ITRALOC Assignment 2, Rank Size, Chapter 7

Rank Size

Assignment 2

Chapter 7

Innovation, Trade and Location 1

Models vs. reality

• Core model gives a long-run equilibrium of either complete agglomeration or spreading. • Agglomeration stronger than spreading

• Krugman model (racetrack economy).

– Agglomeration dominates.

– Economic concentration in one or few locations.

– Distribution of economic activity is evenly spread.

• What do we observe in real life?


Urbanisation

• Urbanization share of 75 per cent or more in developed countries, Latin America and some oil-exporting countries.

• In countries we find multiple centers of economic activity with various size

– Not as some economic models describe it

• A central topic within urban economics is the analysis of urban systems.


Congestion

• Congestion and urbanization goes hand-in-hand.

• Congestion sums up the negative aspects coming from urbanization: – Limited physical space

– Heavy usage of roads

– Communication channels

– Limited local resources

– Environmental pollution


Cities, raison d’être • Increasing returns to scale

– Marshall

• Natural advantages • Home market effects • Consumption externalities • Political factors • Rent seeking • Education versus creative class

– Human capital theory: a city with more human capital will grow more rapidly


Extent of underlying economic forces

• Industrial scope. – This deals with the strength of agglomeration economies

and if it extend across all sectors in a city. • Localization versus urbanization

• Temporal scope. – Time aspect.

• Geographic scope. – Closeness to other cities and the economic density within

the own city.

• Organization and business culture/compitiveness scope. – Competitive environment stimulates growth.


Knowledge spillovers between firms

• Marshall-Arrow-Romer (MAR)

– Between firms that belong to the same industry

• City size due to specialization – Localization externalities

• Jacobs

– Not industry-specific, between firms belonging to different industries.

• City size due to diversity – Urbanization externalities


City size distribution

• Differences between cities arises due to the way positive externalities influnce cities.

• Existence and growth of cities is mainly due to increasing returns to scale.

• These explanations are not very informative when it comes to explaining the city size distribution. – Since focus has been on the growth of indiviudal

cities and not their interdependence.


Urban systems • Core urban

system model (Henderson)

• Core geographical economics model (Krugman)


Core urban system • External scale economies are

industry specific. • Localization economies.

• No transport cost – Market potential is not an issue – Geography is not part of the

analysis.

• The hinterland is not included in the analysis.

• Spreading force: congestion • Focus is on what determines a

city’s size and the interdependence among cities.

• Systems of cities is due to need of different industries. – Each industry has its own

optimum size. – Cities specialize and trade with

each other.

Core geographical model • External scale economies

consist of pecuniary externalities.

• Manufacturing firms have internal economies of scale.

• Transport cost – Market potential


Henderson vs. Krugnman

• Agglomeration – Urban system model: pure local increasing returns to scale (no

transport cost). – Geographical economies model: pecuniary external economies

of scale (transport cost).

• Wage – Urban system model: a function of the labor force. – Geographical economies model: does not have to be a function

of the labor force.

• Cost of living – Urban system model: a function of the labor force (positive). – Geographical economies model: a function of the labor force

(negative).


Conclusion, Henderson vs. Krugman

• Krugman is more applicable at a larger spatial scale (regions, countries). – Market access, spatial interdependencies between

locations more important.

– Broad trends at large spatial scales.

• Henderson more relevant for smaller spatial units (cities). – Local externalities most important.

– Spikes of economic activities.


Geographical economics, congestion

• Congestion: external diseconomies of scale

• As cities grow:

– Increased commuting cost

– Increased rents

– Increased environmental pollution

– Limited storage facilities


Geographical economics, congestion, continued

• Congestion cost is a function of the overall size of the location.

