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The performance of a cellular network can be significantly improved by employing many base stations (BSs), which shortens transmission distances. However, there exist no known results on quantifying the performance gains from deploying many BSs. To address this issue, we adopt a stochastic-geometry model of the downlink cellular network and analyze the mobile outage probability. Specifically, given Poisson distributed BSs, the outage probability is shown to diminish inversely with the increasing ratio between the BS and mobile densities. Furthermore, we analyze the optimal tradeoff between the performance gain from increasing the BS density and the resultant network cost accounting for energy consumption, BS hardware and backhaul cables. The optimal BS density is proved to be proportional to the square root of the mobile density and the inverse of the square root of the cost factors considered.