class: center, middle, inverse, title-slide # Econ 330: Urban Economics ## Lecture 4 ### John Morehouse ### April 7th, 2021 --- class: inverse, center, middle # Lecture IV: City Size and Growth --- name: schedule # Schedule ## Today -- 1) .hi.purple[Clustering] 2) .hi.purple[City Size] 3) .hi.purple[Intro to Growth] -- -- ## Upcoming - .hi.slate[Reading] (Chapter II & III _ToTC_) - .hi.slate[HW 1] (due on April 11th) -- --- # Last Time We discussed some .hi[fundamentals] that lead to the existence of cities -- - .hi.slate[Main takeaway]: - Need some reason (.hi[economies of scale]) for cost of cities (high land prices, for example) to be justified -- -- .hi.slate[Questions]: - Why do cities grow beyond .pink[one factory]? -- - Why are there .purple[differences in size] across cities? - .pink[Where] do cities emerge? -- -- --- # Clustering So we explained _why_ cities exist. Can we explain their size? - Let's start by asking why firms cluster. Where to start? __Axiom 5__ -- __Axiom 5__: .hi[_Competition generates zero economic profit_] -- - If a firm is making positive economic profit, more firms enter the market - What happens to the profit per firm as more firms enter? -- - It decreases. Eventually goes to zero -- --- name: zero_profit #Example How many firms are in the cluster? <img src="lecture_four_files/figure-html/cluster_graph-1.svg" style="display: block; margin: auto;" /> --- name: cluster # Clustering Why does .hi[profit increase] as firms .pink[cluster]? Firms cluster because -- 1) To share intermediate inputs 2) Labor Matching 3) Knowledge Sharing 4) Share the pool of labor -- Let's look at these in some more detail --- # 1: Sharing Inputs Firms in .hi.orange[similar industries] share inputs to take advantage of scale economies<sup>.hi[†]</sup> .footnote[ .hi[†] Scale economies: _bigger_ `\(\rightarrow\)` _cheaper per unit_ ] -- .hi.slate[Example]: High Tech Firms -- - Rapidly changing products that require sophisticated intermediate inputs - Electronic components and testing facilities -- - Firms share intermediate input suppliers -- --- # 2: Labor Matching With .hi[tech firms] -- - Clustering attracts more of the kind of workers they want -- - Firms and workers are .pink[not always perfectly matched] - Mitchmatches .purple[require training] to eliminate skill gap. .hi[Training is costly] -- - Better for firm if they can find a worker to fill role immediately. More likely in a cluster -- --- # 3: Knowledge Sharing __Defn__: .hi[Agglomeration Economies]: benefits that come when firms and people locate near one another together in cities and industrial clusters -- > Agglomeration economies are the benefits that come when firms and people locate near one another together in cities and industrial clusters. These benefits all ultimately come from transport costs savings: the only real difference between a nearby firm and one across the continent is that it is easier to connect with a neighbor. Of course, transportation costs must be interpreted broadly, and they include the difficulties in exchanging goods, people, and ideas Source: [Ed. Glaeser](https://www.nber.org/chapters/c7977.pdf) -- --- name: urban # Firm Clustering Let's refine our language a bit. 1. _.hi[Localization economies]_ - Explains .hi.purple[within the same] industry clustering 2. _.hi.orange[Urbanization economies]_ - Explains .hi.purple[across] industry clustering --- # Localization Economies A _.hi[localization economy]_ occurs when an increase in the size of an industry leads to an increase in productivity of production ## Why? -- - Evidence of higher .hi[labor productivity] - Higher output `\(\rightarrow\)` more productive workers (Henderson, 1986) - Tech workers benefit more from .pink[knowledge spillovers] than manufacturing (Mun & Huchinson, 1995) -- - Evidence of higher .hi.purple[rates of entry] - More