Shared Autonomous Electric Vehicles (SAEVs) are expected to enter the transportation market in the upcoming decades. In this paper, we describe the preparation of a MATSim model for Vienna in which we add this new service as a new transportation mode. We simulate different pricing schemes for various SAEV fleet sizes and analyze their impacts. Our focus is on the impacts in regards of socioeconomic heterogeneity. One main finding of our paper is that the number of SAEV trips does not necessarily decrease for higher fares. It is instead the average travel time of SAEV rides which decreases if the service gets more expensive. Our simulation results for higher pricing schemes show that many people switch from bike or walk mode to SAEV. Public transport is also highly cannibalized by this new service regardless of the price, whereas SAEVs would always replace no more than 10% of car trips. SAEVs help reduce travel times significantly. People who do not have a car available in their household experience the greatest savings in travel time. A similar high share of SAEV trips is done by people older than 35 years. In regards of gender, our results reveal that women tend to use SAEVs for shorter trips.