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					LOCATION
Theories of Location


   Residential location or the location of
    people
   Location of firms
   The human race is, and has always been, a
    race of migrants
   evolved on the African savannahs and began
    walking out into Europe and Asia
   moved and settled and populated areas and
    then moved on to new areas.
   Some times we had to leave because of the
    environment, the weather, climate changes,
    economic conditions, persecution etc and
    sometimes we went because we wanted to .
   But for all those reasons combined,
    movement of people is a complex behavior
    with important regional ramifications.
Residential Location
Theory

    Residential location theory or what is
     usually termed migration theory deals
     with people moving.
Important Questions
   Why do people move? How much is economic, social, political,
    forced, etc.
   When do people move?
   When people migrate, what determines their destination?
   What sorts of formal and informal institutions arise because of
    migration?
   What is the effect of migration on the people who move?
   What is the effect of migration on the people left behind?
   What is the effect of migration on the place left?
   What is the effect of migration on people in the destination
    area?
   What is the effect of migration on the destination area?
Now, beyond these questions are
explanations dealing with interregional
migration as distinct from international
migration.
There are of course, some obvious
differences.
 International migration is more likely
to involve language differences and
higher costs of assimilation, as well as
more political reasons and implications.
But, it is my contention that the same
theory should apply to both.
Why do we care?
   We care because there are consequences to
    migration
   Consequences in the place of origin (some
    governments have actually developed laws to
    encourage out migration)
   These include Turkey, the Phillipines, South
    Korea, Pakistan, Bangladesh, Mexico and Sri
    Lanka.
Why would a country want to
encourage out migration?
   IN some cases it is to help keep pace with their
    expanding labor force. Since their arent enough jobs
    at home, people are encouraged to go
   In some cases, like Egypt and India, the educational
    systems are producing far more highly educated
    workers than can be accommodated.
   Placing such workers in western industrialized
    countries also tends to produce large inflows of
    valuable hard currency for the country of origin.
   In some cases emigration is promoted specifically for
    selected ethnic groups or those that oppose the
    government of the origin country.
   On the other hand there may be serious
    consequences of migration for the origin
    place
   Migration is highly selective and those who
    are most able to leave a declining area and
    most likely to find jobs in a growing
    destination area are also the most educated
    and skilled and this means there may be a
    serious brain drain.
   Additionally when many people leave an area
    and then suddenly return there can also be
    both positive and negative effects. Such
    cases occur in situation of political turmoil
    which comes to an end and refugees return.
Consequences in the
Destination Place
   Migration can alter ethnic, racial, cultural, and even
    political composition of the receiving area. This is
    not only true for international migration but also for
    interregional migration. Areas of Detroit, Chicago,
    New York, and St. Louis can all attest to racial
    changes
   And once international migrants get to a destination
    area, their internal migrations may also have such
    consequences-Nashville and Memphis are clear cases
    of such migration.
   Such sudden change may cause social conflict and
    even violence.
There are also costs and benefits of
migration for social services and
entitlement programs as well as taxation
systems and tax revenues



     Migrants cause pressure on health care
      systems, educational systems, public
      infrastructure, and social welfare.
   Regional Origins of Immigrants to the United
   States, Selected Years
   Immigrants (in thousands)




Source: Immigration and Naturalization Service, 1998 Statistical Yearbook.
Why do people move?
   People move in order to better them
    selves (that is for economic reasons)
   They also move because of fear of
    political or other repression or
    persecution
    Finally they move because they simply
    want to pursue some dream or see
    what’s around the next corner
push factors or pull factors
   Push factors are those circumstances that
    cause you to want to leave somewhere. It
    might be high unemployment or generally
    poor economic conditions, it might be a war
    or famine.
    Pull factors, on the other hand are those
    factors which tend to draw migrants to a
    specific place. Pull factors can include low
    unemployment, high wages, or a generally
    booming economy with lots of perceived
    opportunities, availability of land, availability
    of housing, lower crime rates or simply a
           Population change for a region
           comes from four components

              Births
              Deaths
              In-migration
              Out-migration
The rate of expansion of population due to births minus deaths is referred to as the
natural rate of population increase. The most difficult components to predict, of course,
are in and out- migration. Regions find it difficult to regulate migration at all, while
countries with borders which can be controlled to varying degrees are more likely to try
to control migration and produce government policies for migration.
Migration Theory
First we shall present a few of the more well-known theories from

other fields and then we will move into the economic theories.


