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New workplaces are either located in existing vacant
industrial or commercial buildings, in newly constructed industrial or
commercial buildings or in converted residential buildings.
Before starting the location process, industries are sorted by
decreasing floorspace productivity, or rent paying ability, and processed
in that order.
The total demand for new workplaces of industry s in the region is
 (1)
where DEsli(t,t+1)
are net changes in employment of industry s on land use category l in
zone i modelled in previous submodels resulting from sectoral
decline, lack of building space and intraregional relocation of firms as
well as from exogenously specified public programmes.
a) New Jobs in Vacant Buildings
Declining industries or relocating firms leave buildings vacant that may
be used by other industries. For this purpose, the forty industries have
been divided into groups with similar space requirements.
If this demand is less than the total supply of suitable floorspace, it
is allocated to vacant floorspace with the following allocation
function:
 (2)
where Kslj is the capacity of
existing buildings on land-use category l in zone j for
workplaces in industry s.Vslj
is the number of jobs accommodated.
b) New Jobs in New Buildings
For any remaining demand, new industrial or commercial buildings have to
be provided. This demand is allocated to vacant industrial or commercial
land with the allocation function
 (3)
where Cslj are new workplaces in
industry s built on land-use category l in zone j
between t and t+1. Lslj
is the current capacity of land of land-use category l for such
workplaces in zone i; since it is continuously reduced during the
simulation period, it bears no time label.
The utility uslj(t) used in
Equations 2 and 3 is the attractiveness of land-use category l in
zone j for industry s and has three components:
 (4)
where usj'(t) is the
attractiveness of zone j as a location for industry s,
usl(t) is the attractiveness
of land-use category l for industry s, and
us(clj )(t) is
the attractiveness of the land price of land-use category l in zone
j in relation to the expected profit of economic activity s.
The vs, ws, and
1–vs–ws are multiplicative
importance weights adding up to unity. The three component utilities are
constructed similarly to the components of the housing utility
uhki(t) (see
Housing Market Submodel).
Like all utilities in the model, the
uslj(t) remain unchanged during the
simulation period as calculated at time t. The price or rent of
industrial or commercial buildings is not represented in the model.
The land capacity Lslj is normally
taken as being fixed as specified in the zoning plan. If a piece of land
was formerly in a built-up area, its development implies the demolition of
existing buildings. In addition, under certain restrictions in zones of
high demand, the capacity Lslj may be
extended by demolition of existing buildings with less profitable building
uses to represent displacement processes going on within existing
neighbourhoods. As Lslj is updated
after the location of each industry, it bears no time label. All workplaces
or dwellings displaced by demolition during a simulation period are
replaced in the same period by iterating the industrial and residential
submodels several times.
c) Conversion of Existing Dwellings
In the case of service workplaces, the capacity of a zone may also be
extended by conversion of existing dwellings into offices where the demand
for office space is high in relation to supply in order to represent the
displacement of dwellings by offices observed within or near the CBD. All
dwellings converted to offices during a simulation period are replaced in
the same period by iterating the industrial and residential location
submodels several times.
Retail Location
Retailing is treated like any other industry in the model except that
the zonal attractiveness
usj(t) (see Equation 4) for retailing
includes an attribute n
 (5)
where tq2ijm(t) are
shopping trips (g = 2) of households of income group q from
residential zone i to shopping zone j using mode m,
yhi(t) are retail expenses of
households of income group q in zone i at time t,
Ers(t) is retail
employment in zone j at time t,
Er(t) total regional retail employment,
and vn(.) the value function mapping
attribute n to utility. This attribute indicates retail sales per
retail employee in zone j expressed in units of average turnover per
retail employee in the whole region.
Housing Supply
Housing is represented in the model as a distribution of dwellings
classified by (see
Housing Market Submodel:
- type of building (single-family, multi-family)
- tenure (owner-occupied, rented, public)
- quality (very low, low, medium, high)
- size (1, 2, 3, 4, 5+ rooms)
This housing distribution is collapsed to up to thirty more aggregate
housing types for use in the occupancy matrix, which links dwellings
with households (see
Housing Market Submodel).
Changes to the housing stock in the zones occurs in three submodels:
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(1)
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Ageing of residential buildings, i.e. filtering down the quality
scale, is modelled in the
Public Programmes Submodel.
