URBAN ECONOMICS

SPRING 2010

Why do cities exist?

• Cities are places in which population density is greater than the other parts of the countries.

• In an economic context, what are the factors behind the creation of the cities?

• Let’s build up a model…• Assumptions: 1.The region produces and consumes two

goods: shirts and bread.

2. People use land to grow raw materials and take time to transform raw materials into shirt and bread.

3. Travel within this region is by foot. Residents walk at a speed of 8 kms per hour.

Assumptions (which prevent the formation of

cities): 1.Equal productivity.2.No scale economies in production.3.No scale economies in transportation.

Consequences of these assumptions

• There is no possibility of trade. Each person is self-sufficient.

• No specialization.• No scale economies.• Population will be uniformly distributed

throughout the region.

Relaxing the assumptions to form a city

Assumption 1 : Equal productivity If we relax this assumption, i.e. one part of the region

may have a comparative advantage in shirt production and the other part may have a comparative advantage in bread production.

• Let’s say that the region has two parts: South and North. The production amounts in each region are given below:

Relaxing the assumptions to form a city

Output per hr (of a worker) Opportunity Cost

South North South North

Bread 1 2 1 shirt 3 shirts

Shirts 1 6 1 bread 1/3 bread

South has a comparative advantage in production of bread.

North has a comparative advantage in production of shirts.

Relaxing the assumptions to form a city

Result: Specialization and trade

But, a city does not exist yet….

Relaxing the assumptions to form a city

Assumption 2 : No scale economies in transportation

But, if transport cost per km. decreases as the volume transported increases, it would be cheaper to transport shirts and bread in bulks. This also creates intermediaries in transportation.

What are the implications?

Relaxing the assumptions to form a city

The trading firms will locate at places convenient for the collection and distribution of goods. Hence, marketplaces develop at crossroads, ports and other shipment points.

The location decisions of the trading firms cause the development of market cities. The marketplace will create employment opportunities.

The employees hired by trading firms will live near marketplace to economize on commuting costs.

Relaxing the assumptions to form a city

Hence, demand for land near marketplace increases: Price of land increases.

Residents will economize by occupying smaller lots.

As a result, population density around the marketplace will be higher than the rest of the region.

Relaxing the assumptions to form a city

Assumption 2 : Constant returns to scale in production

Suppose that production is subject to constant returns to scale. This means, each worker can produce either 1 shirt or 1 bread per hour regardless of how much he/she produces: There are no advantages from producing at large scales.

If we relax this assumption, then factory production may replace home production. How?

• If there are scale economies (instead of CRTS) in production, as volume of shirt production increases, labor required to produce one shirt decreases (less input per unit of output, costs decline with output).

Labor time/shirt

Number of shirts

Average labor time

• Why does the average labor time decrease as number of shirts produced increases?

1. Factor speacialization: Each laborer specializes in one task and their productivity increases.

2. Indivisible inputs: Some inputs are indivisible since they have minimum efficient scale. E.g. Machines in a factory. They cannot be scaled down efficiently for use by individual workers. As output increases factory uses more indivisible inputs hence productivity increases.

Initially: 1 hr 1 shirtNow: 0.25 hr 1 shirt (or 1 hr 4 shirts)

What should be the wage level and price of a shirt? Wage should be at least as high as to make workers indifferent between working in the factory and working at home.If the worker works at home: He/she produces 1 loaf of bread/hr.If the worker works at the factory: He/she produces 4 shirts/hr.Hence, minimum wage should be 1 loaf of bread/hr.

Then, production cost of one shirt is 0.25 loaf of bread. Net price of a factory shirt:

Price paid by consumer to firm (0.25 loaf)+

Consumer’s opportunity cost of the time spent traveling to and from the factory

(Loss of bread production due to traveling instead of producing bread).

A resident can produce 1 loaf per hr. It will be sensible to buy a factory shirt if net price of a factory shirt is at most 1 loaf.

Since, production cost is equal to 0.25 loaf, the consumer should consider the time that a trip takes.

0.25 + trip time= 1 Then trip time can be at most 0.75 hr.If it is less than 0.75, the consumer will prefer a factory shirt.

Suppose that walking time is 8 kms per hour.According to these criteria, the market area of the shirt

factory is determined.It is the area for within which the factory will

underprice homemade shirts for residents.In our case, it is defined as the area within 3 ks of the

factory.Why? (We can have at most 0.75 hrs walking time, this

means since walking time is 8 kms/hr, we can have 6 kms for two way walking –to and from the factory-. That is why we end up with a circle with a radius of 3 kms).

Factory causes the development of a small factory city.

Are there any limits to city size?1. Freight cost:

We have assumed that consumers travel between home and factory meaning they they themselves incur freight costs. This cost of transporting goods limits the ability of the factory to exploit economies of scale in production.

What can the factory do? We know that travel speed is 8 kms/hr. and market area is a

circle with a radius of 3 kms. If the firm becomes responsible from freight costs and

creates a method to increase the travel speed, then it can create a greater market area.

E.g. If the firm increases the travel speed to 16 kms per hr (doubles), market area will be a circle with a radius of 6 kms. This will increase the output of the factory, factory’s workforce and population of the factory city.

Are there any limits to city size?

• Decrease in freight cost allows factory to more fully exploit economies of scale, increasing city size.

• Transportation is a very important factor affecting the city size.

• Think about examples from Turkey, Europe…

Are there any limits to city size?

2. Scale economies: As economies of scale beacome more powerful, cost of factory production decreases relative to home production.Hence, market area of the factory increases and size of factory cities increase.

Think about the industrial revolution: Spinning jenny to the machines.

Are there any limits to city size?

3. Commuting costs: Larger cities have larges commuting times.

In larger cities factory must pay workers to compansate for longer commuting times. Since market area is determined according to the net price of the factory shirts, increase in wages is a limit to the city size.

Inverse may also apply: A decline in the unit cost of commuting will cause a city to grow.

E.g. Boston

Boston is a good example of the effects of changes in transit technology on city size. 1850 : Boston was a small walking city with a radius of 2 miles.1860s: Horse-powered railroad; city radius: 2.5 miles.1887: 4 miles. 1890: Electric trolley: Speed and number of passengers doubled.City radius: 6 miles.Last 40 years: Radius is tripled and land area increased ninefold.

A rule of thumb: A city should be small enough that a resident can travel from one edge of the city to the city center in an hour.

Summary

What did we learn today?Economic forces behind the development of cities:1. Comparative advantage2. Economies of scale in transportation3. Economies of scale in production

Determinants of city size.