Mobile-edge computing (MEC) and wireless power transfer are technologies that can assist in the implementation of next generation wireless networks, which will deploy a large number of computational and energy limited devices. In this letter, we consider a point-to-point MEC system, where the device harvests energy from the access point's (AP's) transmitted signal to power the offloading and/or the local computation of a task. By taking into account the non-linearities of energy harvesting, we provide analytical expressions for the probability of successful computation and for the average number of successfully computed bits. Our results show that a hybrid scheme of partial offloading and local computation is not always efficient. In particular, the decision to offload and/or compute locally, depends on the system's parameters such as the distance to the AP and the number of bits that need to be computed.