To calculate the commuting distance at full concentration of employment the maximum
commuting distance, xmax, is determined first. Contrary to Hamilton (1982), who used a limit
of 100 people per square mile, we use the edge of the urban region and so, xmax is the distance
between the city centre and the edge of the urban region. The monocentric model assumes the
city centre to be in the middle of a circle shaped area. This implies that, when determining
the distance of the city centre to the edge of the urban centre, use can be made of the total
surface area of the urban region being the sum of the areas of the different municipalities
within the urban region (CBS-view 1989).
The potential population density function
The potential population density function shows the relationship between the distance to the
city centre and the place of residence of the potential labour force. Again, in contrast to
Hamilton (1982), who starts from the entire population, we use the potential labour force:
the population between 15 and 65 years of age. This part of the total population covers the
commuters best. Considering the entire population would include also children and old-age
pensioners who do not commute. Starting from the presupposition of full employment the
potential labour force equals the potential number of commuters. Hamilton used Mill's (1972)
‘population density gradient’, which showed that, the connection between distance and
population and between distance and employment, are negative exponential functions. This
corresponds to a long tradition of similar findings (see Brueckner 1987; McDonald 1989).
The present analysis, too, starts from the assumption that the function for the density of the
potential labour force is a negative exponential. By using data on the potential labour force of
the municipalities within the four urban regions and the distances of these municipalities to
the centre, the density function of the potential labour force is formulated:
B(x) = C x-τ
(1)
in which:
B(x) = the potential labour force living at a distance x to the city centre; the
density function for the potential labour force
C = the constant
x = distance to the centre of the urban region
τ = the distance gradient
The average commuting distance
Given the residential location and full concentration of employment in the city centre, the
average commuting distance is similar to the average distance of places of residence to the
city centre. The equation enabling us to calculate this average distance is: