Taxi journeys are usually priced according to the distance covered and time taken for the trip. Such a fixed cost strategy is simple to understand, but does not take into account the likelihood that a taxi can pick up additional passengers at the original passenger's destination. In this paper we investigate dynamic taxi pricing strategies. By using domain knowledge, such strategies discount trips to locations containing many potential passengers, and increase fares to those areas with few potential passengers. Identifying a closed form optimal dynamic pricing strategy is difficult, and by representing the domain as an MDP, we can identify an optimal strategy for specific domains. We empirically compare such dynamic pricing strategies with fixed cost strategies, and suggest future extensions to this work.