Hence, if it is largely the case that services offering large discounts also require fewer employees,
i.e., Φ'a<0, then we can expect to find R’’[d]<0. Even when this fails in general, we will still expect
to see such kind of effect at the tail of the distribution. Note that in the presence of increasing
congestion effects on approach to the CBD, there will be a proportionally smaller time penalty when
the customers travel from more remote locations. The generalized traveling cost will be concave in
this case.
If we continue the reasoning above, we can proceed indefinitely to include additional effects into the
model. Once a new effect is introduced, however, we observe a clear tendency that local anomalies
will be further dispersed in space. The large-scale picture we end up with, is a concave function
asymptotically increasing towards a limit where all services are covered by the local sector. In this
large-scale picture the local effects are wiped out, and on the basis of this we suggest to model the
function through an expression of the form
(2.7)
Rlocal sector [ d] = R≈ (1 - eXP[-βd])
Here R8 denotes the value corresponding to the case where all activity remains in the local sector,
and β is a parameter measuring the speed of which the limiting value is obtained. In what follows the
function in (2.7) will be used to model the local sector part of the employment ratio.
3 Spatial dispersion of the CBD
We will now turn to the modeling of the centripetal forces, which promote concentration of business
activities in the city center. As mentioned in section 2, those forces are due to increasing returns and
external economies of scale. External economies of scale, or agglomeration economies, make stores
to clump together in clusters rather than being more evenly spread-out across an area. Based on such
arguments we assumed the existence of a central city, where goods and services are provided at
lower prices (and larger diversity) than in stores at more peripheral locations in the market. We will,
however, take into account that business activities are space-consuming; the city center is not
restricted to one single point in the geography. The dispersion of an urban area can be given
numerous specifications. For example, a trend that has been observed in many metropolitan areas is
the rise of urban subcenters, or edge cities (see Krugman 1995). We will not deal with this kind of
spatial configurations. Our model formulation is based on a monocentric urban area with a traditional
downtown which represents the highest level of agglomeration economies in the geography. Though
such a city center might be dense, it is in general dispersed over a certain distance. In addition, the
relevant centripetal forces are in general effective also in short distances from the city center. Hence,
the concentration of local sector activities might be high also in short distances from the city center,
though they can be expected to fall off rapidly with small increases in distance from the CBD.
We let D represent the dispersion of the city. This means that the population and the business
activities in the city is distributed within the interval [-D,D] . We let E0 and L0 denote the observed
employment/labor within the city, and we wish to model the ratio E/L[x]=Ragglomeration[x]=Ra[x]
subject to the balancing condition
(3.1)
D
∫ Ra [ x ]1[ x ] dx = Eo
- D
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