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Abstract-We consider a network setting, where a single Service Provider (SP) provides wireless data services to a group of users in the downlink. The transmission model is similar to OFDMA and thus the SP allocates spectrum to the users. The SP transmits at specific power spectral density. A user applications are characterized by its received rate which is a function of the allocated spectrum, its link gain to the SP and the transmit power spectral density. The SP obtains the net spectrum requested by all the users from a central clearinghouse. The SP charges the users a two part tariff consisting of a fixed subscription fee and variable usage cost and pays the clearinghouse a spectrum cost. The SP also incurs a cost proportional to the power it transmits to all the users. We model this allocation scheme and characterize the trade-off between transmit power spectral density and net spectrum purchased by the SP as a function of the spectrum and power costs for different classes of concave user utilities. I. INTRODUCTIONTraditional wireless networks, such as 2G cellular, allocate fixed spectrum to its customers. Numerous studies have shown that this leads to spectrum wastage and causes artificial spectrum scarcity [1]. Thus dynamic allocation of spectrum have been proposed for better utilization [2], [3]. In the future it is likely that the spectrum regulatory bodies such as FCC will grant a wireless service providers (SP) with short term licenses [4] so that it can purchase the exact amount of spectrum as needed to serve its customers.Motivated by these developments, we consider a centralized network consisting of a single service provider (SP) that allocates orthogonal chunks of spectrum to its customers dynamically, based on their demand. It then transmits to these users over their allocated spectrum. The user demand of spectrum depend on the received rate which is different for users due to the variations in the link gain. The SP purchases the amount of spectrum needed by its customers, from the FCC. The SP has to pay the FCC for the purchased spectrum and in turn charges the users to recover its costs. In this work we model the dynamic allocation as a SP profit maximization problem and derive the optimal values of the prices.Pricing for profit maximization has been studied under various contexts. Simple wireless settings have been considered in [5], [6] but the full range of relationships between spectrum prices, costs and user demands are not established. On the other hand, several works in microeconomics have considered pricing for profit maximization [7], [8] but for very generic user demand functions and costs. In this work, we have applied