firms are born where .pink[output is higher]; that is, where the industry is .purple[clustered] (Carlton, 1986) - Why? --- # Urbanization Economies _.hi.orange[Urbanization Economies]_ are when the size of a city leads to an increase in productivity ## Why? -- - .hi[Sharing intermediate goods]: (banks, accountants, hotels, transport services) -- - .hi.orange[Pooling]: workers move from industries with low demand to high demand (.orange[across] sector) - .hi.purple[Matching]: common skills across sectors (excel, for example) -- -- Urbanization Economies result in .hi.orange[large, diverse cities] --- # Examples Two major examples of .hi[localization] & .hi.orange[urbanization] economies: 1) .hi.slate[Silicon Valley] -- - .hi[Localization]: firms locate close to each other to share .pink[high-skilled labor pool] despite very high rents -- 2) .hi.slate[Los Angeles] -- - .hi.orange[Urbanization]: Not really any super dominant industries, yet it continues to grow -- --- class: inverse, middle # Checklist .col-left[ 1) .hi[Clustering] ✅ - Reasons for firm clustering - Urbanization vs Localization Economies 2) .hi.purple[City Size] ] .col-right[ 3) .hi.purple[Intro to Growth] ] --- # City Size <img src="lecture_four_files/figure-html/zipf_one-1.svg" style="display: block; margin: auto;" /> --- # What Function? <img src="lecture_four_files/figure-html/zipf_two-1.svg" style="display: block; margin: auto;" /> --- # What Function? <img src="lecture_four_files/figure-html/zipf_three-1.svg" style="display: block; margin: auto;" /> --- name: zipf # Size: Zipf's Law Zipf's Law of city size can be expressed as: `\begin{align*} rank = \frac{C}{N} \end{align*}` - C represents a constant for a country/region - N represents the population level --- # Zipf's Law: Example Assume the _third largest_ city in a region has 200,000 people. - Use Zipf's law to figure out how many people are in the _fifth-largest_ city __2 Steps__ -- 1) Calculate the constant C: `\begin{align*} 3 &= \frac{C}{200,000}\\ C &= 600,000 \end{align*}` -- 2) Use that info to calculate the population of the 5th largest city: `\begin{align*} 5 &= \frac{600,000}{Pop_5} \end{align*}` --- # Zipf's Law: Example Assume the _third largest_ city in a region has 200,000 people. - Use Zipf's law to figure out how many people are in the _fifth-largest_ city __2 Steps__ 1) Calculate the constant C: `\begin{align*} 3 &= \frac{C}{200,000}\\ C &= 600,000 \end{align*}` 2) Use that info to calculate the population of the 5th largest city: `\begin{align*} 5 &= \frac{600,000}{Pop_5} \implies Pop_5 = 120,000 \end{align*}` --- # Zipf's Law: Intuition .qa[Q1]: In words, what does .hi.orange[Zipf's law] tell us about the relationship between .hi[rank] and .hi[city size]? -- .qa[A1]: In words, this equation says: - .pink[A few] cities will be pretty big -- - There is a .hi.purple[big drop] in population as rank increases - Most low rank (high number) cities are .hi[pretty similar] in size -- -- --- # Primate Cities .hi.slate[Definition]: A .hi[primate city] is > A major city that works as the .hi.purple[financial, political, and population center of a country] and is not rivaled in any of these aspects by any other city in that country. Normally, a primate city must be at least .purple[twice as populous as the second largest city] in the country. .hi[Examples]: .smnallest[ .col-left[ __City__ Seoul, South Korea Santiago, Chile Buenos Aires, Argentina Lima, Peru ] ] .smallest[ .col-right[ __Percent of Total Population__ 45.8% 35.5% 33.7% 31.7% ] ] --- # Why Primate Cities? What might generate primate cities? - Large .hi[economies of scale] in exchange - Inadequate .pink[transportation infastructure] elsewhere -- - .hi.purple[Political factors]? -- - Easier for dictators to bribe, surveil populations of a primary city (?) - Capital cities with dictatorships are _45%_ larger than capital cities of other countries - Is this relationship .hi.orange[causal]? <sup>.pink[†]</sup> -- .footnote[ .pink[†] I don't know. Maybe somebody does. But you definitely can't say from the 45% number. Much of modern econ is about figuring out when relationships _are_ causal. For a completely unrelated, but informative and entertaining example, see [this video](https://www.youtube.com/watch?v=6YrIDhaUQOE&t=133s). ] -- --- # Why Zipf's Law? .qa[Q2]: _Why does Zipf's Law_ do pretty well in general at describing city size? -- .qa[A2]: __Axiom 2__: _.hi[Self-reinforcing effects] generate extreme outcomes_ - "Winner take all" situations from policies, agglomeration, knowledge spillovers, etc. -- - Wages grow, workers in, firms enter, `\(\rightarrow\)` labor demand `\(\uparrow\)` `\(\rightarrow\)` wages grow . 🔁 -- .qa[Q3]: What slows this process down? .hi.purple[Discuss] -- <center> <font size="15"> Increases in Cost </font> </center> -- --- # Size Why do costs increase as workers move in? 1) .hi[Commute costs increase] - More people `\(\implies\)` more congestion (all else equal) -- 2) .hi.green[Pollution] increases - More .pink[workers] `\(\implies\)` more .purple[production] `\(\implies\)` more .green[pollution]? -- 3) .hi.orange[Disease] -- - Early 1900's (US), living in a city `\(\rightarrow\)` life expectancy `\(\downarrow\)` 5 years - Now, the US's largest cities life expectancy exceeds the national average -- - In many developing countries, life expectancy in cities is lower than rural areas (why?) --- name: utility # Utility What can we use to model the value individuals place on different attributes of cities? __Utility__ -- .hi.slate[Utility] is an abstract notion of peoples preferences. A few assumptions -- 1) .purple[Higher] levels of utility are .pink[preferred] to .purple[lower] levels. And more consumption is better than less 2) Utility is _ordinal, not cardinal_ meaning only the .hi.pink[rank] of the number matters, .hi.purple[not the level] -- 3) Marginal utility is diminishing (marginal value is diminishing) -- --- # Modeling City Size <img src="lecture_four_files/figure-html/u_f1-1.svg" style="display: block; margin: auto;" /> --- # Modeling City Size <img src="lecture_four_files/figure-html/u_f2-1.svg" style="display: block; margin: auto;" /> --- # Modeling City Size <img src="lecture_four_files/figure-html/u_f3-1.svg" style="display: block; margin: auto;" /> --- name: eq # Locational Equilibrium .hi.slate[Locational Equilibrium] occurs when utility levels (valuations) across cities are the same for all workers -- - In practice, we usually do this by .pink[worker type] (demographic, income level, education, etc) - For now, we will just consider the case when .purple[all workers are equivalent] (_but not cities_) -- - This assumption is mostly for accounting purposes -- -- --- # Locational Eq Graph <img src="lecture_four_files/figure-html/u_loc-1.svg" style="display: block; margin: auto;" /> --- # The Implication? Back to the .hi.orange[real world]: _why is this framework useful?_ - Put differently, if utility really does look something like the above curve, what does this mean for policy? -- _Policies that impact the .hi.purple[spatial distribution] of the population can have far flung effects on individuals it was not designed to impact, .hi[via migration]_ - .hi.slate[Example]: -- - Local school quality improvements `\(\rightarrow\)` increased prices. Higher utility from school quality, lower from higher prices. Some people may be displaced? (Gentrification) -- - Net effect could be positive, but there will be winners and losers -- -- -- More on this later in the term (.pink[place-based] policies). --- class: inverse, middle # Checklist .col-left[ 1) .hi[Clustering] ✅ - Reasons for firm clustering - Urbanization vs Localization Economies 2) .hi[City