Abstract: In this paper, a decision model is developed to determine the optimal price and warranty length for a static demand market. The demand function of the model characterizes both the repurchasing process and the initial purchase process. The cost functions consider both the learning effect and free repair warranty policy. And it is assumed that the time between two failures follows Weibull distribution. Two scenarios are provided, which are based on whether the repurchasing process is affected by price. The maximum principle method is used to obtain optimal solutions. The optimal policies for a special case are further investigated and Lingo11 is used to do some numerical tests. In this paper, it is found that price and warranty have to be considered in the same time, the best policy is to set high price and long warranty in the beginning and reduce them along the product life circle. Considering the repurchasing process, manufacture can get more profit and consumer can have better warranty. Finally, the management implication get from the model solutions is discussed.

Key words: warranty, price, repeat purchase, maximum principle, optimal control, learning effect