   Ravenstein                        Dual labor market
   Stouffer                           theory
   Lee                               World systems
   Zelinsky                           theory
   Neoclassical                      Network theory
    economics                         Institutional theory
   The new economics                 Cumulative
    of migration                       causation
Ravenstein
   Ravenstein put forward what have been
    termed the Laws of Migration, in the 1880s,
    based on observation of patterns in Great
    Britain, supplemented by data from the
    United States:
      * most migrants travel short distances;
      * migration proceeds step by step;
      * longer distance migrants prefer to go to
    great centres of commerce or industry;
      * each stream of migration produces a
    counter_stream;
   * urban dwellers are less migratory than
    people in rural areas;
       * females are more migratory than males
    in internal migration, but males are more
    common in international migration;
       * large towns owe more of their growth to
    migration than natural increase;
       * the volume of migration increases with
    the development of industry and commerce
    and as transport improves;
       * most migration is from the agricultural
    areas to centres of commerce and industry;
       * the main causes of migration are
    economic.
Stouffer
   the level of movement between two
    places is dependent on the number of
    intervening opportunities between them
   Intervening opportunities are the nature
    and number of possible alternative
    migration destinations which may exist
    between place A (migration origin) and
    place B (migration destination).
   the nature of places, rather than
    distance, is more important in
    determining where migrants go.
   People will move from place A to place
    B based on the real, or the perceived,
    opportunity at place B (e.g. work).
   the number of people moving over a
    given distance is directly proportional to
    the number of opportunities at that
    distance, and inversely proportional to
    the number of intervening
    opportunities.
Lee
   Lee tried to explain the factors affecting
    migration in terms of the positive and
    negative characteristics of both the
    origin and destination.
   Migrants must expect to receive some
    added advantage in moving from one
    place to another.
   potential movements from an origin ( such as
    a rural area) to a final destination (such as a
    city) are likely to be influenced by obstacles
    at either source or destination, or en route
   Such obstacles might include family
    pressures, misinformation, national policy,
    travel costs, lack of capital, illiteracy, military
    service and language.
   the same feature might be perceived
    differently by different individuals _ some
    might welcome the opportunity to live in a
    large city, with all the facilities it might offer,
    whereas others might find it cramped and
    depressing.
Zelinsky
   transition to patterns of migration just as
    there is for demographic change. In his
    model there are five stages:
   (i) in a pre_industrial society there is little
    residential migration and limited movement
    between areas;
   (ii) an early transitional stage of considerable
    rural_urban migration and the colonization of
    new lands, with the associated growth of
    longer distance migration (often in the form
    of emigration);
   (iii) in the third stage, rural _ urban migration
    continues and there is a rapid rise in
    migration between cities;
   (iv) rural _ urban migration may continue but
    at a markedly reduced rate; residential
    migration remains high, but in the form of
    migration in and between cities rather than
    emigration. There may be some immigration
    of unskilled workers, and highly trained
    professional workers may be exchanged
    between countries as a result of the
    operations of multi_national companies;
   (v) Advanced societies will have almost
    exclusively inter_ or intra_ urban
    migration although new technology will
    reduce the need for migration and there
    will be less need for some types of
    circulation such as long_distance
    journeys_to_work. Mobility between
    and within countries may be affected by
    state legislation.
Neoclassical economics
   macro theory)
   views geographic differences in the supply and
    demand for labor in origin and destination countries
    as the major factors driving individual migration
    decisions.
   Among the assumptions of this model are that
    international migration will not occur in the absence
    of these differentials, that their elimination will bring
    an end to international movements, and that labor
    markets (not other markets) are the primary
    mechanisms inducing movements.
   Government policy interventions affect migration by
    regulating or influencing labor markets in origin and
    destination countries.
Neoclassical economics
   micro theory
   focuses on the level of individual rational actors who
    make decisions to migrate based upon a cost_benefit
    calculation that indicates a positive net return to
    movement.
   Human capital characteristics that raise the potential
    benefits of migration, and individual, social, or
    technological factors that lower costs, will lead to
    increased migration.
   Differences in earnings and employment rates are
    key variables, and governments influence migration
    through policies that affect these (e.g., through
    development policies that raise incomes at the point
    of origin, decrease the probability of employment at
Classical Model of labor
migration
   Assumptions
   1.Perfect competition exists in all markets
   2.Production functions exhibit constant
    returns to scale.
   3.Factor migration is costless and there are
    no other barriers to migration
   4.Factor prices are perfectly flexible
   5.Factors of production are homogeneous
   6. Owners of labor and capital are completely
    informed about factor returns in all regions.
   labor is hired at any given wage up to the
    point that the marginal revenue product is
    equal to the marginal factor cost (wage)
   the law of diminishing returns states that
    given some fixed input, as you add a variable
    input, you evenutally get tothe point the
    additional variable input yields diminishing
    average, marginal and total returns.
   given an equilibrium situation if we add labor
    we reduce the marginal revenue product of
    wages and will only hire more workers at a
    lower wage
   If we lose workers then the mrp of remaining
    workers rise so that we pay higher wages.
   given the assumptions and these two truths,
    we can see how factor price convergence
    comes from migration. Assume we have
    some output to labor curve in two areas, and
    resulting supply and demand curves.
   This of course requires perfect information,
    lack of costs to move, and lack of other
    barriers to migration. Very limiting
    assumptions. Moreover, it ignores the
    differences between speculative migration
    and job-in-hand moves, it ignores the affect
    of amenities, psychological costs and
    benefits, the bandwagon effect (or beaten
    path effect) personal and family
The human capital model of
migration (Sjaastad, and cooke and Bailey)
    Does not assume a timeless world with
    instantaneous responses.
   Migrant responds to higher earnings of his lifetime.
    Migrants exhibit positive time preferences. (Sooner
    is better than later) so we have to look at the present
    value
   Rij=sum t=1 to T of (Yjt-Yit)/(1+d)raised to the t.
   Where Rij is the gross present value of the lifetime
    increment to earnings expected as a result of
    migration from i to j. T is the number of years of
   working life remaining, 1/(1+d) to the t is the
    discount factor with d as the discount rate. Then
    PV=R-C Better yet is the todaro model whcih looks at
   Problems with these models are the
    lack of information
   Information location and assessment is
    crucial to understanding migration
Migration is a function of
   characteristics of the origin area,
    characteristics of the destination area,
    difficulty of the journey,
   characteristics of the migrant.
New Economics of Migration
   views migration as a family (i.e., group) strategy to diversify
    sources of income, minimize risks to the household, and
    overcome barriers to credit and capital.
   International migration is a means to compensate for the
    absence or failure of certain types of markets in developing
    countries, for example crop insurance markets, futures markets,
    unemployment insurance, or capital markets.
   Wage differentials are not seen as a necessary condition for
    international migration, and economic development in areas of
    origin or equalization of wage differentials will not necessarily
    reduce pressures for migration.
    Governments influence migration through their policies toward
    insurance, capital, and futures markets, and through income
    distribution policies that affect the relative deprivation of certain
    groups and thereby their propensity to migrate
Dual labor market theory
   demand for low-level workers in more
    developed economies is the critical factor
    shaping international migration
   To avoid the structural inflation that would
    result from raising entry wages of native
    workers, and to maintain labor as a variable
    factor of production, employers seek low-
    wage migrant workers.
Dual labor market theory
   International migration is demand-based and
    initiated by recruitment policies of employers
    or governments in destination areas.
   Wage differentials between origin and
    destination areas are neither necessary nor
    sufficient conditions for migration.
   The options for government policy
    intervention to affect migration are
    limited__short of major changes in economic
    organization in destination areas.
World systems theory
   Focuses not on labor markets in
    national economies, but on the
    structure of the world market -- notably
    the "penetration of capitalist economic
    relations into peripheral, noncapitalist
    societies," which takes place through
    the concerted actions of neocolonial
    governments, multinational firms, and
    national elites.
   International migration is generated as land,
    raw materials, and labor in areas of origin are
    drawn into the world market economy and
    traditional systems are disrupted.
   The transport, communications, cultural and
    ideological links that accompany globalization
    further facilitate international migration. In
    this view, international migration is affected
    less by wage or employment differentials
    between countries than by policies toward
    overseas investments and toward the
    international flow of capital and goods.
Network theory
   migrant networks serve to reduce the costs
    and risks of international migration and thus
    to increase the likelihood of movement.
   The development of such networks are often
    facilitated by government policies toward
    family reunification and, once started,
    migrant networks can make international
    flows relatively insensitive to policy
    interventions.
Institutional theory
   once international migration has begun,
    private and voluntary organizations develop
    to support and sustain the movement of
    migrants.
   These include a variety of legal and illegal
    entities that provide transport, labor
    contracting, housing, legal and other services,
    many of which have proven difficult for
    governments to regulate.
Cumulative causation theory
   holds that, by altering the social context of
    subsequent migration decisions, the
    establishment of international migration
    streams creates "feedbacks" that make
    additional movements more likely.
   Among the factors affected by migration are
    the distribution of income and land; the
    organization of agricultural production; the
    values and cultural perceptions surrounding
    migration; the regional distribution of human
    capital
   once a "migration system" has developed, it
Other Migration Concepts
   beaten path, counterstream effect (well beaten
    path eases travel in both directions), chain-
    migration (short moves in one direction forming
    a stream
   Lowery hypothesis, net out migration positively
    related to net inmigration,
   Beale hypothesis high gross out migration can be
    associated with either high net in or high net out
    migration (with Lowery effect dominating in
    prosperous an growing areas and the common
    sense (net out negatively realted to net in )
    dominantig in depressed areas.
Location Decisions
Who makes locations
decisions when and why?
   The location unit is the entity which is
    at risk to being moved,
   whereas the location decision unit is the
    entity that makes the location decision
    for the location unit.
   These may be different.
The primary questions to be
answered by the location unit
are:

   When should a location decision be
    made?

   What constitutes a good location?

   What factors are important to a good
    decision?
Businesses care about location
decisions
   because it costs something to move
   a new location can drastically affect
    overall returns for the business.
“In the United States over $250 billion dollars are spent annually on the
construction of new facilities. It is estimated that depending on the
application 20 to 80 per cent of a facility's total operating cost is spent
on material handling within facilities. Proper location and design of
facilities can potentially result in savings of 5 to 50 percent of operating
costs. Apart from the magnitude of costs involved in facilities, the
frequency with which facility location and layout decisions are made is
also important. It is estimated that the layout of most facilities is
modified approximately every 2 to 5 years. This continual change is
required to keep pace with changes in demand, new product
introductions, product phase-outs, process changes, improved tooling
and technology, new legislation etc. As such most industrial engineers
and often many other engineers are involved several times in their career
in layout or location decisions.”
When is a location decision
made? Only at critical
junctures of the firm’s life.

   Birth, when the initial location must be
    chosen
   When expansion capacity is required
   When a new process or line of output is
    introduced
   When there has been a major change in
    transportation rates
   When the composition of output
    changes
   When there is a major change in input
    requirements
   When there is a shift in markets
   When there is a change in supplier
    locations
   Or some combination of the above.
   A location decision evaluation
    assumes something is wrong with
    the current location.
Business Location Factors
   strongest location factor is inertia.
   The supply (including availability, price,
    and quality) of local or nontransferable
    inputs. Nontransferable or local inputs
    are those inputs which are present at a
    location and which cannot realistically
    be moved. Examples: Land, climate,
    water quality soil composition
    amenities.
   The ability to dispose of nontransferable
    outputs in the local area. Nontransferable
    outputs ore outputs which have to be
    disposed of locally and are not realistically
    transferable elsewhere. Examples include air
    and water pollution and other waste (some is
    indeed transferable).
   Transferable inputs (those input factors
    which are relatively easily moved to a
    given location from their origin. This
    includes things like fuel, materials, and some
    services and increasingly, information.
   Outside demand for transferable
    outputs. This is really the availability of
    the market for the output of the
    business and reflects the relevant
    transfer costs.
The Four Classical
Traditions in Location
Theory
 Land Use – Von Thunen/Alonso
 Industrial Location (Process
   Orientation) –
   Weber/Smith/Isard/Moses
 Central Places/Market Areas-
   Christaller/Losch
 Spatial Competion - Hotelling
Location Theory
   Firms and households can be thought of
    as optimizers.
       Households make decisions to maximize their own
        utility.
       Firms make decisions to maximize profits, or
        minimize costs.
   This applies to locational choices as well.
       We have looked at this in regards to regional
        location.
       We now turn to locational choices within urban
        areas.
The Von Thunen Model
   Von Thunen first discussed the issue of
    locational choice in the context of an
    agricultural land use model.
   We will extend this model to investigate
    locational choice of firms and
    households in urban areas.
       We will get a better understandings of
        economic forces operating within urban
        areas.
Assumptions
   Assume that farmers produce output, q.
       Productivity per acre is constant at q.
   Markets for inputs and outputs are competitive.
   There are constant nonland inputs per acre, C.
   There are linear transportation costs to the
    market.
       There is no congestion.
       Cost per lb per mile is constant at t.
   Rents per acre are R.
Profit Function per acre
    =p*q-C-t*q*u - R
   Access to the market reduces transport
    costs.
   Competition for land would increase the
    price of land.
       This is known as the bid-rent.
   Competition for land would drive out all
    profits.
The Von Thunen Model
   Von Thunen first discussed the issue of
    locational choice in the context of an
    agricultural land use model.
   We will extend this model to investigate
    locational choice of firms and
    households in urban areas.
       We will get a better understandings of
        economic forces operating within urban
        areas.
Assumptions
   Assume that farmers produce output, q.
       Productivity per acre is constant at q.
   Markets for inputs and outputs are competitive.
   There are constant nonland inputs per acre, C.
   There are linear transportation costs to the
    market.
       There is no congestion.
       Cost per lb per mile is constant at t.
   Rents per acre are R.
Profit Function per acre
    =p*q-C-t*q*u - R
   Access to the market reduces transport
    costs.
   Competition for land would increase the
    price of land.
       This is known as the bid-rent.
   Competition for land would drive out all
    profits.
Bid Rent Function
   Set profits equal to zero, and solve for
    R.
    =p*q-C-t*q*u - R=0
   R=p*q-C - t*q*u
   Plot this in R-u space
       Intercept: p*q-C
       Slope: dR/du=-tq
Bid-Rent Function

