  We consider a preferential growth model where particles are added one by one
to the system consisting of clusters of particles. A new particle can either
form a new cluster (with probability q) or join an already existing cluster
with a probability proportional to the size thereof. We calculate exactly the
probability P_i(k,t) that the size of the i-th cluster at time t is k. We
applied our model as a background for a microscopic economic model.
