互补产品供应链的授权与竞争

Authorization and competition in a supply chain with complementary products

产品专利授权是企业寻求合作、互利双赢的一种方式。拥有互补产品的企业进行产品专利授权,会对互补产品销售和参与授权的双方企业收益产生重要影响。本文考虑一条由两家企业组成的供应链,其中一家生产并销售两种互补产品,并将其中一种产品授权给另一家企业进行竞争性生产和销售,研究该授权行为对于参与授权双方的决策与收益、消费者剩余和社会福利的影响。本文进一步利用Stackelberg博弈求解出授权前后两家公司的最优决策、利润、产品需求,以及消费者剩余和社会福利,并对授权前后的结果进行对比。结果表明,授权行为会导致被授权产品定价提高、销量增加,但其互补产品的定价和销量会下降。当专利许可费适中时,授权行为能最大程度提升授权企业的总利润。数值实验结果表明,授权行为能够提升消费者剩余,且在大多数情形下都会提高社会福利,只有当专利许可费较高时会降低社会福利。

Complementary products are a pair of goods in which the consumption of one good must be accompanied by that of the other good,such as cars and petrol,toothbrushes and toothpaste,etc.In recent years,companies keep seeking and practicing more effective complementary product sales strategies to cope with the increasingly complex market environment and fierce business competition.For example,bundling and cross-subsidization have already been widely used to sell complementary products.Furthermore,as a novel form of cooperation,product patent authorization is also gradually being applied by several companies in the sales activities of complementary products.The product patent authorization means a company authorizes its patent for a product to another company for production and sales activities,which can expand product sales,improve profit,and get a win-win situation for the two companies.However,the authorization itself introduces the competition for the sales of the authorized products between the two companies.The interaction of authorization and competition in the supply chain with complementary products makes the pricing decisions of the two companies complicated.This paper looks at a supply chain consisting of one authorizing company(Company A)and one authorized company(Company B).Company A produces and sells two complementary products,namely M and NM.By authorization,Company A licenses the patent of the product NM to Company B,who can therefore produce and sell the same product in the same market.In return,Company B should pay the license fee to Company A.Meanwhile,Company A is still engaged in producing and selling of the authorized product,which forms a competitive relationship with Company B in the product′s market.By solving for the optimal pricing decisions of the two companies before and after the authorization,we intend to investigate the impact of authorization for a complementary product on the optimal decisions and profits of the companies,as well as consumer surplus and social welfare.Specifically,we use a Stackelberg game to model the decision process of the two companies after the authorization,where Company A is the leader,and Company B is the follower.Based on the analysis,the optimal prices,profits,product demands,consumer surplus,and social welfare are derived,and the following conclusions are drawn:Before the authorization,the demand for the two complementary products is only related to the corresponding potential market capacity;After the authorization,with other factors fixed,when the patent license fee increases,the price of product M decreases,and the price of the authorized product NM increases.Furthermore,as the patent license fee increases,the optimal profit of Company A increases first and then decreases,while that of Company B decreases first and then increases.Subsequently,using numerical analysis,we examine the effects of authorization on optimal decisions,profits,consumer surplus,and social welfare and further explore the impacts of competitive degree and patent license fee on these effects.It is found that for the authorizing company(Company A),the authorization behavior increases both the price and demand for the authorized product NM while decreasing both the price and demand for the unauthorized(complementary)product M.When the license fee is moderate,the authorization behavior can maximize the profit of the authorizing company.In addition,the authorization can always increase consumer surplus,and it increases social welfare if the patent license fee is not too high.Based on the findings,this paper provides the following managerial implications.Firstly,patent authorization can increase the sales of the authorized product.Through authorization,the authorizing company can expand the sales of the authorized product.Secondly,setting the patent license fee is crucial for both parties.Managers need to set an appropriate patent license fee to maximize their interests.Thirdly,according to the numerical analysis results,after the authorization,both the price and demand for the authorized product increase,but both the price and demand for the unauthorized(complementary)product decrease.It implies that the authorized product becomes a more significant source of profit for the authorizing company than the unauthorized(complementary)product after the authorization.Therefore,the authorizing company should make a comprehensive trade-off between increased authorized product sales,increased license fee revenue,and decreased unauthorized(complementary)product sales,the key to which is to determine an appropriate patent license fee.