This paper considers a duopoly where switching costs exist. The analysis proves that temporal price reductions can be pure strategy equilibrium where firms earn more profit than in a regular price strategy. Greater profits result from price discrimination in temporal price reductions. The equilibrium is contrasted with previous studies, which explain temporal price reductions as a result of mixed strategy. In a given model with an assumption about forming switching cost, firms can control their range of loyal consumers by properly setting their regular and promotional prices. The model shows that temporal price reduction tends to raise the regular price and decrease the range of loyal consumers.