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This paper tries to analyze the energy saving capabilities of two common power saving techniques being suggested - introduction of sleep modes and bandwidth (BW) variation. The framework for this analysis assumes users and base stations (BSs) to be independently marked point processes in R2. The relationship between spatially averaged rate, user density, and base station density, which is an extension of findings in , is used in an affine power model to estimate the energy that can be saved by the two methods under consideration. The primary contribution of this paper constitutes an analytic relationship between spatially averaged rate, user density, BS density, transmit power, and the noise power. Another key contribution is a proof that shows that power saved by using sleep modes (or turning off BSs) is always greater than the power saved by varying the BW, for a system model implementing an affine power model (described here) when traffic densities below full load are considered.