    R(u)

             Profits are zero




                                distance
                                to market (u)
Model of Land Use




           A   u1   u2


           B
Generalizing the Model
    Apply to land use patterns in cities.
        Develop for firms
        Develop for households
    Start with simple model, and then add
     realism.
        Amenities and disamenities
        Fiscal factors
Standard Urban Location Model

    We will evaluate both firm and household
     location models
        Firms: Choose location within city to maximize
         profits.
             Generates a land rent function.
        Households: Choose location within city to maximize
         utility.
             Generates a housing price function, and an underlying land-
              rent function.
    Look at firms first and then households.
Simplistic City Assumptions

   Look at a turn of the century city
   Characteristics
       Monocentric with central export node.
       Horse-drawn wagons to node for manuf.
       Workers/shoppers commute using
        streetcars (hub & spoke system).
       Agglomeration economies exist for office
        industry.
    Manufacturers location
   Attraction to city proximity to export node.
   Produce output B with K,L,T, other inputs.
   Prices constant at PB.
        Input and output markets competitive.
        Cost of K,L constant at C.
        Expenditure on land is R*T
        Substitution possible.
   Transport prices are constant/ton/mile, t.
        Distance is u
   Look at profit function.
    Bid-Rent for Manufacturing
   Look at the profit function
     = PBB - C - t*B*u - R*T
   Competition for space drives out all profits.
     = PBB - C - t*B*u - R*T=0
     Solve for R= (PBB - C - t*B*u)/T

      dR/ du= -tB/T
   Since t,B, T are positive, this is negatively
    sloped.
Convexity of Bid-Rent Curve

    Simple Von Thunen model did not allow
     substitution, and this lead to constant slope
     function.
    Here do allow substitutablity. Look at effect on
     slope:
     dR/ du= -tB/T
           (slope at a point, so T cannot vary at that point)
    Now treat T usage as dependent on distance.
     d2R/du2= +dT/du*(tB)/T2
      Since dT/du>0, then d R/du >0
                            2    2
   Zero Profit Bid Rent Curve
              R
(PBB - C)/T
                  Slope of Bid-Rent:
                  dR/ du= -tB/T


                  Locational equilibrium
                  R*T = -tB*u

                            Bid Rent
                               u
Office Firms

   Attraction agglomeration economies.
   Consultations (A) with clients take place in CBD.
   Travel is by foot since they cannot rely on public transport
    system (too irregular).
   Produce output A with K,L,T, and other inputs.
   Prices constant at PA.
       Input and output markets competitive.
       Cost of K,L constant at C.
       Expenditure on land is R*T
       Substitution possible.
   Transport prices per consultation are constant at m*W.
       m=minutes, W=wage/minute, Distance is u.
   Look at profit function
     Bid-Rent for Office Firms
   Look at the profit function
     = PAA - C - m*W*A*u - R*T
   Competition for space drives out all profits.
     = PAA - C - m*W*A*u - R*T=0
     Solve for R= (PAA - C - m*W*A*u)/T

      dR/ du= -m*A*W/T
   Since m,W,A, and T are positive, this is
    negatively sloped.
   Zero Profit Bid Rent Curve
              R
                  Slope of Bid-Rent
(PAA - C)/T
                  dR/ du= -m*W*A/T


                  Locational Equilib:
                  (R)*T= -m*W*A*u

                            Bid Rent
                              u
Which is Steeper?
   Since W*m for office firms, is likely
    greater than t*u.
   On the other hand the ability to
    substitute away from land is more
    difficult for manufacturing. Thus, T is
    likely greater in the manuf. sector.
   Thus, bid-rent for office is steeper.
Zero Profit Bid Rent Curve
    R

            Land rent function is
            outer envelope.




                               Manuf. Bid Rent
                        Office Bid Rent
                           u
Retail firms
   Attraction is because hub of streetcar system
    drops them in CBD.
   Their markets are related to the density of
    their demand, the scale economies associated
    with production, and transportation costs.
       Central Place theory determines market size.
       Firms carve up the city into submarkets.
What determines WTP for Land?

   Customers come to the firm to buy goods.
   Profit Function: =G*(PG-ACG)
       where G=volume of goods, P=price, AC=avg. cost.
   If P-AC is constant, then profit max. at max G.
       This is maximized at the center.
   Conclusion:
       Willingness to pay for land depends on accessibility
        of land to customers, and thus it increases with
        access to CBD.
            These bid rents vary by firm.
Zero Profit Bid Rent Curve
    R

            Land rent function is
            outer envelope.




                               Manuf. Bid Rent
                        Office and Retail
                         Bid Rent
                           u
Land Use Patterns




          Office
           O
          Retail
          Manuf.
Residential Location Models
   Households choose locations to maximize
    utility.
   Household characteristics
       Households choose between Housing (H) and
        other goods (X), thus: V=(X,H) (identical tastes)
       Households work in the CBD
            Assume away decentralized employment.
       Income is constant at W.
       Commuting costs per mile are constant at t.
   Look at optimization problem:
Constrained Optimization
   L=V(X,H)+(I-PXX-PHH-t*u)
   We will look at the First Order Condition with
    respect to u:
    dL/ du= -dPH/du*H - t) = 0
   What does binding constraint imply?
   Thus, dPH/du*H - t =0 or dPH/du=- t/H
   In addition, given substitutability, this is
    convex since: d2PH/du2=+(t*dH/du)/H2>0
Bid Housing Price Function
     P
           Slope: dPH/du= -t/H

           Locational Equilibium
           PH*H= -t *u



                     Bid Rent
                        u
Family of Bid Functions
              Utility falls as we move
     P        to higher bid functions.
                      Why?

              Which is most relevant?
                   Related to S and D
                   for labor.




                        u
From Bid Housing Price to
Housing Price Gradient
     Slope: dPH/du= -t/H
     The housing price gradient is simply the
      percent change in housing prices
      brought about by a unit change in
      distance.
     Divide the numerator by PH to get:
     (dPH/PH)/du= -t/(H*PH)
         What does this mean?
From Bid Housing Price to Bid
Rent
   Demand for land by households is derived
    from the demand for housing.
       Thus, the bid housing price function generates a
        bid-rent function.
   Book shows this using revenue & cost
    function:
    profit=P(u)*Q - K-R(u)*T
    R(u)=(P(u)*Q - K)/T
            where P(u) is price per square foot of housing,
             Q=number of square feet, K=nonland inputs, T=land
             inputs.
Derivation of Bid Rent
      $


                         K
                         P(u)*Q



                                  u
                              R
    Rent-Gradient and Housing
    Price Gradient
   Since the demand for land is derived from
    the demand for housing, the gradients are
    also related.
   (dR/R)/du=1/landshare*(dPH/PH)/du
   Land share = Rent exp./Housing exp.
   If land share is say 0.1, which is steeper?
   Land Rent gradient is steeper.
Land Use Patterns in the
Monocentric Model



           Office
            O
           Retail
           Manuf.

          Households   Why are households
                       at most distant location?
Does SUM say anything about
Population Density?
    Density falls as consumption of housing
     increases.
    H decreases as u decreases for two
     reasons.
        Builders substitute away from land as R
         increases.
        Households substitute away from housing
         as PH increases.
    Summary
   SUM predicts:
       Downward sloping, and convex rent gradient.
       Downward sloping, and convex housing price
        gradient.
       Steeper rent gradient than housing price gradient.
       Declining density.
       Accessibility matters to households.
       Rings of activity in Monocentric city
   Lets look at some empirical evidence
Rent Gradient Evidence
   There is not a lot of evidence here since
    land rent is not typically observed. That
    is, there are few transactions on
    undeveloped land.
       Mills shows that rent gradients are
        downward sloping, and have been falling
        over time.
       Chicago, 1928, rents fall about 20%/mi.
       Chicago, 1960, rents fall about 11.5%/mi.
Housing Price Gradient
   Evidence from Jerry Jackson
   Some support here.
       Housing prices fall by approximately 2.5%
        per/mile.
   More later!
Land Rent vs. Housing Price
Gradient

   If land rent share is 0.1 to 0.2, then we
    get the following prediction on rent
    gradient:
   (dR/R)/du=1/LS*(dPH/PH)/du
    LS=0.1 implies (dR/R)/du=1/0.1*2.5=25%/mi.
    LS=0.2 implies (dR/R)/du=1/0.2*2.5=12.5%/mi.
   Thus, some support here.
    Declining Population Density

