In this paper, we study the problem of minimizing the area power consumption in wireless cellular networks. We focus on the downlink of a single-tier network, in which the locations of base stations (BSs) are distributed according to a homogeneous Poisson point process (PPP). Assuming that a mobile user is connected to its strongest candidate BS, we derive bounds on the optimal transmit power in order to guarantee a certain minimum coverage and data rate. Under the same quality of service constraints, we find the optimal network density that minimizes the area power density. Our results show that the existence of an optimal BS density for minimizing the power consumption depends on the value of the pathloss exponent.