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.