dorsal/arxiv
View SchemaBipartite Producer-Consumer Networks and the Size Distribution of Firms
| Authors | Wang Dahui, Zhou Li, Di Zengru |
|---|---|
| Categories | |
| ArXiv ID | physics/0507163 |
| URL | https://arxiv.org/abs/physics/0507163 |
| DOI | 10.1016/j.physa.2005.08.006 |
Abstract
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.
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"abstract": "A bipartite producer-consumer network is constructed to describe the\nindustrial structure. The edges from consumer to producer represent the choices\nof the consumer for the final products and the degree of producer can represent\nits market share. So the size distribution of firms can be characterized by\nproducer\u0027s degree distribution. The probability for a producer receiving a new\nconsumption is determined by its competency described by initial attractiveness\nand the self-reinforcing mechanism in the competition described by preferential\nattachment. The cases with constant total consumption and with growing market\nare studied. The following results are obtained: 1, Without market growth and a\nuniform initial attractiveness $a$, the final distribution of firm sizes is\nGamma distribution for $a\u003e1$ and is exponential for $a=1$. If $a\u003c1$, the\ndistribution is power in small size and exponential in upper tail; 2, For a\ngrowing market, the size distribution of firms obeys the power law. The\nexponent is affected by the market growth and the initial attractiveness of the\nfirms.",
"arxiv_id": "physics/0507163",
"authors": [
"Wang Dahui",
"Zhou Li",
"Di Zengru"
],
"categories": [
"physics.soc-ph",
"q-fin.GN"
],
"doi": "10.1016/j.physa.2005.08.006",
"title": "Bipartite Producer-Consumer Networks and the Size Distribution of Firms",
"url": "https://arxiv.org/abs/physics/0507163"
},
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