: 110%;"> 3 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 3 </td>
   <td style="text-align:center;"> 9 </td>
   <td style="text-align:center;"> 5 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 4 </td>
   <td style="text-align:center;"> 16 </td>
   <td style="text-align:center;"> 7 </td>
  </tr>
  <tr>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 5 </td>
   <td style="text-align:center;"> 25 </td>
   <td style="text-align:center;"> 9 </td>
  </tr>
</tbody>
</table>

Let's fill in the table. What do you notice?

--

At .pink[every level of labor], the .purple[marginal cost of labor] exceeds the .pink[wage]

--

---
# Graph of Monopsony

<img src="07-labor_files/figure-html/monop1-1.svg" style="display: block; margin: auto;" />

---
# Graph of Monopsony

<img src="07-labor_files/figure-html/monop2-1.svg" style="display: block; margin: auto;" />

---

class: inverse, middle
# Checklist
.pull-left[
0) .hi[Rehash model from last class]: ✅

1) .hi[Labor Markets and Urban Econ: overview]: ✅

2) .hi[Urban Labor Demand]: ✅
]

.pull-right[

3) .hi[Urban Labor Supply]: ✅

4) .hi[Equilibrium]: ✅

]

---

exclude: true

```r
p_load(pagedown)
pagedown::chrome_print(here::here("009-labor_one","lecture_nine.html"))
```