Abstract: It is assumed that the demand is a linear function of price and service level.firstly use the optimal control method is used to solve the optimal price function and service level function.Then the effects of the time decay factor on optimal price as well as the characters of demand elasticity are analyzod.Finally,this paper recurs to numerical calculation to research the trajectories of control variables and the state variables along with the effects of parameters of model on objective function.

Key words: dynamic pricing, demand elasticity, service level