Chapter -7Chapter -7cities and congestion: the cities and congestion: the economics of Zipf`s Laweconomics of Zipf`s Law

Group three - membersGroup three - members::

GalinaGalina

JuanJuan

Vlastimil Vlastimil

MitikuMitiku

IntroductionIntroduction

The long run equilibrium by: Complete agglomeration Even spread

Depends on: Initial distribution of MLF A few structural parameters like: TC,

ε, δ

Objectives Objectives

Analyzes the extension of the core model Show how the inclusion of congestion

changes the nature of LRE Apply the core model with congestion to

the ultimate empirical regularity of city- size distribution

Structure Structure

• How congestion can be introduced in the core model& how alerts the working of the model

• City-size distribution to measure Zipf`s Law• The core model with congestion – use of

simulation to city size distribution in accordance with the empirical facts of Zipf`s low

• Conclusion

The relevance of urbanization & congestionThe relevance of urbanization & congestion

• Urbanization is a highly relevant phenomenon• As world bank development indicators: 46% lived in

urban area, out of this : 63.5% lived in small & medium sized cities(<1m),21.4%

lived in large cities(1-5m); 15.1% in mega cities(>5m )• middle &high income countries around 75%• Use to explain why in the reality the main spread force in

the core model of GE• The major draw back of urban agglomeration to be in

congestion such as EP, heavy usage of roads, communication channels& storage facilities

• Specific example –traffic congestion- indicates Î in urban agglomeration went along with no. vehicles & per km

Table 7.1 Urban population as % of total population, 1998

Argentina 89 Australia 85

Belgium 97 Brazil 80

Canada 77 Chile 85

Cuba 75 Czech Republic 75

Denmark 85 France 75

Gabon 79 Germany 87

Israel 91 Japan 79

S-Korea 80 Kuwait 97

Lebanon 89 Libya 87

Netherlands 89 New Zealand 86

Norway 75 Oman 81

Russian Federation 77 Saudi Arabia 85

Spain 77 Sweden 83

United Arab Emirates 85 UK 89

USA 77 Uruguay 91

Venezuela 86

Table 7.2 Congestion: number of motor vehicles, selected countries

Vehicles per 1000 people Vehicles per kilometer road

1980 1998 1980 1998

Belgium 349 485 28 33

Finland 288 448 18 30

France 402 530 27 35

Germany 399 522 51 69

Italy 334 591 65 108

Netherlands 343 421 -- 57

Poland 86 273 10 28

Spain 239 467 120 54

UK 303 439 50 67

Congestion as an additional spreading forceCongestion as an additional spreading force

• Urban agglomeration driven by positive external economies give rise to external diseconomies of scale

• EDS also arise from EP, or drawbacks of crowdedness in general

• The direct consequence of congestion is straight forward since it provides incentive for Firms &MW

• How it affects the balance between agglomeration & spread force

The modeling of congestionThe modeling of congestion

• The production structure of the core model can be easily adapted to introduce Congestion cost

• Congestion costs for each firm depends on the over all size of location of production.

• The size of the cityr is measured by the total no. of manufacturing firms, Nr in that city

• The case of negative location specific external economies arising from congestion are relevant, in which 0<Τ<1

Figure 7.1 Total and average labor costs with congestion*

0

1

2

3

4

0 1 2 3 4 5

output

total N = 100 average N = 100 total N = 400

average N = 400 total no cong. average no cong.

* Parameter values: = 1, = 0.2; = 0.1 for N = 100 and N = 400, = 0 for "no cong."

..

• .Location decision has an impact on production function

• Income equation is not affected by congestion parameters

• How ever, congestions results from Wage rate & price index

To assess the relevance of To assess the relevance of congestioncongestion

• Relay on simulation on two steps:

• 1St illustrate relevance of in the two cities model-allow as to apply core model in congestion with empirical phenomenon of city –size distribution

• 2Nd introduce many cities & congestion racetrack economy of the core model

Two location and congestionTwo location and congestion

• To determine the direction of MLF & stability LE• Focus on the real wage of city 1 relative city2• Plot the welfare achieved in two cities together

• *Re-4 No congestion cost for SE is stable when high T, where as full agglomeration in either city is stable for low T

• However, this is not satisfactory out come from the empirical point of views ,

Five different stages –for possibility Five different stages –for possibility of LE by using congestion of LE by using congestion

1. very high T, spreading is the only stable (& welfare maximizing) equilibrium

2. As T decrease still stable& allowing partial agglomeration rather than complete as SE

3. Complete agglomeration in either city is SE as T continue to fall

4. As T becomes very small , their impact relative to congestion is limited.

5.For very low T , spreading is again the only stable

From this three conclusions From this three conclusions emergeemerge

1st . the rage of possible LRE outcomes with congestion is wider than with out congestion

2nd . The phenomenon of partial agglomeration establishes the possibility of small and large economic centers as a stable LE out come

3rd . The welfare implication of the GE model have tendency to coincide with SLE

a. T = 1.9

0.92

1

1.08

0 0.5 1

w 1/w 2 w elfare

b. T = 1.7

0.93

0.965

1

1.035

0 0.5 1

w 1/w 2 w elfare

c. T = 1.61

0.94

0.96

0.98

1.00

1.02

w 1/w 2 w elfare

Many location &congestionMany location &congestion

• Two city model in congestion allow as for viability of small economic centers of Manufacturing extend to many cities

The results of such simulation with congestion: * many cities still have manufacturing production (MP) in

the LE * these cities vary in economic size from empirical point

of view * the final distribution of MP is well structured around two

center of economic in cities 3&15 * the individual city economic size in LE largely depends

on the relative place in the initial distribution of city sizes (cities20&23)

Figure 7.3 The racetrack economy with congestion ( = 5; = 0.7; = 0.1)

a. T = 1.21

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2324

initial final b T = 1.31

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initial final