Size] ✅ - Zipf's Law - Utility & City Size - Locational Eq ] .col-right[ 3) .hi.purple[Intro to Growth] ] --- name:growth_factors # Growth .hi[Econ in General]: Economic Growth is defined as an increase in per-capita income. .hi.purple[Urban Economics]: .hi.slate[Economic Growth] is an increase in the _utility level_ of a typical resident -- - Urban definition accounts for factors other than wage -- 1) Increases in natural resources (.pink[gold is found under a city]) -- 2) Increases in physical capital (.pink[computers] 💻) -- -- 3) Increases in human capital (.pink[education] 🎓) -- -- 4) Technological progress (.pink[computers invented]) -- -- 5) Agglomeration Economies 🏙 -- --- name:example # Example: Innovation .col-left[ <img src="lecture_four_files/figure-html/u_innov-1.svg" style="display: block; margin: auto;" /> ] .col-right[ - __Initially__: 2 cities, both with same utility curve - Population each city: .pink[800k] (total pop, 1.6 m) ] --- # Example: Innovation .col-left[ <img src="lecture_four_files/figure-html/u_innov2-1.svg" style="display: block; margin: auto;" /> ] .col-right[ - Productivity shock brings one city's curve up (due to say, higher wages) - In the absence of migration, utility is now higher in the higher productivity city ] --- # Example: Innovation .col-left[ <img src="lecture_four_files/figure-html/u_innov3-1.svg" style="display: block; margin: auto;" /> ] .col-right[ - Migration induces workers toward the more productive city and away from the less productive city - .hi.orange[New locational eq] (u^*): utility is equalized (higher than before). populations change ] -- - .hi.slate[Note]: We rested on - the implicit assumption that .pink[people are perfectly mobile] (and they are the same) - High skilled workers are generally far more mobile than low skilled (for a variety of reasons). Thoughts? -- --- # Example Recap <div style="text-align: left"> Consider two cities: each with an equilibrium population of 800k and the same utility per worker curve</div> - .hi[Innovation] (tech progress) in one city .pink[shifts utility per worker] curve up -- - Workers in the innovative city enjoy a .purple[higher level of utility] - Workers migrate to the innovative city from the city that failed to innovate -- - Eventually, a .pink[new equilibrium] is reached where .hi[utility per worker] is the .hi[same across both cities] - Innovative city is larger -- -- --- name:economy_wide # Economy - Wide Growth .hi.slate[Note]: If there is an .hi.orange[innovation for the entire economy], then: - .hi[Both cities] experience .pink[upward shift] of utility curve - No utility gap at original populations, so .pink[no migration] -- - Increase in utility in .purple[both cities] - Still economic growth, but city sizes stay the same -- --- class: inverse, middle # Checklist .col-left[ 1) .hi[Clustering] ✅ - Reasons for firm clustering - Urbanization vs Localization Economies 2) .hi[City Size] ✅ - Zipf's Law - Utility & Size of Cities - Locational Eq. ] .col-right[ 3) .hi[Intro to Growth] ✅ - Factors that lead to urban growth - Example with utility curves - Economy wide vs regional ] --- # Table of Contents .col-left[ ### Clustering .smallest[ 1. [Reasons for Firm Clustering](#cluster) 1. [Urbanizations vs Localization](#urban) ] ### City Size .smallest[ 1. [Zipf's Law](#zipf) 1. [Utility](#utility) 1. [Locational Eq](#eq) ] ] .col-right[ ## Growth .smallest[ 1. [Growth factors](#growth_factors) 1. [Example](#example) 1. [Economy Wide Growth](#economy_wide) ] ] --- exclude:true ```r p_load(pagedown) pagedown::chrome_print(here::here("004-growth","lecture_four.html")) ``` <!-- --- --> <!-- exclude: true --> <!-- ```{R, generate pdfs, include = F} --> <!-- system("decktape remark 02_goodsmarket_part1.html 02_goodsmarket_part1.pdf --chrome-arg=--allow-file-access-from-files") --> <!-- ``` -->