)1P)
!x
!"# xx=maoxx B(x)dxdy
(2)
in which:
A = average commuting distance, given full concentration of employment
x = the distance to the centre of the urban region
B(x) = the density function for the potential labour force
P = the potential labour force in the area
dxdy = area within circle at distance x
The potential labour force in the area (P) is:
! x =
P = !"# xx==0max B (x) dxdy (3)
Substituting (1) in (2) results in:
2 - τ
))))
x
max
(4)
3 - τ
The integral comprises the entire area between 0 and xmax on the horizontal axis, the
integration limits and the function B(x). The average optimum commuting distance can be
determined with the help of this function and the distance between the city centre and the
edge of the urban region. However, there is no potential labour force living at a distance less
than one kilometer from the city centre. This area is the location of employment. So the
area between 1 kilometer from the centre (x=1) and xmax is calculated.
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