Abstract:

The problem of optimal control of product innovation (improving product quality) and process innovation (reducing marginal production costs) of a monopoly company producing a single product in a continuous time is discussed, and a dynamic control model under network externality conditions is established to discuss the stable equilibrium of the system and investment strategy issues related. The result shows that there exists a unique saddle equilibrium. When the sign of the change rate of investment in product innovation and process innovation is the same (opposite), the two investments are complementary (alternative). When the fixed intensity of network externality decreases, the steady-state product innovation and process innovation investment of the company increases as the product quality improves, and as the marginal production cost of the product decreases; when product quality and marginal production cost change around the steady state, the product innovation and process innovation investment are complementary. In addition, the investment in both product innovation and process innovation under the condition of maximizing social welfare is higher than the corresponding investment under the condition of maximizing the profits of the company. Although the product price under the condition of maximizing social welfare is determined by the company, the product price under this condition is still higher than that under the condition of maximizing the profit of the company.

Key words: product innovation, process innovation, network externaliy

摘要：

讨论了一个生产单一产品的垄断企业在连续时间内进行产品创新(提高产品质量)与过程创新(降低边际生产成本)的最优控制问题，并建立了网络外部性条件下的动态控制模型，探讨系统的稳定均衡以及相关的投资策略问题。研究结论表明：系统存在唯一的鞍点均衡。当产品创新和过程创新投资变化率的符号相同(相反)时，两种投资具有互补性(替代性)。当网络外部性的固定强度减小时，企业的稳态产品创新与过程创新投资随着产品质量提升而增加，随着产品边际生产成本的降低而增加，且产品质量和边际生产成本在稳态状态附近变动时，产品创新和过程创新投资具有互补性。此外，社会福利最大化条件下的企业产品创新和过程创新投资均高于企业利润最大化条件下的相应投资；尽管社会福利最大化条件下的产品价格由企业决定，该情形下的产品价格依然高于企业利润最大化条件下的产品价格。

关键词: 产品创新, 过程创机关报, 网络外部性