class: center, middle, inverse, title-slide .title[ # Urban Labor Markets ] .subtitle[ ## Set 07 ] .author[ ### Andrew Dickinson ] .date[ ### Fall 2022 ] --- class: inverse, middle # Content - .hi-white[(i) Urban labor markets] - .hi-white[(ii) Urban labor demand] - .hi-white[(iii) Urban labor supply] - .hi-white[(iv) Urban labor EQ] --- # Housekeeping .hi[Assignments:] - .hi[PS02] is posted - due date .hi-red[Sun Oct 30.] - go over solutions + review on .hi-blue[Mon Oct 31] - .hi[Reading] - finish up to .hi[chapter 5] before the midterm -- <br> .hi[Midterm:] .hi-red[Wed, Nov 2] --- class: inverse, middle # Urban labor markets --- # Urban labor markets _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> .hi[Q:] Modeling .hii[individual] location decisions, what should we consider? --- # Urban labor markets _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> Introducing large amounts of .hi[high paying jobs] + .hi-red[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 -- .hi-blue[Labor] and .hii[urban] economist model labor markets (supply) differently -- .hi-blue[Labor:] Discuss labor supply as being generated from labor-leisure trade off - 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 # Labor demand --- # Labor demand Both fields generally model .hi[Labor demand] similarly -- .hi[Definition: Labor Demand] - Set of quantities of labor demanded corresponding to a _set_ of wages -- .hi[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 --- # 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 .hii[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 --- # Labor demand Derive a condition for EQ labor the firm will hire in the competitive model? `\begin{align*} \pi &= P*Q - TC \end{align*}` --- # 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 --- # Labor demand .hi[Claim]: Firm hires labor .hi[if and only if] _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 --- # Labor demand .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 -- - `\(MRP_L = P*\frac{\Delta F(L,K)}{\Delta L}\)` --- # 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*}` --- # 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 offsets the marginal revenue product of labor]] --- # Labor demand <img src="07-labor_files/figure-html/supply_demand-1.svg" style="display: block; margin: auto;" /> --- # 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 --- # Labor demand .hi[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;" /> --- # Labor demand .hi[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 # Urban labor markets: Labor supply --- #Labor Supply Labor supply is driven from location decisions of individuals .center[.hi[What generates location choices?]] -- .hi[(i.)] .hii[Wages] -- .hi[(ii.)] .hi-red[Rents] -- .hi[(iii.)] .hi-light-blue[Amenities] -- .hi[(iv.)] .hi-dark-grey[Other] (birth location, family ties) --- # Labor Supply A _set_ of quantities of labor supplied corresponding to a _set_ of wages. .hi[q:] What causes _movement along_ the labor supply curve? -- - A change in wages. That's it! -- <br> .hi[q:] What causes a _shift_ of the labor supply curve? -- - Changes in amenities (building of a nicer school, eroding of air quality) - 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[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 .hi[q:] _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 # Equilibrium --- #Equilibrium .hi[Definition:] A .hi[labor market equilibrium] is a pair of points `\((L^*, W^*)\)` such that there is no excess supply or demand - quantity supplied `\(=\)` quantity demanded -- We think of cities as being "separate" labor markets - equilibria can be .hi-red[different] across cities --- # Equilibrium: Example <img src="07-labor_files/figure-html/eq1-1.svg" style="display: block; margin: auto;" /> --- class: inverse, middle # Competitive labor markets --- # Characteristics of a competitive market To start we will look at an extreme market structure -- .ul[.hi[Competitive labor market:]] Industry structure in which their are many workers supplying (homogeneous) labor to many firms .hi[(i).] Many potential buyers and sellers of labor .hi[(ii).] Labor is homogeneous; same human capital across workers .hi[(iii).] Perfect information; workers know the going wage `\(w\)` .hi[(iv).] Firms take wages as given; no incentive to offer above or below `\(w^*\)` .hi[(v).] No barriers to entry/exit; `\(\Pi \rightarrow 0\)` --- # Competitive model: Example .hi[Recall our assumptions for the competitive model:] .hii[(i).] Firms seek to maximize profits -- .hii[(ii).] Markets are perfectly competitive (in .orange[both] inputs and output) -- Suppose we have the following linear `\(L_D\)` and `\(L_S\)` curves: `\begin{align*} W_D &= 40 - 5L_D \\ W_S &= 5 + 2L_S \end{align*}` Solve for equilibrium `\(W^*, L^*\)` --- # Competitive model: Example `\begin{align*} W_D &= 40 - 5L_D \\ W_S &= 5 + 2L_S \end{align*}` -- <img src="07-labor_files/figure-html/comp_eq-1.svg" style="display: block; margin: auto;" /> --- # Competitive model We built up labor .hi[supply] and .hi[demand]. Where do these come from? - Firms demand and households supply -- Recall our result about labor demand from earlier: A firm will hire labor until labor costs (wage) .hi[exactly offsets] the .hii[marginal revenue product of labor] -- Summing each firm's `\(MRP_L\)` curve across the entire market generates the market labor demand curve -- _que example_ --- # Competitive model Perfectly competitive markets are not super realistic; .hii[extreme] outcome -- Labor market structures share many of the .hi[same