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Power conservation is one of the most important issues for ad hoc wireless networks where nodes are likely to rely on limited battery power. Transmitting at unnecessarily high power not only reduces the lifetime of the nodes and the network, but also introduces excessive interference. It is in the network designer's best interest to have each node transmit at the lowest possible power while preserving network connectivity. In this paper, we investigate the optimal common transmit power, defined as the minimum transmit power used by all nodes necessary to guarantee network connectivity. In particular, we show that for a given route BER and node spatial density, there exists a global optimal data rate at which the transmit power can be globally minimized. Moreover, we also show that there exists a critical node spatial density at which the optimal transmit power is the minimum possible for a given data rate and a given route BER.