Note—Optimal Long-Run Equilibrium Advertising Level for the Blattberg-Jeuland Model
基于Blattberg-Jeuland广告模型求解动态优化问题，发现均衡最优广告水平随衰减率非单调变化，并分析插入成本和贴现率的影响。
The purpose of this note is to formulate and solve a dynamic optimization problem based on the Blattberg-Jeuland advertising model. Also examined is the behavior of the optimal long-run equilibrium level of advertising with respect to changes in some important parameters of the problem. In particular, a new interesting result, showing that the equilibrium optimal level of advertising for the B-J model is a nonmonotone function of the rate of decay parameter, is derived. That is, the equilibrium optimal level of advertising is an increasing function of the rate of decay for smaller rates of decay and a decreasing function for larger rates of decay than a critical rate of decay. This phenomenon is analogous to a sink effect and is intuitively appealing. It is also shown that the equilibrium optimal level of advertising is a decreasing function of the insertion cost and discount rate parameters. Finally, the framework presented in this note is also useful in analyzing further extensions of the problem solved here.