Chapter 1 – Why Cities Exist
The two main forces identified by economists that lead to spatial concentration of jobs are scale
economies and agglomeration economies. With scale economies business enterprises become more
efficient at large scales of operation, producing more output per unit of input than at smaller scales.
Agglomeration economies capture the benefits enjoyed by a firm when it locates amid other
business enterprises. Transportation costs also influence where a firm locates, and they can lead to
spatial concentration of jobs.
Output per worker is higher when a factory has many workers then
when it only has a few, because of the division of labor. When a
factory has many workers, each can efficiently focus on a single task
in the production process, rather than carrying out all the steps
himself. The factory’s output, Q, is represented on the vertical axis
and the number of workers, L, on the horizontal axis. Because the
curve shows output increasing at an increasing rate as L rises, scale
economies are present.
Figure 1 - Internal return to scale
Pecuniary agglomeration economies
Pecuniary agglomeration economies lead to a reduction in the cost of a firm’s inputs without
affecting the productivity of the inputs. Consider a big city, with a large concentration of jobs and
thus a large labor market, there are more specialized workers in this
city compared to a smaller city. The labor market of a small city
probably would contain no workers of the desired type and attracting
them comes with large costs. Thus, by locating in a big city, a firm
may lower its cost of hiring specialized labor. The existing
employment concentration in the big city thus attracts even more
jobs as firms locate there to reduce their hiring costs.
Technological agglomeration economies
Technological agglomeration economies arise when a firm’s inputs
are more productive if it locates in a big city, amid a large Figure 2 - External returns to scale
concentration of employment, than if it locates in a small city. The beneficial effect of location in
larger cities could be a result of knowledge spillovers across firms, which are a type of externality.
The big / small city distinction may be less relevant for knowledge spillovers than it is for pecuniary
agglomeration economies. Instead, what may matter is the extent of the city’s employment
concentration in the relevant industry. A larger job pool gives more competition to the employees,
incentivizing them to be more productive than they might be in a
smaller city with a smaller job pool.
Transport costs and firm location
Transportation-cost savings can be viewed as a type of pecuniary
agglomeration effect, which may draw firms to a large city when
both its market and suppliers are located there. When the
market and suppliers are far apart, the firm’s location decision is
less clear. Shipping costs exhibit economies of distance, in the
sense that the cost per mile of shipping a ton of material declines
with the distance shipped. The terminal cost must be incurred
1
,regardless of the distance, this is the cost of (un)loading the shipment. The variable cost is
dependent on the distance. Weight-gaining production processes should a be located close to the
market, while weight-losing processes should be oriented to the mine / input.
Another type of agglomeration effects is retail agglomeration: the spatial concentration of retail
outlets. Two forces contribute to retail agglomeration. Firstly, there is a desire by consumer to limit
the costs of shopping trips, which include both time costs and out-of-pocket costs. Stores are likely
to attract more customer traffic when they are spatially concentrated than when they are dispersed
and this gain can stimulate retail agglomeration. Secondly, there is a benefit to consumers of
comparison shopping, which can arise even when only one purchase is being made. The ability to
compare similar products will generate a better purchase decision, raising the benefits from
shopping. Besides, price competition will lead to lower prices, which is beneficial for the consumer.
Chapter 2 – Analyzing Urban Spatial Structure
We assume that all jobs are located in the city center, called the central business district (CBD). Let x
denote distance from a consumer’s residence to the CBD. The cost of commuting to work is higher
the larger is x. This cost has two components, an out-of-pocket cost and a time cost / opportunity
cost. Parameter t represents the per-mile cost of commuting. Total commuting cost per period is
then tx. Let the income earned per period at the CBD by each resident be denoted by y. Then
disposable income, net of commuting cost, for a resident living at distance x is equal to y−tx. Bread
consumption is denoted by c. Housing consumption is denoted by q, the square footage of floor
space in a dwelling. The price per unit of housing is the price per square foot of floor space, denoted
by p. The consumer’s budget constraint will be: c + pq= y−tx .
The consumer’s utility function, which gives the satisfaction from consuming a particular (c, q)
bundle, is given by u ( c , q ) . The consumer is utility maximizing subject to the budget constraint. The
equilibrium condition says that consumer must be equally
well off at location, achieving the same utility regardless of
where they live in the city. Since higher commuting costs
mean that disposable income falls as x increases, some
offsetting benefit must be present to keep utility from
falling. This is a lower price per square foot of housing at
greater distances from the CBD. Even though consumers
living far from the center have less money to spend, their
money goes farther given a lower p, allowing them to be
just as well off as people living closer in. The lower p
compensates for the disadvantage of higher commuting
costs at distant locations. Dwelling size q rises as distance from CBD increases, this substitution in
favor of housing and away from bread is the consumer’s response to the decline in the relative price
of housing as x increases.
