We study the problem of revenue management in a cognitive spectrum underlay network, where the primary user chooses the bandwidth and tolerable interference levels for the secondary users. We show that the interference received by each secondary user is the same in a large system regime, and a simple pricing scheme achieves the efficient resource allocation at the market clearing equilibrium. We further show that the key for the primary user to maximize revenue is to consider the secondary users' power-interference elasticity, which is a new concept proposed and is different from all elasticity concepts used in the previous networking literature. When this elasticity is negative (positive, respectively), the primary user should increase (decrease, respectively) the bandwidth and tolerable interference level to increase revenue.
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