  We propose a simple yet very predictive form, based on a Poisson's equation,
for the functional dependence of the cost from the density of points in the
Euclidean bipartite matching problem. This leads, for quadratic costs, to the
analytic prediction of the large $N$ limit of the average cost in dimension
$d=1,2$ and of the subleading correction in higher dimension. A non-trivial
scaling exponent, $\gamma_d=\frac{d-2}{d}$, which differs from the
monopartite's one, is found for the subleading correction. We argue that the
same scaling holds true for a generic cost exponent in dimension $d>2$.
