Today Chapter 7 –Cities and congestion: economies of scale, urban systems and Zipf’sLaw More on the role of geographical space –relevance of non-neutral space for urban systems –background paper Stelder (2005) on Nestor

Issues Typical outcome of CP model is agglomeration into just a few cities (of equal size) reality: urban hierchies=many cities of different size with some regularities accross countries and time VL model and the Bell Shape curve better in this respect but does not allow interregional migration How can Geographical Economics account for this?

Sources of agglomeration economies Marshall (1920) (remember box 2.1) Knowledge spill-overs Labour pool Backward linkages –1: pure/technological –2: pecuniary

Scope of agglomeration economies Rosenberg & Strange (2004) –industrial scope (locailzation urbanization) –temporal scope (path dependency) –geographical scope (density inside city proximity to other cities) –organisation and business culture/competitiveness scope (diversity -> competition)

People or firms? Florida (2002) –"creative class" concept –spill-overs between people rather than between firms Gleaser (2004) –"bohemien" index insignificant when modelled together with human capital indices

Scope of scale economies MAR (Marschall/Arrow/Romer) externalities: spill-overs between jointly located firms/industries of the same type; also known as localization economies (Sillicon Valley/ Detroit); a firm is more productive in the vicinity of many identical firms Jacobs externalities: urban spill-overs between all types; also known as urbanisation economies; a firm is more productive in the vicinity of many firms whatsoever/ in a larger city Duranton (2007): current consensus is that both are relevant and of comparable importance CP model: –firms group together because local demand is high, and demand is high because firms have grouped together -> –positive externality is associated with the number of firms, not with specialization -> –models urbanization rather than localization

Interdependence? main focus of empirical studies on (samples of) individual cities "free floating islands" agglomeration forces get more attention than spreading forces no role for interdependence between cities and between cities and their hinterland

Urban versus Geographical economics Combes, Duranton & Overman (2005) –wage curve –cost of living curve –net wage curve –labor supply curve

The urban model prototype Henderson (1974) Only cities no hinterland Industry-specific spill-overs Counter force: negative economies of scale (congestion) (non- industry specific) fig 7.3: will lead to full specialization of each city into one industry (p ) –all cities specializing in industry x must be of the same size –cities specializing in an industry with higher scale economies will be larger (higher wage can bear more congestion costs) –inter-city trade --> urban system of specialized cities of different size trading with each other

Figure 7.3 Core urban economics model Labor supply curve A B Wage curve industry 2 Wage curve industry 1 N A N B N A N B H A H B Net Wage A = Net Wage B W(N)-H(N) W(N) W A W B Net Wage Industry 2 Net Wage Industry 1 Cost of Living Curve

Figure 7.4 Core geographical economics model A B N f = N H = 0.5 Low transport cost: Net Wage Home = Net Wage Foreign Low Transport cost Home Low Transport cost Foreign High Transport cost Foreign HighTransport cost Home High transport cost: Net Wage Home = Net Wage Foreign Low Transport cost High Transport cost Cost of living curves Wage curves N H = 1N F = 1 W(N) WhWh HhHh W(N)-H(N) Net wage curves Home Foreign H(N) unstablestable

The CP model in fig 7.4 difference with the urban model of fig 7.3 –cost of living falls with city size –real wage may or may not increase with city size, depending on transport costs

Scale and relevance Combes, Duranton & Overman: urban model more relevant for cities, local externalities more important than long-distance inter-city relations CP model more relevant for regions and countries, market access and inter-region/country interdependencies more important\ critique: is inter-location interdependency more important at larger distances?

Introducing congestion L = N τ(1-τ) ( α + βx) -1 < τ < 1 if 0 < τ < 1 negative externalities if -1 < τ < 0 (additional) positive externalities if τ = 0 no congestion effects 1.Y r = δ λ r W r + φ r ( 1 – δ ) 2.I r = ( Σ s λ s 1-τε T rs 1-ε W s 1-ε ) 1/(1-ε) 3.W r = λ -τ ( Σ s Y s T rs 1-ε I s ε-1 ) 1/ε with τ =0 (1)-(3) reduces to the CP model

Figure 7.5 Total and average labor costs with congestion Parameter values:  = 1,  = 0.2;  = 0.1 for N = 100 and N = 400,  = 0 for "no cong."

