溢出效应与集群企业创新时间的选择

为考察溢出效应对产业集群企业创新时间的影响，将溢出效应系数引入创新时间和投入之间的线性函数以及创新成功时间的概率函数中，建立了集群企业创新期望净收益函数．将该收益函数对创新时间和溢出效应系数变量求出二阶偏导数以建立最优创新时间和溢出效应系数之间的一阶导数关系．对一阶导数符号的分析显示，当竞争企业数量较大时，无论创新类型、资金成本、研发风险参数如何变化，最优创新时间都随技术溢出效应的增强而缩短．

Spillover Effect and Determination of Innovation Time for Industrial Cluster

To understand the effect of technology spillover on innovation time for an industrial cluster, a spillover coefficient was added to the probability function of time for an innovation to succeed and to the linear function describing the correlation between innovation time and investment. An expected net revenue function of innovation by an industrial cluster was proposed. The partial derivatives of second order to the innovation time and spillover effect for the expected net revenue function were obtained to establish the partial derivative of first order for the correlation between the optimal innovation time and spillover coefficient. The symbolic analysis of the first order partial derivative shows that if there are a large number of competitors the optimal innovation time would be shortened with an increase in technology spillover coefficient, regardless the variation in innovation type, capital cost and risk of research and development.