Consumer's optimal policies for purchasing durable goods

With a new durable good appearing, the price of old model tends to decrease and the performance of the new one tends to be improved. Thus, a consumer who has purchasing desire could make decision of buying a new one or the old one. The purchasing problem is presented as a Discrete Time Markov Decision Process (DTMDP) model with consumer reserve prices to different durable generations as the states, and the objective is to maximise consumer's purchasing value. Then, a modified MDP model and several assumptions are given. With a new concept of perceived coefficient introduced, purchasing value reward in a stage could be described by durables' physical and perceiveds values. It is shown that the optimal purchasing points exist in a special case with two generations attracting the consumer in one stage and optimal purchasing decisions vary with the consumers' preference, which are shown with a numerical example.