The model assumes that floor space is produced with land and building materials alone. The
production function for housing floor space is written as Q=H ( N , l ), where Q is the floor space
contained in a building, N is the amount of building materials, l is the land input and H is the
production function. There is a diminishing marginal product of capital, meaning that with the land
input fixed, extra doses of building materials lead to smaller and smaller increases in floor space. The
2
, revenue earned by the developer is equal to pH ( N , l ). In order for developers to be willing to build
housing in all locations, the profit from doing so must be the same everywhere.
Floor space close to the CBD has a higher price, so developers
will compete vigorously for land in this location, driving up the
land rents. Developers’ lower demand for suburban land leads
to a lower land rent. Since competition for land among
developers will bid up rent until profit is exhausted, the
uniform profit achieved through compensation land-rent
differentials is in fact a zero profit level. With the price of
capital fixed and land rent rising moving toward the CBD, the
land input becomes more expensive relative to the capital
input as distance x declines. Producers generally shift their
input mix in response to changes in relative input prices. As land becomes more expensive compared
to capital, developers economize on the land input and use more capital in the production of floor
space. By making this substitution, the developer is building taller structures.
Population density
Population density, denoted by D, is equal to people per acre. The
central-city location has a tall building that is divided into smaller
dwellings, while the suburban location has a short building divided
into large dwellings. Since suburban buildings have less floor space
per acre of land and contain larger dwellings than central-city
buildings, the suburbs have fewer dwellings per acre than the
central city. Thus, D falls moving away from the CBD.
The city’s land area is the result of competition between housing
developers and farmers for use of the land. Suppose thar farmers are
willing to pay a rent of RA pre acre of land. The agricultural rent will be high
when the land is very productive or when the crops grown on it command
a high price. A landowner will rent his land to the bidder who offers most
for it. The housing developer is the highest bidder at locations inside the
intersection point of the r curve and the RA line while the farmer is the
highest bidder at locations outside this intersection. The city’s supply-
demand equilibrium depends on four key parameters of the model:
population (L), agricultural rent (RA), commuting cost (t) and income (y).
When t increases, the existing spatial pattern of housing prices does not
adequately compensate for long suburban commutes. As a result,
suburban commuters will want to move toward the center to reduce their
commuting costs. This movement bids up housing prices near the CBD and
reduces them at suburban locations. As a result, the housing-price curve
rotates in a clockwise direction.
Chapter 3 – Modifications of the Urban Model
Suppose that we have two income groups, rich and poor earning income
y P< y R . With rich and poor households, there will be two housing-price
3
The two main forces identified by economists that lead to spatial concentration of jobs are scale
economies and agglomeration economies. With scale economies business enterprises become more
efficient at large scales of operation, producing more output per unit of input than at smaller scales.
Agglomeration economies capture the benefits enjoyed by a firm when it locates amid other
business enterprises. Transportation costs also influence where a firm locates, and they can lead to
spatial concentration of jobs.
Output per worker is higher when a factory has many workers then
when it only has a few, because of the division of labor. When a
factory has many workers, each can efficiently focus on a single task
in the production process, rather than carrying out all the steps
himself. The factory’s output, Q, is represented on the vertical axis
and the number of workers, L, on the horizontal axis. Because the
curve shows output increasing at an increasing rate as L rises, scale
economies are present.
Figure 1 - Internal return to scale
Pecuniary agglomeration economies
Pecuniary agglomeration economies lead to a reduction in the cost of a firm’s inputs without
affecting the productivity of the inputs. Consider a big city, with a large concentration of jobs and
thus a large labor market, there are more specialized workers in this
city compared to a smaller city. The labor market of a small city
probably would contain no workers of the desired type and attracting
them comes with large costs. Thus, by locating in a big city, a firm
may lower its cost of hiring specialized labor. The existing
employment concentration in the big city thus attracts even more
jobs as firms locate there to reduce their hiring costs.
Technological agglomeration economies
Technological agglomeration economies arise when a firm’s inputs
are more productive if it locates in a big city, amid a large Figure 2 - External returns to scale
concentration of employment, than if it locates in a small city. The beneficial effect of location in
larger cities could be a result of knowledge spillovers across firms, which are a type of externality.
The big / small city distinction may be less relevant for knowledge spillovers than it is for pecuniary
agglomeration economies. Instead, what may matter is the extent of the city’s employment
concentration in the relevant industry. A larger job pool gives more competition to the employees,
incentivizing them to be more productive than they might be in a
smaller city with a smaller job pool.
Transport costs and firm location
Transportation-cost savings can be viewed as a type of pecuniary
agglomeration effect, which may draw firms to a large city when
both its market and suppliers are located there. When the
market and suppliers are far apart, the firm’s location decision is
less clear. Shipping costs exhibit economies of distance, in the
sense that the cost per mile of shipping a ton of material declines
with the distance shipped. The terminal cost must be incurred
1
,regardless of the distance, this is the cost of (un)loading the shipment. The variable cost is
dependent on the distance. Weight-gaining production processes should a be located close to the
market, while weight-losing processes should be oriented to the mine / input.
