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We propose a unified static framework to study the interplay of user association and resource allocation in heterogeneous cellular networks. This framework allows us to compare the performance of three channel allocation strategies: Orthogonal deployment, Co-channel deployment, and Partially Shared deployment. We have formulated joint optimization problems that are non-convex integer programs, are NP-hard, and hence it is difficult to efficiently obtain exact solutions. We have, therefore, developed techniques to obtain upper bounds on the system's performance. We show that these upper bounds are tight by comparing them to feasible solutions. We have used these upper bounds as benchmarks to quantify how well different user association rules and resource allocation schemes perform. Our numerical results indicate that significant gains in throughput are achievable for heterogeneous networks if the right combination of user association and resource allocation is used. Noting the significant impact of the association rule on the performance, we propose a simple association rule that performs much better than all existing user association rules.