   There is substantial evidence here.
       McDonald(1989, Journal of Urban Economics)
        has a lengthy review article on this evidence.
       Next time, I will briefly review this article
    Does Accessibility Matter?
   Jackson article suggest that the answer is yes.
   However, Bruce Hamilton published an
    influential article in 1982 (JPE) that cast doubt
    on the predictability of the SUM.
        Measured wasteful commuting, by looking at pop.
         and employment density functions for cities.
             He found that there was 8 times more commuting taking
              place than could be explained by SUM.
Also Add other Realism
   Add in amenities/disamenities
   Add in fiscal factors
Weber/Losch/Isard/Smith
   Theories of plant location
Alfred Weber’s

   Theory of Industrial Location
Location of industry
   is concerned with the least cost location
   transport costs become an essential
    decision factor in the location decision
Alfred Weber
   Brother of Max
   Sociologist/Economist
   in 1909, Alfred Weber put forth the first
    developed general theory of industrial
    location
       Über den Standort der Industrie (Theory of
        the Location of Industries)
Background to the Problem
   At the beginning of the industrial revolution,
    transportation was limited and roads, canals etc were
    of poor quality.
   Most factories developed near their source of energy
    (coal)
   By the end of the 19th century, the industrial
    revolution had drastically changed location
    possibilities
   Firms were able to choose from more possible
    locations because of developments in rail transport,
    energy, telecommunications
   urban growth also provided more options for
    distributing firms
Weber realized
   locational factors may attract or repel
    various aspects of industry
   locational factors can lead to three
    areas of industrial change
        splitting of production and distribution
       diversification within the plant
       division of labor between industries
Location may affect
   cost of real estate
   cost of raw materials and intermediate
    inputs
   labor costs
   transport costs
   distribution costs
definitions
   factory or plant = the building or
    place where manufacturing takes
    place
   The industry = all factories, plants,
    or companies providing a similar
    product or service
   site =actual physical location
Assumptions
   raw materials are concentrated in specific sites rather
    than evenly distributed.
   size and location of markets are fixed and known
   uniform transportation surface
   Isotropic plane
   labor is unlimited, but immobile at fixed locations
   perfect competition
   Costs of land, labor, and capital are fixed and do not
    vary by location
   no scale economies and no input substitution
Raw Material or Market
Site
   First, consider whether a firm should
    locate at a raw material site or at the
    site of the market.
   two special cases
       weight losing case
       weight-gaining case (usually because some
        ubiquitous (available everywhere) raw
        material such as water comprises part of
        the final product
   Two possible locations
   The material site (I)
   The market site (M)
   Located 10 miles apart
   Transportation costs =$1 per lb.per mi.
   Inputs weigh 2lb. Output weighs 1lb.
   Locate in the center and calculate the costs
    or benefits of moving in either direction
   Move 1 mi. toward I- cost of transporting
    input decreases by $2 while cost of
    transporting output increases by $1. Keep
    moving and reducing net cost until get to
    raw material site. Now look at opposite
    case.
In special two cases
   Locate at market if weight gaining
    process
   Locate at raw material site if weigh
    losing process
Material Index
   Weber constructed an index to separate
    weight losing and weight gaining industries
                           Weight of raw material inputs
Material Index = -------------------------------------------------------------
                              Weight of finished products
   Only those raw materials which tend to occur at
    particular sites (i.e. localized materials) are included in
    the weight calculations - water, sand, clay, which are
    found virtually every where (i.e. ubiquitous materials),
    are excluded.
   If the process is neither weight losing or weight gaining
    there is a material index of 1.0. Such a plant could be
    located at the market or the input site, or any place in
    between. It is regarded as a footloose pattern of location.
    (eg.electronic information companies)
   Weight losing processes would have a material index in
    excess of 1.0 and would locate at the input site
   Weight gaining processes would have a material index
    less than 1.0 and would locate at the market
Example
   production of 10 tons of cement requires 11 ton of
    limestone, 3 ton of clay, 3 ton of coal, and .5 ton
    of gypsum for a total of 17.5 ton of inputs
    (assumed to be at the same location) then:
   Material Index = (17.5 ton / 10.00 ton) =1.75 a
    weight losing process so locate at the input
    site….but what if there is more than one input site?
two raw material sources
   The point of least cost
    is a result of the pull
    from different
    directions of the raw
    material and market
   For more complicated
    locations we develop
    Weber’s complete
    model
Some mathematical notation
   ai = weight of material “I” per unit of product
    weight (technical coefficient)
   ri = transport rate for input “i” ($/unit
    weight/unit distance)
   di =distance that input “i” is shipped
   n-1= number of inputs
   n = the product (thus an = 1)
   If wi = is weight needed of I to make wn of
    the output then wi / wn = ai
Weber’s theory
   Bus assuming constant prices and no
    input substitution, in order to maximize
    profit, total revenue and total
    production costs are unrelated to
    transportation costs so in order to
    maximize profit, we minimize total
    transportation costs
Minimizing TTC
   Min TTC = Σ wi ri di           (i=1 to n)



   We assume no terminal costs so         Σ (wi(i=1 to n)


    ri di )/ wn is equivalent for minimization, so
    this is the same as
   Min TTC = Σ ai ri di           (i=1 to n)



   In Weber’s analysis there is no input
    substitution so both ai and ri are fixed so the
    only unknown is distance.
   Now Weber defines the material index as
    MI= (Σ       wi )/ wn which is also equal to
                    (i=1 to n-1)


    Σ       ai
     (i=1 to n-1)
   So MI is the sum of the technical
    coefficients.
   Location weight = weight of the product
    plus weight of the materials in the product
    divided by the total weight of the product:
    LW = (Σ wi )/ wn which is also equal to
                  (i=1 to n)


    Σ ai therefore LW=MI+1
     (i=1 to n)



   Weber says that in general, high location
    weights imply that the weight of inputs is
    significant with respect to the product and
    means you have attraction toward the
    material site and a low LW implies attraction
    toward the market site.
   LW<2 implies MI<1 implies weight gaining
   LW>2 implies MI>1 implies weight losing
Relaxation of assumption
   Let transport rates be variable so ri is not
    the same for all “i”
   Define Ideal weight IW for input “i” or the
    product to be the technical coefficient times
    the transport rate
   I Wi = ai ri for each i, a and r are constant
    so IW is also constant for a given i
    regardless of location so IW for the product
    is simply rn since an =1
   So we want to minimize Σ IWi di in order
                              (i=1 to n)


    to minimize transportation rates.
Again assume two transferable inputs
and one market


                            n=3
                           M = market site

                           RM1=raw material site 1

                           RM2=raw material site 2

                          Eliminate outside the
                             polygon because it is
                             always the longer
                             distance
Assume you locate at the “factory site”
   Draw lines from each
    location to the factory
    site.
   As move down toward
    any 1 place you are
    decreasing
    transportation costs for
    that material but
    increasing for the other
    two.
   Think of this as forces
    pulling toward each
    vertex.
Varignon Frame
Some quick rules
   If I Wk = > Σ     IWi then solution is to locate
                 (ik to n)


    at k. This is a dominant ideal weight.
   The method of optimal plant location decision
    is to compute IW for all i, and decide whether
    there is an ideal weight. If there is, you have
    a corner solution, if not you have an interior
    solution.
   This also pertains to transportation networks.
If no dominant ideal weight

   Find isotims and isodapanes.
   Isotim=locus of equal transport costs for the
    shipment of one input or output. Costs will
    depend on technical coefficients
   Isodopane = locus of equal total transport
    costs.
   To find lowest cost find the isodapane where
    three isotims give cross and give lowest total
    costs.
Isotims – Cost surface
Isodapanes / Critical
Isodapane
   R and M represent a raw
    material source and a
    market respectively.

    thin lines are isotims
    which represent transport
    cost from the raw
    material source or the
    market per unit distance
   The isodapane is shown
    by the thicker line joining
    points A - F.
   The critical isodopane is
    the one that delimits the
    area in which a firm can
    operate at a profit
   A factory will not locate
    outside the critical
    isodopane
cheap labor
   a site of relatively cheap labor in a region
    may divert a factory from the site of lowest
    transport costs if the saving in labor cost
    exceeds the additional costs of transport
    incurred in moving to the site of cheap labor
    supply
effect of agglomeration
   agglomeration, like labor supply,
    as a factor which may divert a
    factory from the site of cheapest
    transport costs
   Assume that a factory can save $5
    per ton of output if it locates near
    to two others.
   no one factory must incur
    additional transport costs of more
    than $5
   Where three critical isodapanes
    overlap, as shown by heavy
    shading, additional transport costs
    are more than offset by the gains
    of agglomeration, and it would be
    worthwhile for factories A, B and
    C to move near to one another.
Weakness
   unreality of some of his basic
    assumptions To be fair, however, many of the criticisms have only
    arisen since the technical and economic changes in modern transportation have
    invalidated many of Weber's original assumptions
        Weber assumed that transport costs increase proportionately with
         distance and weight carried. Later workers, such as E.M. Hoover, have
         shown that freight rates are not directly proportional to distance, but
         tend to taper off with increasing distance. Hoover recognized that
         transport costs usually increase through a series of steps
        Transport costs are not the same tonne-for tonne on finished products as
         they are on raw materials, but vary between sea, rail and road carries,
         depending on the distances involved