𝑙𝑖𝑟 = 𝑁𝑟

𝜏1−𝜏 𝛼 + 𝛽𝑥𝑖 ; −1 < 𝜏 < 1


Short-run equilibrium of the core model with congestion

• Income equation (not affected by congestion, τ)

• Wage equation (increase in the share of manufacturing workers=> increases congestion=>reduce the wage rate in city r)

– Other cities more attractive

• Price index equation (as the wage rate in city r decrease=>reduce the price index in other regions)

– Other cities more attractive


Long-run equilibrium of the core model with congestion

• Two-city model with congestion

– Since the aim is to explain the distribution of cities, a two-city model will not do

=> Racetrack model with many cities and congestion

• Focus on the relative real wage of city 1 compared to city 2

– Can from this determine the direction of change of the distribution of the labor force

=> Gives the stability of long-run equilibria.


• Long-run equlibrium: – Relative real wage is equal to 1 – All employees agglomerated in one city

• Long-run with congestion: – Small congestion forces alters the possibilities for

long-run equilibria. • High transport cost: spreading • Decreased transport cost: spreading+partial agglomeration • Decreased transport cost: complete agglomeration • Small transport cost: partial agglomeration • Very low transportation cost: spreading

Conclusions: Wider range of possible long-run equilibrium

outcomes with congestion Partial agglomeration is possible=> cities of different

sizes can coexist


Many locations and congestion, long-run equilibrium

• Many locations have manufacturing production • Cities varies in size • The distribution of manufacturing activities is

structured around two centers. • If a city increase or decreases depends on its

relative place in the initial distribution of cities – Size of the neighborhood cities

• Isolated: shrinks • Cluster: grow • Surrounded by large cities: grow

• The importance of the path dependence (history) varies.


City size distribution

• There is an uneven distribution of economic activity in many countries and the distribution have some regularity features.

• The Rank-size distribution have gained empirical success for many countries=> there is a well-ordered pattern underlying the distribution of economic activity.


Zipf’s Law

• Also called rank size rule

• A special case of the Rank Size distribution.

• Stating that the largest city is twice as large as the second largest city, five times as large as the fifth largest city etc.


Zipf’s Law, measured

1. Collect data on the size of all cities in a particular region (normally a country). Size can be defined in numerous ways, one is by the inhabitants (www.scb.se).

2. Order the observations in decreasing size. • Their rank

3. Take the natural logarithm of the rank and the size.

4. Log(Mj)= log (c) –qlog(Rj) 5. Log(Rj-0,5)= log (c) –qlog(Mj) (chapter 1)


Zipf’s Law, measured

• ”Zipf’s law holds if and only if, q=1”, why?

• Empirical studies for the US have confirmed Zipf’s law and also that it is stable over time.

• Estimation problems:

– OLS is biased and inefficient.

– Small cities do not follow the rank size distribution.

– How to define a city.

– The largest city (rank 1) is much larger than what Zipf’s law predict (primate city).


Assignment

• Calculate Zipf’s law for your home country. – make sure that you make clear how you define a

city, how you measure the size of the cities and what cities you use.

• Choose two years so that you can make an comparison of your results (preferably more than 3 year timespan).

• The assignments should be approximately five pages and no more than seven pages, in total.


Practical information • The deadline for this assignment is on the 14th of

March, 17:00. • The assignment shall be handed to me in paper-

form, not by e-mail. There will be a box outside my office where you shall hand-in the assignment.

• The assignments can be written in groups of two or alone.

• The assignment gives 1,5 hp. • If you miss the deadline, the highest grade you

can get is C (79).


Structure • The assignment should have a similar structure to a thesis;

– an introduction, – theory part (explain why cities exist but also why cities of different

sizes coexist), – Background with some information about the country, number of

inhabitants, population density, number of big cities etc. – method part (Zipf’s law), – analysis, and – concluding section. – References shall be included and referred to in a correct manner.

• In the text: Geographical economics is important (Brakman et al, 2009) • Reference list: Brakman, S., Garretsen, H., and van Marrewijk, C. (2009), The

new Introduction to Geographical Economics, Cambridge University Press, New York


Urkund

• The assignment shall be send into Urkund, [email protected]

in order to pass.

• If you have any questions do not hesitate to contact me: [email protected], 036-101746, B5010


mailto:[email protected]

mailto:[email protected]

ITRALOC Assignment 2, Rank Size, Chapter 7

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