A dynamic advertising problem when demand is sensitive to the credit period and stock of advertising goodwill

The article formulates a joint dynamic trade credit and advertising problem in which the demand rate varies simultaneously with the length of the credit period offered to the customers and the stock of advertising goodwill depending on the retailer’s current and past advertising efforts. The proposed problem is analysed in the multi-period setting over an infinite horizon in which demand at each period depends on the current and past advertising efforts through the goodwill dynamics. We first show that the retailer would adopt a static credit period strategy, and then demonstrate that the optimal path of the advertising effort is unique and converges monotonically to its corresponding equilibrium over the long run in the opposite direction as the stock of advertising goodwill. Moreover, a set of structural properties is developed to characterise the impacts of model parameters over the optimal decisions. Finally, we offer concluding remarks and suggestions for future studies.