         Transport costs: a cornerstone of the Weber model - make up a
         relatively small part of the total costs of production for the
         modern factory
        Weber's Concept of an Isotropic Surface lacks Credibility
   Factor            Location                     Example
   Bulk loss         Raw material   Sugar milling
   Bulk gain         Market         Glass bottle manufacture
   Fragility loss    Raw material   Packing goods for shipment
   Fragility gain    Market         Camera manufacture
   Hazard loss       Raw material   Micro-film recording
   Hazard gain       Market         Explosives manufacturing
   Perishability lossRaw material   Palm oil refining
   Perishability gainMarket         Newspaper printing
   . Hoover recognized that in addition to weight changes
    experienced during processing, there are certain other
    qualities which may be of equal or greater importance
   Weber saw the market as a fixed point
    on the isotropic surface. However,
    many firms nowadays attempt to
    diversify their markets as a measure to
    increase sales and to provide some
    degree of economic security.
   Perfect Competition does not exist
   Industries today are not merely
    processing industries
   Labor is not fixed in location, but is
    mobile.
Merits
   useful insights into the manner in which location is
    determined and has drawn attention to the
    importance of transport costs as a factor in location.
   provided a useful conceptual instrument for
    understanding the broad locational patterns of
    industries
   With modification, the 'least-cost' assumption of the
    Weber model is still appropriate, but at a different
    level of geographic scale from that usually
    envisaged. At the global scale, large Multi-national
    Corporation seek cheap locations, for example in
    Taiwan or Hong Kong, could be readily interpreted
    through Weber's idea of the critical isodapane
   Weber, however, emphasized, and
    demonstrated at the end of several
    chapters, that these "pure" rules of location
    are insufficient unless tested by real-world
    local, sociological, and political conditions.
   The issue of industry location is increasingly
    relevant to today's global markets and
    trans-national corporations. Focusing only
    on the mechanics of the Weberian model
    could justify greater transport distances for
    cheap labor and unexploited raw materials.
    When resources are exhausted or workers
    revolt, industries move to different
    countries.
Theories of Plant Location
   Median Location Principle
   Linear Market Competition
   Weber’s Theory of Location
   Losch’s Economic of Location
   Isard’s Space Economy
   Smith’s Spatial Margins
Isard’s Space Economy
   General theory of location by
    integrating von Thunen, Weber and
    Losch
   Based on substitution principle
       The substitution of one thing for another
            Ex: capital can be substituted for labor
            Ex: substitution of transport costs
Location S to:           Location T to:
M1 = 4 miles             M1 = 2 miles
M2 = 5 miles             M2 = 7 miles




If we were to plot these as
coordinates, this is the result




Movement along the line will demonstrate
the substitution of distances (or more
appropriately, transport costs
Smith’s Spatial Margins
   Simplified real world conditions
   Profit motive
   Processing costs vary
   Most profitable location is where total
    revenues exceed total costs by the
    greatest amount
           Total cost line or space-
           cost curve

          Total revenue

     Spatial margins to profitability


A: Weber, revenues are equal everywhere
B: Losch, variable revenue, but equal cost
C: Integration of theories
Weber’s Uncertainty Effect
   All firms share in uncertainty
   More realistic
   Greater uncertainties results lower
    investment of capital
   Uncertainty increases with greater
    separation from the market
   Satisficing rather than optimizing
Manufacturing: Regional
Patterns and Problems
   Patterns:
       Evenly spaced or random
       Evenly distributed or linear
       Maybe random
   How do we address these patterns and
    apply logic to their spatial arrangement?
Importance of Manufacturing
   Manufacturing activities are being displaced
    by service sector activities and high tech
    industry
   Why?
       Financial and consulting services
       Increases in consumer income
       Increases in public sector employment
       Research and development
       Advertising and promotion
   Can this sustain economic growth?
High Tech Industry
   Research and Development
   Are these services replacing manufacturing or
    are they complimentary?
   Locate near metropolitan regions due to large
    technical labor force
   What happens if there is a shift in resources
    dedicated to manufacturing?
       Regional economic growth will decline
       Results in less expenditures for research and
        development
       Loss of future opportunities
Regional Patterns and
Processes
   Cycle Theory
       Industrial regions progress through a
        sequence of stages over time
       Regions do not change at a consistent rate
       Regions do not follow the sequence
       Regional Cycle Theory
            Youth
            Maturity
            Old Age
   Regional Cycle Theory
        Youth:
              Experimentation and rapid growth
              High levels of investment
              Recognition of cost-saving locations
              New technology spurs more growth
              Competitive advantage (low production cost, large
               geographic market)
        Maturity:
              Dominance exerted over other regions
              Competition increases among regions
              Branch plants located in other markets
              Small loss of employees to branch plants
              Maintain locational cost advantage
        Old Age:
              Market shifts
              Cheaper raw materials
              Labor cheaper elsewhere
              Taxes, competitive land uses
              Employees leave for higher paying jobs
   Regional Examples:
       New England
            Grew through the industrial revolution
       Can anyone think of any smaller, local
        examples?
Manufacturing w/i the Urban
System
   Large cities are most attractive
       Large markets
       Better access to surrounding regions and markets
       Access to national market
       Transportation connections (interstate, railway, air
        links)
       Large pools of skilled labor
       Convenient business services (warehousing,
        communication links)
Manufacturing w/i the Urban
System
   Smaller cities are advantageous
       Lower cost of labor
       Manufacturing will be focused on
        processing raw materials
            Remember weight losing materials?
            Perishable food items
            Reflects the type of economy
                 Mining, agricultural, forestry
Diffusion of Manufacturing
   Rate and direction of change
   Diffusions occurs from a point or points
   Spreads the fastest where there are no
    barriers
       Physical
       Cultural
       Political
Manufacturing Regions

   American Manufacturing Belt / Rustbelt
       New York City: leading in manufacturing
       Chicago: second
       Regional concentrations:
            New England District
            New York and the Middle Atlantic
            Central New York and Mohawk Valley
            Pittsburgh-Cleveland-Lake Erie
            Western Great Lakes
            St. Lawrence Valley and Ontario District
Manufacturing Regions
   New England District:
       Oldest of the regions in the Northeast
       Clothing and textile industry originally
       Today its focus is electronic products,
        electrical machinery and fabricated metal
       Skilled labor pool from prestigious
        universities
Manufacturing Regions
   New York and Middle Atlantic:
       Centered on NYC
       Access to Intl. ports
       Fortune 500 companies
       International and national trade opportunities
       Financial, communications, and media
       Apparel, iron and steel, chemicals, machinery
       Publishing industry
Manufacturing Regions
   Central NY and Mohawk Valley
       Electrical machinery, chemicals, optical
        equipment
       Erie Canal and Hudson River
       Access to Atlantic and Great Lakes
       Niagara hydro-electric plant
Manufacturing Regions
   Pittsburgh-Cleveland-Lake Erie
       Oldest steel producing region in North America
       Centered on Western Pennsylvania and Eastern
        Ohio
       Electrical equipment, machinery, machine tools
   St. Lawrence Valley and Ontario
       Most populated
       Abundance of skilled labor
       Iron and steel, pulp and paper, processed food
Manufacturing Regions
   Western Great Lakes
       Detroit: automobile manufacturing
       Chicago: railcars, tractors, implements,
        food processing
       Milwaukee: iron and steel, fabricated
        metals, machinery, printing
       Popular distribution point because of
        transport connections
Manufacturing Regions

   Other regions in the US
       Gulf Coast
            Texas to Florida panhandle
            Chemicals, petroleum industry
       Southeastern
            Textiles, aluminum, lumber, transportation equipment
       West Coast
            Aerospace and aircraft industry
            Electrical components, ships, machinery
            Silicon Valley
       Pacific Northwest
            Aircraft, lumber, processed foods
    Manufacturing Regions
   Growth in population and economies occurs in the
    Sunbelt after WWII
   Sunbelt: southern and western US
       Climate
       Market shifts
       Labor cost locations
       Tax advantages/breaks

   California and Florida experience population booms
   Development of urban fringe
   1977 to 1982, 13% to 20% increase in
    manufacturing in many western states
   Regardless, NYC increased # of jobs, why?
Median Location Principle
   Assumptions:
       Production costs do not vary
       Delivery costs may vary
   Seek a location with minimal delivery
    costs
       Becomes location of maximum profit
   Example:

    Two possible
    median
    locations
Linear Market Competition
   Assumptions:
       Two manufacturers
       Same production costs
       Uniform demand
       Example:
         Infrastructures

Modes                      Users

        Transportation

              imprint
              Spatial


                             Urban Form
Introduction and Motivation
   Several examples of strategic interaction are
    used to set the stage.
   Strategic situations are ubiquitous.
   Individual interests are rarely either
    completely identical or perfectly opposed.