characteristics] -- Understanding the .hii[extreme outcomes] inform us of the spectrum of labor markets in between <br> -- Perfectly competitive is one extreme; what is the market structure on the other side of the spectrum? -- .center[.hi[Monopsony]] --- class: inverse, middle # Monopsony --- # Monopsony .hi[Definition:] .hi[Monopsony] - A labor market situation which there is only .hi[one buyer] -- A firm is a .hi[monopsonist] if they are .hii[the only employer] of labor in the area A firm has .hi[monopsony power] if they have influence on the market wage -- Not to be confused with .hii[monopoly] (only one .hi[seller] of a good) -- .hi[Can you think of any examples?] -- .pull-left[ - Coal towns - Universities (go GTFF!) ] .pull-right[ - Amazon / Walmart Towns?] -- .center[ [*I owe my soul to the company store*](https://youtu.be/CPW3YikDwEM?t=10) - 16 Tons] --- # Monopsony So what are the main consequence(s) of .hi[monopsony]? .center[.hi[Monopsonists have the ability to pay a wage below the marginal value]] -- The consequences? -- - .hi[Higher profit] for the firms - Deadweight loss; inefficient outcomes (ie less surplus) -- <br> Lets formalize monopsonies in a labor market model -- .hi[Recall:] In the competive model, the firm pays the worker `\(w = MRP_l\)`. -- - Is this what the monopsonist would do? --- # Monopsony Competitve model: Firms seek to maximize profits but can't influence wages -- 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 Monopsonist can influence wages by the amount of labor they hire -- Now `\begin{align*} \pi &= TR - w(L)L - rK \end{align*}` -- where `\(w(L)\)` is an .purple[increasing function] of the .purple[amount of labor hired] -- Firm will hire labor until marginal cost is equalized to marginal benefit - or: _.purple[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 `\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 `\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*}` -- .hi[Definition:] Marginal cost of labor - The additional cost of hiring one additional worker $$ MC_L = \frac{\Delta TC(L)}{\Delta L} $$ --- count: false # Monopsony: Formalizing the Result Notation: `\(TC(L) =w(L)*L\)` is the TC from labor in monopsony `\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 competitive outcome: `\begin{align*} MRP_L & = W \end{align*}` .hi[Important:] In the competitive model, marginal cost of labor was constant (equal to wage) -- Monopsony: Marginal cost is increasing because monopsonist is the _only_ buyer --- # 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;"> .purple[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;"> .purple[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;"> .purple[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 .hi[every level of labor], the marginal cost of labor .hi[is double] the 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;" /> --- # Monopsony: Example Suppose a firms `\(L_D\)` and `\(L_S\)` are described by the following functions: `\begin{align*} W_D &= 40 - 2*L \\ W_L &= 4 + 2x \end{align*}` .hii[(i).] What is the `\(MC_L\)` curve for the firm? .hii[(ii).] What is the EQ wage `\(w^*\)` and quanity of Labor `\(L^*\)`? --- # Monopsony: Example `\begin{align*} W_D &= 40 - 2*L \\ W_L &= 4 + 2x \end{align*}` --- class: inverse, center, middle # Minimum wage --- # Minimum wage Minimum wages are a form of .hi[price controls]. Specifically, a minimum wage is a .hi[price floor] - .hi[Price floor:] Dictates the .hii[minimum] allowed price for transactions in a marketplace -- A price floor is .hi[binding] if it has an impact on the market equilibrium -- A price floor that is below the market price is .hii[nonbinding] --- # Minimum wage Is the following price floor binding? <img src="07-labor_files/figure-html/min1-1.svg" style="display: block; margin: auto;" /> --- # Minimum wage The following is .hi[nonbinding] <img src="07-labor_files/figure-html/min1.5-1.svg" style="display: block; margin: auto;" /> --- # Minimum wage Is the following binding? <img src="07-labor_files/figure-html/min2-1.svg" style="display: block; margin: auto;" /> --- # Minimum wage The following is .hi[binding] <img src="07-labor_files/figure-html/min3-1.svg" style="display: block; margin: auto;" /> --- # Minimum wage <img src="07-labor_files/figure-html/min4-1.svg" style="display: block; margin: auto;" /> --- exclude: true # 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;" /> ] --- exclude: true #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] --- exclude: true # 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 --- # Monopsony and Minimum Wage - So we saw the .purple[monopsonist] outcome leads to .hi[lower employment and wages] than the .purple[competitive outcome]. -- - In perfect competition, what happens to unemployment with a minimum wage? -- - Is it the same with a monopsony? No! --- # Minimum wage: Example Let's compare the effect of a minimum wage on both market structures: - Competitive market - Monopsony -- Suppose we have two cites (A and B). City A follows the following `\(L_D\)` and `\(L_S\)` `\begin{align*} W_D^A &= 25 - 5 \cdot L_D^A \\ W_S^A &= 3 +3 \cdot L_S^A \\ \end{align*}` And city B follows the following `\(L_D\)` and `\(L_S\)` `\begin{align*} W_D^A &= 25 - L_D^A \\ W_S^A &= 1 + 3 \cdot L_S^A \\ \end{align*}` --- # Minimum wage: Example --- # Minimum Wage: Monopsony -- <img src="07-labor_files/figure-html/min_wage_monop-1.svg" style="display: block; margin: auto;" /> --- exclude: true ```r p_load(pagedown) pagedown::chrome_print(here::here("009-labor_one","lecture_nine.html")) ```