Figure 4.1 The relative real wage in region 1 w s = W s I s - δ stableunstable T =1.7

Figure 4.2 The impact of transport costs Higher T: spreading more likely

Figure 7.6 The 2-region core model with congestion (  = 5;  = 0.4;  = 0.01) c. T = ,94 0,96 0,98 1,00 1,02 w1/w2 b. T = 1.7 0,93 0, ,035 00,51 w1/w2 00,51

Figure 7.6 (cont)-

CP- congestion model range of possible outcomes wider partial agglomeration as stable equilibrium possible -> less “black hole” results

Figure 7.7 The racetrack economy with congestion (  = 5;  = 0.7;  = 0.1) a. T = initialfinal b T = initialfinal

Figure 7.7 continued

Zipf’s Law A special case of the power law phenomenon: uneven distribution with few (very) large values and many small values log (M i ) = c – q log(R i ) Perfect Zipf: q=1 Research: some countries q>1 some q<1, some quite close to 1 (USA) Depends strongly on data, definitions and sample size City proper versus agglomeration The “tail” of the distribution does not work The role of the primate city

Table 7.4 Primacy ratio, selected countries

Table 7.5 Summary statistics for q City proper Urban agglomeration Mean Standard Error Minimum Maximum Average R # observations Estimated q for 48 countries q ≠ 1 more often than not; Zipf's law rarely holds

Figure 7.4 Frequency distribution of estimated coefficients* More city properurban agglomeration

A theory on Zipf? should accept and explain deviations from q =1 should allow for changing q over time can congestion-CP model do this?

Other approaches Simon (1955): –Random growth on a random distribution predicts that q =1 Gabaix (1999): –Gibrat' s law: city growth is independent of its size –uniform growth rate with normal distribution variance leads to q =1 –only when either assuming CRS or with DRS and IRS levelling out problem: no q ≠ 1 possible Shirky (2005): networks create power laws –

Zipf simulation 24-location racetrack model feed with random history three periods: –pre-industrialization δ=0.5 ; ε=6 ; T=2 ; τ=0.2 –industrialization δ=0.6 ; ε=4 ; T=1.25 ; τ=0.2 –post-industrialization δ=0.6 ; ε=4 ; T=1.25 ; τ=0.33

Figure 7.10 Simulating Zipf N-shape over time: q increases and later decreases

The role of geography Extra literature: stelder.pdf on nestor geography=neutral  simulate how history matters history=neutral  simulate how geography matters “no history assumption” = “in the beginning there were only little villages” or: initial distribution=equal distribution only possible in non-neutral space because no history in neutral space = immediate long term equilibrium (real wage identical everywhere)

symmetric spaceasymmetric space Hotelling beach racetrack

Equilibrium distribution in a racetrack economy with 12 locations.  =0.4,  =4,  =0.4

Equilibrium distribution in a Hotelling economy with 12 locations.  =0.4,  =4,  =0.4

Equilibrium distribution in a Hotelling economy with 12 locations.  =0.4,  =4,  =0.4 ( no history)

Equilibrium distribution in a Hotelling economy with 371 locations.  =0.4,  =4,  =0.3 ( no history)

Equilibrium distribution in symmetric space with 3x3=9 locations.  =0.4,  =6,  =0.4

Equilibrium distribution in symmetric space with 3x3=9 locations.  =0.1,  =4.8,  =0.52

Equilibrium distribution in symmetric space with 9x9=81 locations.  =0.4,  =6,  =0.4

Equilibrium distribution in symmetric space with 10x10=100 locations.  =0.4,  =6,  =0.4

Equilibrium distribution in symmetric space with 11x11=121 locations.  =0.4,  =6,  =0.4

Equilibrium distribution in symmetric space with 51x51=2601 locations.  =0.5,  =5,  =0.4

Equilibrium distribution in symmetric space with 51x51=2601 locations.  =0.5,  =5.5,  =0.4

Equilibrium distribution in symmetric space with 51x51=2601 locations.  =0.5,  =6,  =0.4

rank size distribution A - B - C

A two-dimensional grid in geographical space AB=1; AC=  2; AF=2+2  2 (shortest path)

Asymmetrical space with 98 locations  =0.3,  =5,  =0.2 The USA model: “going to Miami”

USA  =0.3,  =6,  =0.3

USA  =0.3,  =6,  =0.4

Adding foreign trade

USA  =0.3,  =6,  =0.3 with foreign trade

Structure of the European grid (n=2637)

The European grid extended with sea transport

δ(B n,A n ) versus number of predicted cities

Conclusions geography matters more differentiated urban hierarchies with –increasing number of regions –increasing non-neutrality