   Readings:    Dutta, chapter 1.
            McMillan, chapters 1, 2 & 3.
Game Theory: Background
   “In war the will is directed at an animate
    object that reacts.”                    --Karl
    von Clausewitz

       Environment includes other individuals and there is
        uncertainty about how they will act (or react).

       We can resolve some of this uncertainty if we assume that
        people act in a manner which is consistent with the
        achievement of their own goals.
Game Theory -- Definitions
    Study of rational behavior in situations
    involving interdependence. (McMillan)
       rational - actions are consistent with goals; not
        consistently making the same mistake.
       Interdependence - any player is affected by what
        others do; actions must depend upon prediction of
        others’ responses.

   A formal way to analyze interaction
    among a group of rational agents who
    behave strategically. (Dutta)
       Strategic behavior - Each player accounts for
Interdependence
   In order to decide what to do, you must
    determine how others are going to act (or
    react).
   This requires a knowledge of
       others’ aims (where they believe their interests lie), and
       the options available to them.
   What action will some player choose?
       Complicated by the fact that the best action will typically
        depend upon what others do.
       How is one to guess what others’ choices will be?
Why do economists care?
   “The typical problems of economic
    behavior [are] strictly identical with the
    mathematical notions of suitable games
    of strategy.”             – Von Neumann &
    Morgenstern

   Examples
       Buyer and seller negotiating over a price
       Employer and employee interaction (negotiation,
        creating incentives)
       Firm and its competitors
Applications outside
Economics
   Presidential candidates
   Congress and the President
   Opposing generals at War
   King Lear and his daughters (strategic
    bequests)
   Contests in the animal kingdom
   Strategic voting
   … and the list goes on
Examples of strategic
situations
   Several examples are used to set the stage.
    These are used to introduce important
    themes for the semester. I expect you to be
    familiar with the details of each example, as
    well as with the strategic principles they
    illustrate.

   Two firms competing over sales
       Time and Newsweek must decide upon the cover
        story to run in some given week.
       The big stories of the week are a presidential
        scandal (labeled M) and a proposal to deploy US
Example (simultaneous move)
   Time and Newsweek (continued)
       Each magazine’s sales depend upon both
        cover stories.
       When deciding on a cover, neither knows
        which story the other magazine will choose
                    New sweek
        to run.     M           K
        Here’s a convenient way to organize the
            M     35, 35      70, 30
        Time




    

        sales information: 15, 15
            K     30,70
Example (simultaneous
moves)
   This is called a “simultaneous move” game
    (even though choices need not be made at the same
    instant in time!)
   What stories will the two magazines choose
    to run?
   What would you choose (as the editor of
    Time)?        New sweek
                  M           K
   How do your answers change if the sales
          M     25, 25      50, 50
      Time




    figures are as follows:
             K   50,50    25, 25
Example (sequential moves)
   Interaction between a firm and a potential
    competitor.
   F is a monopoly and G is a potential entrant.
    (F is the only barber in Seville, G is thinking
    of getting into the business) .
   G gets to move first and must decide whether
    to stay out (O) or to enter (E) the market. If
    he chooses to enter, then F gets to move
    and his choices are to either start a price war
    (W) or to accommodate (A) entry.
   We will call this a game with sequential
    moves.
Example - continued
   This information (including the order of
    moves) can be conveniently organized using
                               (1,1)
    a tree:       F
                       A

         E
    G                 W

         O                  (-1,-1)

              (0,3)




   What should G do? What is the outcome
    likely to be?
Example (continued)
   The example of the barbers also raises the
    question of threats and their credibility: F
    would like to persuade G to stay out of the
    market. In the event that G enters, he
    threatens to shave his patrons for free.

   Should (will) G believe this?

   What can F do to make such a threat likely to
    be credible?
Prisoners’ Dilemma
   Story is familiar … (payoffs are prison terms)
                      T
                N          C
        N      3, 3       25, 1
    M
        C     1, 25       10, 10


   Individually best strategies lead to an
    outcome that is inefficient (there are feasible
    outcomes which are jointly preferred).
   Not a game of pure conflict (opportunities for
    cooperation)
Prisoners’ dilemma
(continued)
   Applications
       Arms Control: Two countries, each likes best the
        situation where they have a huge arsenal while
        their adversary does not. Disarming while the
        other keeps its weapons is the worst outcome.
        When both are armed, neither has a tactical
        superiority over the other and they jointly prefer
        the outcome where neither has a stockpile of
        weapons.
       Stability of cartels
       How can small armies of tyrannical dictators
        control large populations? Coordinated action
        would have a good chance of success. Difficulties
Negotiation with a deadline
   The case of Mortimer and Hotspur (“in the
    way of a bargain, mark you me, I’ll cavil on
    the ninth part of a hair”) [McMillan, p.16]
   Mortimer and Hotspur are to divide $100
    between themselves. Each of the bargainers
    knows that the game has the following
    structure:
       Stage 1: Mortimer proposes how much of the
        $100 he gets. Then either Hotspur accepts it, in
        which case the game ends and Hotspur receives
        the remainder of the $100; or Hotspur rejects it,
        in which case the game continues.
Mortimer and Hotspur
(continued)
   Analysis - McMillan, p. 17. (In what ways is
    this game similar to the example of the two
    barbers above?)
   Suppose we modify the game so that it ends
    after stage 1 (only, if Hotspur rejects the
    offer the game ends with neither player
    receiving anything). What happens now?
   The value of a “take it or leave it” offer.
   Credibility issue: that you will indeed walk
    away from any counteroffer.
   Achieving commitment.
Location, Location, …
   “Our cities become uneconomically large and
    business districts within them are too
    concentrated. Methodist and Presbyterian
    churches are too alike; cider is too
    homogeneous.”         -- Harold Hotelling
    (1929)

   … presidential candidates take similar centrist
    positions, television networks target their
    programs at bland middle of the road tastes,
    …
The Location Game
(continued)
   Case 1. Assume the vendors move sequentially (and
    are not allowed to change their decisions).
   Case 2. The locations are chosen independently and
    simultaneously.
   Case 3. Initial locations are chosen at random, and
    then the vendors choose (sequentially) a best
    response to the choice of the other.
   Equilibrium - A combination of choices such that each
    person’s choice is a best response to those of others.
   Introspective and evolutionary approach to
    equilibrium.
Location (concluded)
   Hotelling seems to suggest that there is
    excessive homogeneity, that the state of
    affairs is inefficient. In what sense is this the
    case?

   Remarks on the use of models in economic
    theory.
       Observation of a real world phenomenon (clustering)
       Identifying the logic of the situation(model)
       (Internal) analysis of the model (equilibrium, efficiency)
       Conclusions drawn about the real world
Thoughts … concluded
   Identifying essential features of a
    situation
       Decisions (impersonal environment) and games
        (choices interact)
       Games against nature (hurricane Floyd) (how
        uncertainty matters)
       Simultaneous and sequential move games (how time
        matters)
       Single play and repeated interaction
       Games of pure conflict and games with common
        interests.
       Games where the players have full information versus
        those with limited information.
The Location of Tertiary Activities
   Classic location theory
       Central place theory
            Insight into the urban structure
            Locational patterns of retail and services
            Relationships between markets and consumers
            Relationships between places
Locational Patterns of Cities
   3 elements
       Transport centers:
            Provide break of bulk services
                  Typically aligned along major transport routes
                  Found at junctions of diff/ transport modes
                      Rivers and coastal locations


       Centers of specialized functions:
            Centers dominated by one function
                  Agglomeration of activity, clustering
                  Examples include Pittsburgh and Orlando
       Central places:
            Centers for exchanging goods or services
            Provides retail, wholesale, financial, educational, govt. services
Cities and Trade
   3 types of services/trade
       Settlement forming trade:
            Business conducted totally w/i the city and its hinterland
            Reliance on population and size of center
       Settlement building trade:
            Activities conducted outside the hinterland (national
             level)
            No reliance on population and size of center
       Settlement serving trade:
            Internal business such as the sale of goods and services
             to its residents
            Reliance on population and size of center
Service Areas
   Cities service areas larger than themselves
       Hinterlands:
       Tributary areas:
            source of materials and labor supply
       Market areas:
            area surrounding central places that includes potential
             customers for whom price and transport cost can be justified
       Urban fields
            source of materials and labor supply
   Areas of dominant influence
   Nodal regions
Reilly’s Law of Retail Gravitation
   Used to estimate trade areas among
    competing centers
   Weaknesses:
       Cultural and economic differences of people are
        ignored
       Ease/accessibility of transport network ignored
       Multi-purpose trips are ignored
       Specific services may have a threshold related to
        distance
   Useful in examining underlying processes and
    large populations
Probability Model
   David Huff
       Uses some functions of the gravity model
       Assumes there are multiple centers
       Assigns a probability or weight to each center
       Creates a probability surface (similar to contours)
Central Place Theory
   4 questions:
       How many central places will develop?
       Why are some central places larger than others?
       Where will the central places develop?
       What will the size of the market area be?
Basic Theory Assumptions
   Isotropic surface (uniform costs)
   Uniform distribution of demand and population
   No transport barriers
   Dependent on trade with hinterland
   Producers and consumers are optimized
   No social class or govt. intervention/regulation
   Ubiquitous production inputs @ same price
   No shopping externalities
   Linear market with evenly spaced consumers
Additional Concepts
   Threshold of a good
       minimum level of demand that will allow a
        business to operate
   Range of a good
       max distance that people are willing to travel for a
        good
   Different goods have different ranges and
    thresholds
       Low order goods: frequently purchased
       High order goods: infrequently purchased
       Also applies to places: low order vs. high order
         Walter Christaller’s Central Place
   German geographic, 1930’s
   Theory basics:
       Primary function is providing goods and services for a
        surrounding market
       Greater numbers of good and services provided
        equates to a higher order of place
       Low order places offer convenience goods w/i a small
        market area
       High order places are few in number, providing goods
        with a greater range
       There is a hierarchy of central places that makes the
        arrangement of these goods efficient
Christaller
   3 major principles found in the most efficient
    systems of central places
       Marketing principle: equal access, central places
        located at midpoints
       Transportation principle: maximizing connectivity
        while minimizing network length
       Administration principle: primary market has
        several dependent markets
    Relationships Between Central Places
   The larger the central place, the greater the
    distance to an equivalent center
   The larger the central place, the more variety
    of services
   Central places similar in size offer a similar
    set of services
   Higher levels of central places, less of them
Central Place Theory

