Today

1. 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

2. 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?

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

4. 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)

5. 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

6. 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

7. 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

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

9. The urban modelprototype 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 (p285-286) • 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

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

11. Figure 7.4 Core geographical economics model Home Net wage curves Foreign W(N) Wh Wage curves Low Transport cost High Transport cost Cost of living curves Hh H(N) Low Transport cost W(N)-H(N) Home High Transport cost Foreign Low transport cost: B Net Wage Home = Low Transport cost Net Wage Foreign Foreign High transport cost: Net Wage Home = High Transport cost A Net Wage Foreign Home NF = 1 Nf = NH = 0.5 NH = 1 unstable stable

12. 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

13. 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?

14. Introducing congestion • L = Nτ(1-τ) ( α + βx) -1 < τ < 1 • if 0 < τ < 1negative externalities • if -1 < τ < 0(additional) positive externalities • if τ = 0 no congestion effects • Yr = δλr Wr + φr ( 1 – δ) • Ir = ( Σsλs1-τε Trs1-εWs1-ε )1/(1-ε) • Wr = λ-τ ( Σs Ys Trs1-εIsε-1 )1/ε with τ =0 (1)-(3) reduces to the CP model

15. Figure 7.5 Total and average labor costs with congestion a b t t Parameter values: = 1, = 0.2; = 0.1 for N = 100 and N = 400, = 0 for "no cong."

16. 2-region base scenario 1,03 E B C 1 w1 /w2 D A F 0,97 0 0,2 0,4 0,6 0,8 1 lambda 1 Figure 4.1 The relative real wage in region 1 T =1.7 ws = Ws Is-δ stable unstable

17. Variations in transport costs T 1.1 1.3 1.5 w1 / w2 1 1.7 1.9 2.1 0.9 0.000 0.200 0.400 0.600 0.800 1.000 lambda 1 Figure 4.2 The impact of transport costs Higher T: spreading more likely

18. e d t Figure 7.6 The 2 - region core model with congestion ( = 5; = 0.4; = 0.01) b. T = 1.7 c. T = 1.61 w1/w2 w1/w2 1,02 1,035 1,00 1 0,98 0,965 0,96 0,94 0,93 0 0,5 1 0 0,5 1

19. Figure 7.6 (cont) -

20. Figure 7.6 (cont)

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

22. e d t Figure7.7 The racetrack economy with congestion ( = 5; = 0.7; = 0.1) initial final initial final b T = 1.3 a. T = 1.2 1 1 24 2 24 2 23 3 23 3 22 4 22 4 21 5 21 5 20 6 20 6 19 7 19 7 18 8 18 8 17 9 17 9 16 10 16 10 15 11 15 11 14 12 14 12 13 13

23. Figure 7.7 continued

24. Figure 7.7 continued

25. Zipf’s Law • A special case of the power law phenomenon: uneven distribution with few (very) large values and many small values • log (Mi) = c – q log(Ri) • 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

26. Table 7.4 Primacy ratio, selected countries

27. Table 7.5 Summary statistics for q City proper Urban agglomeration Mean 0.88 1.05 Standard Error 0.030 0.046 Minimum 0.49 0.69 Maximum 1.47 1.54 2 Average R 0.94 0.95 # observatio ns 42 22 Estimated q for 48 countries q≠ 1 more often than not; Zipf's law rarely holds

28. Figure 7.4 Frequency distribution of estimated coefficients* city proper urban agglomeration 12 10 8 6 4 2 0 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 More

29. 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?

30. 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 • http://www.shirky.com/writings/powerlaw_weblog.html

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

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

33. 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)

34. racetrack Hotelling beach symmetric space asymmetric space

35. Equilibrium distribution in a racetrack economy with 12 locations. p=0.4, s=4, t=0.4

36. Equilibrium distribution in a Hotelling economy with 12 locations. p=0.4, s=4, t=0.4

37. Equilibrium distribution in a Hotelling economy with 12 locations. p=0.4, s=4, t=0.4 (no history)

38. Equilibrium distribution in a Hotelling economy with 371 locations. p=0.4, s=4, t=0.3 (no history)

39. Equilibrium distribution in symmetric space with 3x3=9 locations. p=0.4, s=6, t=0.4

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

41. Equilibrium distribution in symmetric space with 9x9=81 locations. p=0.4, s=6, t=0.4

42. Equilibrium distribution in symmetric space with 10x10=100 locations. p=0.4, s=6, t=0.4

43. Equilibrium distribution in symmetric space with 11x11=121 locations. p=0.4, s=6, t=0.4

44. Equilibrium distribution in symmetric space with 51x51=2601 locations. p=0.5, s=5, t=0.4

45. Equilibrium distribution in symmetric space with 51x51=2601 locations. p=0.5, s=5.5, t=0.4

46. Equilibrium distribution in symmetric space with 51x51=2601 locations. p=0.5, s=6, t=0.4

47. rank size distribution A - B - C

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

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

50. USA =0.3, =6, =0.3