Urban Economics City Size

Urban Economics City Size

Utility and City Size Question: Why do cities differ in size and scope? While NYC has a population of more 18 million, the smallest urban area in the U.S. has only 13,000. A well observed regularity within a given region: There are a few large cities, a moderate number of medium cities, and a large number of small cities!

Utility and City Size Agglomeration economies cause firms to cluster, increase productivity, and raise wages. As a city grows, the benefits of higher wages are at least partially offset by several disamenities like: Longer commuting times Greater densities Congestion and pollution How does an increase in city size affect the utility of a typical worker?

Utility and City Size The Benefits and Costs Wages reflect labor productivity and are higher in larger cities. Workforce (millions) Wage Labor Income Com. cost Utility 1 $ 8 64 5 $59 2 $10 80 10 $70 4 $11 88 22 $66 There is an utility optimum regarding growing cities. Cities can be too big! The costs of the city size are associated with an increasing rate of commuting costs (simplified model).

Utility within a City Locational Equilibrium, Land Rent We now consider location decisions of typical workers within a city (2 million inhabitants). Land rents will adjust to make all workers indifferent among their residential location. Distance Com. cost Land Rent Labor income Rental income Utility 0 0 $25 $80 $15 $70 5 $10 $15 $80 $15 $70 10 $20 $ 5 $80 $15 $70

A System of Cities How is a region s workforce distributed among its cities? Are there many small cities or a few big cities? Assumptions: Region with 6 million workers and three possible configurations Six cities 1 million workforce each Three cities 2 million workforce Two cities 3 million workforce

A System of Cities Cities Are Not Too Small Finding the equilibrium (we start with six cities): 70 68 59 S M L z U Self-reinforcing effects generate extreme outcomes 1 2 3 Workers per city (millions)

A System of Cities Cities Are Not Too Small An illustration (Krugman, 1996): 29.04.2009 Fachgebiet Internationale Wirtschaft Prof. Dr. Volker Nitsch Nicolai Wendland

A System of Cities Cities Are Not Too Small An illustration (Krugman, 1996): 29.04.2009 Fachgebiet Internationale Wirtschaft Prof. Dr. Volker Nitsch Nicolai Wendland

A System of Cities Cities May Be Too Large We now start with two big cities (3 million each). 70 68 59 S M L z U 1 2 3 Workers per city (millions)

Specialized and Diverse Cities Do cities specialize in a narrow set of economic activities or do they create diverse environments? We find BOTH types of cities: The typical region contains a wide variety of cities, from highly specialized to highly diverse ones (Henderson, 1988). Specialization happens because of localization economies Diversification happens because of urbanization economies The city types are complementary serving different functions in a market economy.

Specialized and Diverse Cities Setting 1 (based on Duranton and Puga, 2001): A firm experiments in a diverse city and later moves to a specialized area. Assumptions: Six potential production processes Firm observes other firms in diverse city to find ideal production process Prototype is found and produced by imitation Discovery of ideal process takes an average of three years After the discovery, the firm will move to a specialized city and will start making profit

Specialized and Diverse Cities Setting 2: A firm experiments in a specialized area. Assumptions: There are trade-offs responsible for the decisions on where to locate: Good lower prototype costs: Each city has specialized inputs for the production process, so inputs will be cheaper. Bad higher moving costs: Search for ideal process requires moving around. On average, a firm will need three moves. If moving costs are large relative to the savings in prototype costs, profit will be lower, when the firm experiments in specialized cities.

Specialized and Diverse Cities Evidence of laboratory cities: Duranton and Puga, 2001 Diverse cities serve as laboratories for innovative industries: Data from French firms shows that over 7 in 10 relocated from a diverse city to a specialized city. Firms move as they mature. Highest frequency is observed for most innovative industries with 93% for R+D, 88% for pharmaceuticals and cosmetics, and 82% for IT. Also high frequency: Business services, printing and publishing, aerospace equipment and electronic equipment. Low frequency: Less innovative branches like clothing and furniture.