•Central Place Theory (CPT) is an attempt to explain the
spatial arrangement, size, and number of urban centers.
“The best analogy is to a planetary system in which the
units are held in in place by the gravitational forces
between them. Thus central place theory purports to show
that each particular urban settlement is, so to speak, held in
place within a system of cities, it suggests that the
development of each is affected in a predictable way by its
position within the system." (James Heilbrun 1989).
Central Place Theory

•Central place theory is an economic theory which
explains patterns of urbanization and establishment of
market areas for different goods and services.

• "Central place theory offers insight into why specific
goods and services are or are not present in a
particular community.It specifically recognizes that
no community's trade sector can be viewed in
isolation."
(Shaffer, Community Economics, page 125)
Central Place Theory


 •Christaller noticed that towns of a certain size were
 roughly equidistant; By examining and defining the
 functions of the settlement structure and the size of
 the hinterland, he found it possible to model the
 pattern of settlement locations using geometric shapes
 (usually triangles and hexagons).
 .
Central Place Theory

 •Christaller examined the factors which caused
 variation or deviation from this and other settlement
 hierarchy models.


 •Some of the data necessary to simulate CPT were the
 distance from various sizes of settlements, and the
 locations and functionality of built up areas.
Assumptions of CPT

 Isotropic plain – uniform terrain;Uniform distribution
  of population and income
 Equal ease of transportation
 A central place is an urban center that evolves because
  it provides a set of functions for the surrounding
  region. The urban center depends completely on trade
  with its hinterlands.
 Producers and consumers are optimizers (minimize
  distance, maximize profit).
 Assumptions of CPT

 Central places compete with each other for customers.
 There must be enough people wishing to buy a
  service or a good (minimum demand)
 People are willing to travel a certain distance to
  satisfy their needs (at a certain price of the product)
 People within a range must not have competitive
  stores to go into.
What can you do with CPT

 Central Place Theory focuses on four questions:
       How may central places will develop?
       Why are some places larger than others?
       Where will cities locate?
       What will be the size of each city’s trade area?
Range and Threshold

•In order to determine level of a central place, you must rank
all goods and services according to their thresholds

• Threshold (inner range) – minimum level of demand needed
that will allow a firm to stay in business (minimum level of
sales, minimum population)

•Central places of a given level provide not only goods and
services that are specific to its level, but also all other goods
and services that lower order centers provide
Range and Threshold

•Range – (outer range) average maximum distance
people are willing to travel to purchase a good.

•Threshold and range vary for each good and service.

•Just as we have different levels of goods, we have
different levels of centers

• The level of a center is determined by the highest
order good that it offers
     Range and Threshold
•Differences in thresholds and ranges of different
products result in a hierarchy of central places
• Each level of the hierarchy is characterized by a
specific mix of goods
•Thus, The central place hierarchy is a system of
nested centers and market areas
• Lower order centers and their market areas nest
under market areas of higher order centers
•Each level of the hierarchy is characterized by equal
distances between centers of the same order
         Range and Threshold

•High-order goods are available only at a few
locations
   They are expensive and purchased infrequently
   They have a high threshold and wide ranges


•Low order goods provided by a large number of
locations
   They are relatively cheap and purchased frequently
Range and Threshold

              •Normally, the threshold is
              found within the range, as the
              diagram shows. Can you
              think of examples from the
              past in Europe and from the
              United States today in
              which the range is larger
              than the threshold yet
              businesses thrive and
              market towns temporarily
              come alive?
 Range and Threshold

•Itinerant merchants in medieval Europe who would sell
their wares in a different town each day or two to
"collect" sufficient threshold (market) to keep their
business going
•in the US multi-million dollar businesses have
insufficent thresholds because the range for their products
are too small; hence, professional althelitc teams and
popular entertainers travel throughout the country, and
catalog companies completely "annihilate" space.
(Source: I. Vogeler, 1996)
Range and Threshold

•What happens if range is less than threshold?

     - Producer will not be able to stay in business
     - Periodic markets in developing countries (arts
  festivals, swap meets) is the context where range is
  less than threshold
Details of Central Place Theory

   •Christaller noted three different arrangements of
   central places:

   1.The marketing principle (K=3 system);
   2.The transportation principle (K=4 system);
   3.The administrative principle (K=7 system).

•Christaller found that the number of settlements at any
level in either of these hierarchies is directly related to
which hierarchy it is.
K=3




•To cover the whole service area and not leave an area
unserved, the range circles must overlap. But
consumers can only shop in one place in this theory!
What is the spatial solution?
•Answer: hexagons (six-sided shapes) that
completely cover an area without overlap or unserved
areas.
         K=3
•   Provides for the largest provision of goods and services
    from the minimum number of central places
•   Each higher order CP is surrounded by six places of the
    next lowest order
    Market area of the higher order center is 3 times as large
    as that of the smaller center
•   In the K=3 network smaller centers are not accessible to
    the highway network connecting higher order centers
K=3 System
K=4 System




       Transportation Line
K = 7 System
K=3
• Christaller noted that this type of hierarchy
  prevailed where it was most important for
  society to ensure equal provision of goods
  and services. Examining the pattern using
  hexagons Christaller found that central
  places emerge at the center of a hexagon,
  containing six lower-order settlements.
 K=4
                      The market principle predicts evenly
                      spaced cities; but the transportation
                      and political principles modify
                      these regularities. With the
                      transportation principle, towns not
                      on major transportantion routes are
                      smaller than expected from the
                      market principle.
Tranportation routes, such as a railroad in this
illustration, attract business and allow more and larger
towns to develop along the railroad. Rivers, canals,
and highways also reflect the transportation principle.
 K=4

Lower order centers are located at midpoint of each side of the
hexagonal trade area rather than the corners (as in K=3)
By shifting lower order centers to a point midway between each
higher order center, highway network provides better
accessibility
As many places as possible lie on direct traffic routes between
more important centers
 K=4

•Central places are lined up on straight traffic routes that radiate out from a
central point
• Each lower order center is ¼ the size of the higher order center
• Each central place dominates 1 full market area and ½ of the six
surrounding market areas
•Traffic center requires more centers at each level in order to provide goods
and services
•Though it provides a more efficient transportation system for moving goods
cheaply, consumers must travel greater distances to reach a center (at a
given level of the hierarchy)
K=7
                   Political principle. Political
                   boundaries also "distort" the even
                   spacing of cities.
                   Why is the city on the Nevada side
                   of the Nevada-Utah border larger?

