With the rapid growth of the Internet of Things (IoT), millions of devices have been interconnected within the network. Cloud computing and edge computing are jointly playing a crucial role in processing and analyzing the large number of tasks generated by end devices. Considering the latency and energy consumption, we propose a novel task offloading framework in collaborative edge-cloud computing. This framework first introduces tiered pricing for task offloading services inspired by electricity pricing. The tiered pricing strategies are transformed into continuous functions using the convex approximation method for the Sign Function. Then, we propose a task offloading strategy to optimize the utilities for both end devices and edge nodes. End devices offload tasks to edge nodes to minimize their task processing costs. After receiving the tasks, each edge node determines whether to offload them to the cloud center and in what proportion, aiming to maximize the profit. To facilitate efficient task offloading, we introduce a one-to-many matching algorithm to establish stable matches between end devices and edge nodes. Simulation results demonstrate that the utilities of end devices and edge nodes can converge within a certain number of iterations. We then analyze the impact of pricing on the strategies of edge nodes and end devices. We also compare the proposed algorithm with other algorithms, revealing that our algorithm achieves stable matching as well as effective load balancing of edge nodes.