Abstract

We introduce the knowledge spillover equation on a network. We construct a tool to investigating the knowledge spillover in terms of network. The mean-filed asymptotic solution of the equation has the following characteristics: (1) the growth rate is common for all agents on the network regardless of the degree; (2) the growth rate is dependent on the mean degree of nearest neighbors, whereas it is independent from the mean degree; (3) the TFP is proportional to degree; (4) the more heterogeneous the network is, the greater the growth rate is. Among representative networks: regular, random, and scale-free networks, the growth rate is the greatest in a scale-free network and the least in a regular one. We investigate other types of knowledge spillover equations. Using the knowledge spillover equation, we show that the growth rate is large if the region size is small, the density of firms is high, or network formation cost is low. We show that the knowledge spillover equation can be applied to the problem of network formation mechanism.

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