Networks of firms and the ridge in the production space

Abstract

We develop complex networks that represent activities in the economy. The network in this study is constructed from firms and the relationships between firms, i.e., shareholding, interlocking directors, transactions, and joint applications for patents. Thus, the network is regarded as a multigraph, and it is also regarded as a weighted network. By calculating various network indices, we clarify the characteristics of the network. We also consider the dynamics of firms in the production space that are characterized by capital stock, employment, and profit. Each firm moves within this space to maximize their profit by using controlling of capital stock and employment.We show that the dynamics of rational firms can be described using a ridge equation.We analytically solve this equation by assuming the extensive Cobb-Douglas production function, and thereby obtain a solution. By comparing the distribution of firms and this solution, we find that almost all of the 1,100 firms listed on the first section of the Tokyo stock exchange and belonging to the manufacturing sector are managed efficiently.