Differences in City Size The role of localization economies and urbanization economies in determining the size of a city: u* s m b U 1 3 6 Workers per city (millions)

Differences in City Size And Local Goods We switch the focus to the consumer side of an urban economy. We distinguish between industries that export their products and those that sell locally to residents of the city. Goods are locally sold if the per-capita demand is large relative to the associated economies of scale. E.g. a barber can be supported by only a few hundred people -> will exist even in small cities. Goods are exported (or regionally sold) if the per-capita demand is low relative to the associated economies of scale. E.g. it takes many people to support operas and theaters -> they will only survive in big cities.

Differences in City Size And Local Goods This generates specific patterns of travel behavior: Since all goods are available in big cities compared to only a small variety in small cities consumers travel to them to get high order products (surgery, luxury goods). Residents from bigger cities will not travel to a small city for a pizza.

Differences in City Size Local Employment Amplifies Size Differences Export employment supports local employment. A big city supports a wider range of consumer goods Export Employment Local Employment Total Employment 1 million 0.5 million 1.5 million 3 million 3 million 6 million 6 million 12 million 18 million

The Size Distribution of Cities The size distribution of cities or rank-size distribution describes a remarkable regularity including sizes of businesses, lengths of rivers, particle sizes (e.g. sand) and others. It is also known as Zipf s law. In many cases, the distribution of cities can be approximated by the application of the rank-size rule, which estimates the relationship between a city s rank in the national hierarchy and its size (population). Rank-size rule: Rank times population is constant across cities

The Size Distribution of Cities If the largest city has a population of 24 million (rank 1), the second largest city will have 12 million and the third largest will have 8 million inhabitants. The hypothesized relationship is : where C is a constant, N is population, and b is to be estimated. The rule holds if b=1.

The Size Distribution of Cities Agglomerations in Switzerland, 2007 1 2 3 4 5 6 7 8 9 10 Zürich 1 111 909 Genève 497 386 Basel 486 952 Bern 344 724 Lausanne 313 074 Luzern 200 282 St. Gallen 145 627 Winterthur 130 076 Lugano 128 541 Baden-Brugg 110 348 1 111 909 994 772 1 460 856 1 378 896 1 565 370 1 201 692 1 019 389 1 040 608 1 156 869 1 103 480 29.04.2009 Fachgebiet Internationale Wirtschaft Prof. Dr. Volker Nitsch Nicolai Wendland

The Size Distribution of Cities Zipf Plot 29.04.2009 Fachgebiet Internationale Wirtschaft Prof. Dr. Volker Nitsch Nicolai Wendland

The Size Distribution of Cities Nitsch (2005) analyzes the results of 29 studies regarding the rank-size rule. Two-thirds of the estimates considered find a value between 0.8 and 1.2 (median =1.09). This is consistent with earlier cross-country findings. They suggest that the population is slightly more evenly distributed than predicted by the rule. However, in most cases, political boundaries are considered instead of economic boundaries of metropolitan areas. Adjusting the sample reveals: b (median)= 1.02, which is very close to the rank-size result

The Size Distribution of Cities 29.04.2009 Fachgebiet Internationale Wirtschaft Prof. Dr. Volker Nitsch Nicolai Wendland

The Size Distribution of Cities 29.04.2009 Fachgebiet Internationale Wirtschaft Prof. Dr. Volker Nitsch Nicolai Wendland

Urban Giants Many nations (especially in developing countries) have relatively large primary cities: Metro Area Population Share of National Pop Tokyo 19,037,361 15.76 Mexico City 16,465,487 20.97 Saõ Paulo 15,538,682 11.46 Buenos Aires 10,759,291 35.47 Santiago de Chile 4,227,049 34.87 Montevideo 1,157,450 39.36

Urban Giants There are several theories to describe the large concentration of population in primary cities: Historically grown primary trading cities: strong agglomeration economies developed in a certain core region (ports, trade centers). Disproportionate investments in infrastructure: In developing countries, major investments occur around the capital, leaving cities at the periphery behind. The role of politics: Ades and Glaeser (1995) suggest that countries run by dictators have larger primary cities. Resources are gathered from the hinterland and concentrated in the capital. The study across 85 countries finds that cities within a dictatorship are 45% larger than in other countries.

Urban Giants 29.04.2009 Fachgebiet Internationale Wirtschaft Prof. Dr. Volker Nitsch Nicolai Wendland