In this paper, we analyze and investigate the effect of transmission power on the throughput capacity of finite ad hoc wireless networks. We prove that, independent of nodal distribution and traffic pattern, the capacity of an ad hoc wireless network is maximized by properly increasing the nodal transmission power. Under the special case of our analysis that the maximum transmission power can be arbitrary large, we prove that the fully connected topology (i.e. the topology under which every node can directly communicate with every other node in the network) is always an optimum topology, independent of nodal distribution and traffic pattern. Our result stands in sharp contrast with previous results that appeared in the literature for networks with random nodal distribution and traffic pattern, which suggest the use of minimal common transmission power that maintains connectivity in the network, showing it to asymptotically achieve a throughput level that is in the order of the throughput capacity. We also derive a linear programming (LP) formulation for calculating the capacity of finite ad hoc wireless networks. Our LP based performance evaluation results confirm the capacity improvement attained under our recommended approach, as well as identify the. magnitude of capacity upgrade that can be realized for networks with random topologies and traffic patterns.