Dynamic marketing model: optimization of retailer’s role

We study a vertical control distribution channel in which a manufacturer sells a single kind of good to a retailer. The state variables are the cumulative sales and the retailer’s motivation. The manufacturer chooses wholesale price discount while retailer chooses pass-through. We assume that the wholesale price discount increases the retailer’s sale motivation thus improving sales. In contrast to previous settings, we focus on the maximization of retailer’s profit with respect to pass-through. The arising problem is linear with respect to both cumulative sales and the retailer’s motivation, while it is quadratic with respect to wholesale price discount and pass-through. We obtain a complete description of optimal strategies and optimal trajectories. In particular, we demonstrate that the number of switches for change in the type of optimal policy is no more than one.