Another type of agglomeration effects is retail agglomeration: the spatial concentration of retail
outlets. Two forces contribute to retail agglomeration. Firstly, there is a desire by consumer to limit
the costs of shopping trips, which include both time costs and out-of-pocket costs. Stores are likely
to attract more customer traffic when they are spatially concentrated than when they are dispersed
and this gain can stimulate retail agglomeration. Secondly, there is a benefit to consumers of
comparison shopping, which can arise even when only one purchase is being made. The ability to
compare similar products will generate a better purchase decision, raising the benefits from
shopping. Besides, price competition will lead to lower prices, which is beneficial for the consumer.
Chapter 2 – Analyzing Urban Spatial Structure
We assume that all jobs are located in the city center, called the central business district (CBD). Let x
denote distance from a consumer’s residence to the CBD. The cost of commuting to work is higher
the larger is x. This cost has two components, an out-of-pocket cost and a time cost / opportunity
cost. Parameter t represents the per-mile cost of commuting. Total commuting cost per period is
then tx. Let the income earned per period at the CBD by each resident be denoted by y. Then
disposable income, net of commuting cost, for a resident living at distance x is equal to y−tx. Bread
consumption is denoted by c. Housing consumption is denoted by q, the square footage of floor
space in a dwelling. The price per unit of housing is the price per square foot of floor space, denoted
by p. The consumer’s budget constraint will be: c + pq= y−tx .
The consumer’s utility function, which gives the satisfaction from consuming a particular (c, q)
bundle, is given by u ( c , q ) . The consumer is utility maximizing subject to the budget constraint. The
equilibrium condition says that consumer must be equally
well off at location, achieving the same utility regardless of
where they live in the city. Since higher commuting costs
mean that disposable income falls as x increases, some
offsetting benefit must be present to keep utility from
falling. This is a lower price per square foot of housing at
greater distances from the CBD. Even though consumers
living far from the center have less money to spend, their
money goes farther given a lower p, allowing them to be
just as well off as people living closer in. The lower p
compensates for the disadvantage of higher commuting
costs at distant locations. Dwelling size q rises as distance from CBD increases, this substitution in
favor of housing and away from bread is the consumer’s response to the decline in the relative price
of housing as x increases.
The model assumes that floor space is produced with land and building materials alone. The
production function for housing floor space is written as Q=H ( N , l ), where Q is the floor space
contained in a building, N is the amount of building materials, l is the land input and H is the
production function. There is a diminishing marginal product of capital, meaning that with the land
input fixed, extra doses of building materials lead to smaller and smaller increases in floor space. The
2
, revenue earned by the developer is equal to pH ( N , l ). In order for developers to be willing to build
housing in all locations, the profit from doing so must be the same everywhere.
Floor space close to the CBD has a higher price, so developers
will compete vigorously for land in this location, driving up the
land rents. Developers’ lower demand for suburban land leads
to a lower land rent. Since competition for land among
developers will bid up rent until profit is exhausted, the
uniform profit achieved through compensation land-rent
differentials is in fact a zero profit level. With the price of
capital fixed and land rent rising moving toward the CBD, the
land input becomes more expensive relative to the capital
input as distance x declines. Producers generally shift their
input mix in response to changes in relative input prices. As land becomes more expensive compared
to capital, developers economize on the land input and use more capital in the production of floor
space. By making this substitution, the developer is building taller structures.
Population density
Population density, denoted by D, is equal to people per acre. The
central-city location has a tall building that is divided into smaller
dwellings, while the suburban location has a short building divided
into large dwellings. Since suburban buildings have less floor space
per acre of land and contain larger dwellings than central-city
buildings, the suburbs have fewer dwellings per acre than the
central city. Thus, D falls moving away from the CBD.
The city’s land area is the result of competition between housing
developers and farmers for use of the land. Suppose thar farmers are
willing to pay a rent of RA pre acre of land. The agricultural rent will be high
when the land is very productive or when the crops grown on it command
a high price. A landowner will rent his land to the bidder who offers most
for it. The housing developer is the highest bidder at locations inside the
intersection point of the r curve and the RA line while the farmer is the
highest bidder at locations outside this intersection. The city’s supply-
demand equilibrium depends on four key parameters of the model:
population (L), agricultural rent (RA), commuting cost (t) and income (y).
When t increases, the existing spatial pattern of housing prices does not
adequately compensate for long suburban commutes. As a result,
suburban commuters will want to move toward the center to reduce their
commuting costs. This movement bids up housing prices near the CBD and
reduces them at suburban locations. As a result, the housing-price curve
rotates in a clockwise direction.
Chapter 3 – Modifications of the Urban Model
Suppose that we have two income groups, rich and poor earning income
y P< y R . With rich and poor households, there will be two housing-price
3
