  A bipartite producer-consumer network is constructed to describe the
industrial structure. The edges from consumer to producer represent the choices
of the consumer for the final products and the degree of producer can represent
its market share. So the size distribution of firms can be characterized by
producer's degree distribution. The probability for a producer receiving a new
consumption is determined by its competency described by initial attractiveness
and the self-reinforcing mechanism in the competition described by preferential
attachment. The cases with constant total consumption and with growing market
are studied. The following results are obtained: 1, Without market growth and a
uniform initial attractiveness $a$, the final distribution of firm sizes is
Gamma distribution for $a>1$ and is exponential for $a=1$. If $a<1$, the
distribution is power in small size and exponential in upper tail; 2, For a
growing market, the size distribution of firms obeys the power law. The
exponent is affected by the market growth and the initial attractiveness of the
firms.