Answer: the city on the Nevada-Utah border is larger
because all of the gambling business from Utah can only
be met in Nevada and gamblers want to drive the shortest
distance to gamble, which in Nevada is the border city,
not the interior city
K=7

Central place network depends on political boundaries
Centers that are shared pose problems
Any pattern of control that cuts through functional units is
problematic
K=7 seeks an arrangement where lower order centers are
entirely within a higher order center
Results in a more economically and politically stable
arrangement of settlements
Each center controls six dependent centers
Hinterlands are larger than in K=3 or K=4 systems
Applications of CPT

The cities need the ‘export dollars' provided by people in
small towns, and the small towns need the specialized
services provided by the cities. A strategy which helps
both of them develop--in which state level development
resources are shared can be analyzed thro CPT.
Applications of CPT


CPT does a good job of describing the location of trade
and service activity. It also does a good job of describing
consumer market oriented manufacturing. Small-town
community economic developers can secure quite
specific, relevant information about what kind of trade or
service enterprise will likely work, and what kind of
enterprise will not likely work in a given small
community.
    August Losch
   Refined central place theory
   Lowest order places upward (reverse of
    Christaller)
   Assumptions
       Isotropic, homogeneous plain
       Dispersed pattern of activity
       Equal demand among activities
       Economic raw materials equally distributed
   How can economic differences develop?
Losch
   Surplus in production of consumer goods
   Transport costs limit the potential market
   Consumption declines with increases in price
Central Place Applications

   The indifference curve: the application of
    distance and town size in consumer behavior
   The DeTemple Model: diffusion of innovations
       Attempts to demonstrate the diffusion of and idea
        or behavior geographically
       Diffusion based on size of town & distance to
        central places
       Creates a probability surface to predict the
        diffusion
   Wyckoff Model: the integration of urban
    places into the national urban system
Spatial Competition
   Classic central place theory does not
    acknowledge the idea of competing centers
       Assumption that consumers traveled to nearest
        center
   Consumers are indifferent to minute changes
    in price or quality
   Large changes will however cause a reaction
   Idea of overlapping and competing markets
Spatial Competition
   Nicos Devletoglou: realistic model using
    distance and overlapping areas
       Concept illustrated:
     Retail Location

   Central place theory can be applied to retail
    location in metro areas
       Remember the central place hierarchy, this applies
        to retail as well
   Structure is more complicated
       No longer an isotropic plain
            Population varies
            Density varies
            Income structure
Retail Location
          Populations in urban areas are more sensitive to
           accessibility constraints
                Results in the clustering of people, activities
                Ever notice fast food restaurants cluster
                Enhances competition
     Urban retail market is highly variable
          Changing structure of the CBD
                At one time, served at the commercial/industrial center
                Most accessible place, clustering of activities around the
                 CBD
                The location of retail centers away from the CBD would not
                 be as accessible
          Innovations in transportation/highway systems
                Population disperses throughout the urban area, more
                 suburban locations
                    Requires retail services

                    Establishment of retail centers competitive w/ the CBD
    Classification of Tertiary Activities
    Ribbon development:
        oriented to highway traffic
        Fast food stops, convenience stops
        Major arteries
    Specialized functional areas
        Industrial parks
        Auto rows
        Medical centers
        Comparative shopping, specialized services
    Hierarchy of business centers
        Regional centers, community centers, neighborhood centers
Summary of major concepts
   Central place theory
       What is it? (slide 1)
   3 major location patterns
       What are they? (slide 2)
   3 types of services/trade
       What are they? (slide 3)
   4 types of service areas (slide 4)
   Reilly’s law of retail graviation (slide 5)
       What is it?
       What are its weaknesses
   Basic assumptions of central place theory (slide 8)
   Threshold and Range of a good, low vs. high order
    goods (slide 9)
   Basics of Christaller’s central place theory (slide 10)
   3 principles of theory (slide 11)
   Applications of central place theory (slide 15)
   Spatial competition (slide 16)
   Retail location (slide 18, 19)
   Classification of Tertiary Activities (slide 20)
Transportation and Urban
Form
             Infrastructures

    Modes                      Users

            Transportation

                  imprint
                  Spatial


                                 Urban Form
Nodes, Linkages and Urban
Form
   Road / transit linkage
   Rail linkage
   Maritime linkage
   Air linkage




   Built area
   Accessibility node
   Economic node
One Hour Commuting
According to Different Urban
Transportation Modes

                      Streetcar line
                      Freeway




                     Walking
   10 km             Streetcar
                     Cycling
                     Automobile
                     Automobile with
                     freeways
Average Journey to Work
Travel Time, 1990
          40
          35
          30
          25
Minutes




          20
          15
          10
          5
          0
               United   Western   Japan   Other Asia   Australia
               States   Europe
       Evolution of the Spatial
       Structure of a City




A                        B                           C
    Core activities          Peripheral activities       Major transport axis
    Central activities       Central area
Evolution of Transportation
and Urban Form in North
American and European Cities
                                North America



      I
           II   III        IV
                                         I - Walking-horsecar era (1800-1890)
                                         II - Streetcar era (1890-1920)
                                         III - Automobile era (1920-1945)
                                         IV - Highway era (1945-)

                                          Streetcar line
                      IV                  Highway
           II
      I

                                Europe
     III
Evolution of Transportation
and Urban Form in European
Cities




     Built up area prior to introduction of mechanical transport
     Development consequent on steam railways
     Development consequent on tramways
     Development consequent on motor buses
     Development consequent on private car
          Evolution of Urban Densities in
          North America and Europe
               North America                                      Europe

                                        r(NA)                                         r(E)




                                                    Density
Density




                                   IV
                             III
           I      II                                          I       II        III          IV


                   Distance                                            Distance
                       I - Prior to mechanized transport
                       II - Early forms of mechanized transport (tramways)
                       III - Diffusion of motor vehicles (buses, automobiles)
                       IV - Suburbanization
                           Density and Car Use in North
                           American Cities, 1991
                           40
Urban density (pers./ha)




                           35      Montreal


                           30

                           25        Toronto                                 Los Angeles

                           20
                                               New York
                           15                             Chicago
                                    2
                                   R = 0.694
                           10
                                                                       Phoenix
                                                                                   Houston
                           5
                           5,000          7,000       9,000      11,000    13,000          15,000
                                                   Car use per capita (km)
Rings of Mobility
               C

               B    Pedestrian
                    Road and parking
     Density
               A    Cycling

                    Transit

                    Terminal
Transportation and Urban
Form
             Infrastructures

    Modes                      Users

            Transportation

                  imprint
                  Spatial


                                 Urban Form
Nodes, Linkages and Urban
Form
   Road / transit linkage
   Rail linkage
   Maritime linkage
   Air linkage




   Built area
   Accessibility node
   Economic node
One Hour Commuting
According to Different Urban
Transportation Modes

                      Streetcar line
                      Freeway




                     Walking
   10 km             Streetcar
                     Cycling
                     Automobile
                     Automobile with
                     freeways
Average Journey to Work
Travel Time, 1990
          40
          35
          30
          25
Minutes




          20
          15
          10
          5
          0
               United   Western   Japan   Other Asia   Australia
               States   Europe
       Evolution of the Spatial
       Structure of a City




A                        B                           C
    Core activities          Peripheral activities       Major transport axis
    Central activities       Central area
Evolution of Transportation
and Urban Form in North
American and European Cities
                                North America



      I
           II   III        IV
                                         I - Walking-horsecar era (1800-1890)
                                         II - Streetcar era (1890-1920)
                                         III - Automobile era (1920-1945)
                                         IV - Highway era (1945-)

                                          Streetcar line
                      IV                  Highway
           II
      I

                                Europe
     III
Evolution of Transportation
and Urban Form in European
Cities




     Built up area prior to introduction of mechanical transport
     Development consequent on steam railways
     Development consequent on tramways
     Development consequent on motor buses
     Development consequent on private car
          Evolution of Urban Densities in
          North America and Europe
               North America                                      Europe

                                        r(NA)                                         r(E)




                                                    Density
Density




                                   IV
                             III
           I      II                                          I       II        III          IV


                   Distance                                            Distance
                       I - Prior to mechanized transport
                       II - Early forms of mechanized transport (tramways)
                       III - Diffusion of motor vehicles (buses, automobiles)
                       IV - Suburbanization
                           Density and Car Use in North
                           American Cities, 1991
                           40
Urban density (pers./ha)




                           35      Montreal


                           30

                           25        Toronto                                 Los Angeles

                           20
                                               New York
                           15                             Chicago
                                    2
                                   R = 0.694
                           10
                                                                       Phoenix
                                                                                   Houston
                           5
                           5,000          7,000       9,000      11,000    13,000          15,000
                                                   Car use per capita (km)
Rings of Mobility
               C

               B    Pedestrian
                    Road and parking
     Density
               A    Cycling

                    Transit

                    Terminal
Performance by Urban
Transport Mode
                                                 Performance Index
                           0   2        4        6       8         10        12          14         16

1/3 full ligh rail/metro

  Full light rail/metro

           1/3 full bus

              Full bus

   Car with 1 person

  Fully occupied car
                                                             Space required per person (in sqr m)
                Cyclist
                                                             Speed (km/hr)
           Pedestrian                                        Performance index

                           0       10       20          30              40          50              60
  The Rationale of a Ring Road
Avoiding the congested
central area




                         City
                         Center
                                  Secondary
                                  Center



                                  Structuring suburban
                                  development
Type I - Completely Motorized
Network




   Road   Highway   Activity center
Type II - Weak Center




     Road
     Highway
     Transit line
  Activity center
Type III - Strong Center




   Road   Highway   Transit line   Activity center
Type IV - Traffic Limitation




     Road
     Highway
     Transit line
  Activity center
Suburban Development along
an Highway Interchange
                   Retail
                   Office
                   Industrial
                   Residential
                   Highway
                   Railway




            Core
Formal and Functional Land
Use
 Formal Land Use   Road
                   Parking
                              Functional Land Use   Road
                                                    Parking
                   Building                         Residential
                   Other                            Commercial
                                                    Institutional
                                                    Industrial
                                                    Other
Relationships between Land
Uses
Land Use                     Relationships

                                        A               G
         C
                               B                C
             B
                 A
             G           D
     F
                     E
                               F                E


                                   Passengers
                                                    D
                                   Freight

				
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