Mobile Edge Computing (MEC) is relatively a novel concept in the parlance of Computational Offloading. MEC signifies the offloading of intensive computational tasks to the cloud which is generally positioned at the edge of a mobile network. Being in an embryonic stage of development, not much research has yet been done in this field despite its potential promises. However, with time the advantages are gaining growing attention and MEC is gradually taking over some of the resource-intensive functionalities of a traditional centralized cloud-based system. Another new idea called Task Caching is emerging rapidly with the offloading policy. This joint optimization idea of task offloading and caching is relatively a very new concept. It has been in use for reducing energy consumption and delay time for mobile edge computing. Due to the encouraging offshoots from some of the current research on the joint optimization problem, this research initiative aims to take the progress forward. The work improves upon the “prioritization of the tasks” by adopting a very practical approach discussed forward, and proposes a different way for task offloading and caching to the edge of the cloud, thereby bringing a significant enhancement to the QoS of MEC. We propose a novel priority-based offloading and caching model considering the joint optimization of offloading and caching along with the local computing policy. The simulation results show that our proposed model is able to reduce more delay time and energy cost of MEC than any other model proposed earlier.