The live video streaming services have been suffered from the limited backhaul capacity of the cellular core network and occasional congestions due to the cloud-based architecture. Mobile Edge Computing (MEC) brings the services from the centralized cloud to nearby network edge to improve the Quality of Experience (QoE) of cloud services, such as live video streaming services. Nevertheless, the resource at edge devices is still limited and should be allocated economically efficiently. In this paper, we propose Edge Combinatorial Clock Auction (ECCA) and Combinatorial Clock Auction in Stream (CCAS), two auction frameworks to improve the QoE of live video streaming services in the Edge-enabled cellular system. The edge system is the auctioneer who decides the backhaul capacity and caching space allocation and streamers are the bidders who request for the backhaul capacity and caching space to improve the video quality their audiences can watch. There are two key subproblems: the caching space value evaluations and allocations. We show that both problems can be solved by the proposed dynamic programming algorithms. The truth-telling property is guaranteed in both ECCA and CCAS. The simulation results show that the overall system utility can be significantly improved through the proposed system.