Abstract: To explore the optimal control of product quality improvement and process innovation in a monopoly enterprise, considering the influence of reference quality and reference price on consumer demand, a dynamic control model under the double reference effects is established, and the steady-state equilibrium and investment strategy is analyzed. The results show that under the condition of enterprise profit maximization, there exist admissible parameter constellations such that the system is a saddle point equilibrium. The steady-state investment of the enterprise is affected by product quality, marginal production cost, reference quality, and reference price. With the increase of the reference quality, the instantaneous investment rate of the enterprise in quality improvement increases while that in process innovation decreases. The two instantaneous investment rates decrease with the increase of the reference price, and the portfolio with the same symbol is complementary. The enterprise enhances consumer demand and enterprise competitiveness through the choice of quality and innovation investment strategy.

Key words: quality improvement, process innovation, reference quality, reference price, dynamic control

摘要： 为探讨垄断企业产品质量改进与过程创新的最优控制问题，考虑参考质量和参考价格对消费者需求的影响，建立了双参考效应下的动态控制模型，分析系统稳态均衡及投资策略并进行数值模拟。研究结果表明：企业利润最大化条件下，存在可行的参数取值使系统为鞍点均衡，企业稳态投资受到产品质量、边际生产成本、参考质量及参考价格的影响。随着参考质量的增大，企业对质量改进的瞬时投资率不断增长而对过程创新的瞬时投资率不断下降，两种瞬时投资率随参考价格的增长而下降，且符号相同时投资组合具有互补性。企业通过对质量与创新投资策略的选择提升消费者需求及企业竞争力。

关键词: 质量改进, 过程创新, 参考质量, 参考价格, 动态控制