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(2)
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Public housing programmes specified exogenously by the user are
executed in the
Public Programmes Submodel.
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(3)
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Maintenance/Upgrading and new housing construction are modelled in
this submodel.
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a) Maintenance/Upgrading
Landlords are assumed to invest in their housing stock if by doing so
they can expect to raise their profits. The proportion of dwellings
upgraded in each period is calculated for each dwelling type in each zone
as a function of the expected rent increase in that submarket after
improvement. As the eventual rent increase is not known at this point in
time, the landlords employ a simple rent expectation model based on vacancy
rates at the beginning of the simulation period:
 (6)
where Uki(t,t+1) is
the number of dwellings of housing type k in zone i to be
upgraded if a sufficient number of dwellings of the same housing
characteristics (size and building type) but lesser quality exits in the
zone, Dki(t) is the number of
dwellings of this type in the zone and
Vki(t) is the number of vacant dwellings of
this type. The exogenous elasticity curve f(.) controlling landlord
investment behaviour specifies that landlords upgrade their stock if the
number of vacancies is low.
Filtering and maintenance/upgrading work in opposite directions. Their
net effect may result in an overall deterioration or improvement of the
housing quality in a zone.
b) New Housing Construction
The submarkets of the housing construction submodel are the housing
types of the aggregate (30-type) housing classification, or rather a subset
of them, as only good quality housing is assumed to be built.
Before starting the location process, housing types are sorted by
decreasing price or rent per square metre and processed in that order.
The demand for new housing of type k to be built during the
period from t to t+1,
Dkli, is estimated by the model using a similar rent
expectation model as in the maintenance/upgrading submodel:
 (7)
where Ck(t,t+1) is
the number of dwellings of housing type k to be built between times
t and t+1. The difference to Equation 9 is that the
estimated demand is totalled over all zones, as the location of new housing
has yet to be determined.
The housing demand thus estimated is allocated to vacant residential
land by a multinomial logit model:
 (8)
where Ckli(t,t+1)
are new dwellings of type k built on land-use category l in
zone i between t and t+1 and
Lkli is the capacity of that vacant land for
dwellings of type k. Lkli
bears no time label as it is successively reduced during the
simulation period by land uses with similar land requirements. The utility
ukli(t) expresses the
attractiveness of land-use category l in zone i for dwellings
of housing type k:
 (9)
where uki(t) is the
attractiveness of zone i as a location for housing type k,
ukl(t) is the attractiveness
of land use-category l for housing type k, and
u(ckli)(t) is the
attractiveness of the land price of land-use category l in zone
i in relation to the expected rent or price of the dwelling. The
vk,
wk and
1–vk–wk
are multiplicative weights adding up to unity. The component utilities are
constructed similarly to the components of the housing utility
uhki(t) (see
Housing Market Submodel).
Like all utilities used in the model, the
ukli(t) remain unchanged during the
simulation period as calculated at time t.
Dwellings built during a simulation period utilise land immediately, but
become available to the housing market only in the subsequent period.
Price Adjustment
At the end of each simulation period housing prices and rents are
adjusted to reflect changes in the composition of housing stock. Upgraded
and new dwellings are more expensive than existing ones, so dwellings of a
certain housing type become more expensive in zones with much building
activity than in zones with little new housing construction.
Changes of housing prices and rents due to changes in demand are dealt
with in the
Housing Market Submodel,
price increases through inflation in the
Ageing Submodel.
Prices or rents of industrial and
commercial floorspace are not considered in the model.
Zonal land prices by land use category are adjusted as a function of the
demand for land of that land use category in the zone in the period just
completed, i.e. by the proportion of newly developed land of that category
in the zone:
 (10)
where plj(t) is land price
per square metre of land use category l in zone j at time
t, llj(t,t+1) is the amount of
land of category j newly developed in zone l, and
Llj(t) is the amount of
developable land of that land use category in zone j at time
t. The function f(.) is an S-shaped elasticity curve entered
exogenously resulting in a reduction of land prices if no development took
place in the period and a price increase if the rate of development was
high. In built-up inner-city zones with little or no developable land a
similar function of the proportion of redevelopment is used. No attempt is
made to determine equilibrium land prices. The price adjustment model
reflects price adjustment behaviour by land owners. If they decrease or
increase prices too much, this will become apparent and be corrected in the
subsequent simulation period.
© 1998 Michael Wegener, IRPUD
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