In this letter, we investigate the price-based power allocation for non-orthogonal multiple access (NOMA) networks, where the base station (BS) can admit the users to transmit by pricing their power. Stackelberg game is utilized to model the pricing and power purchasing strategies between the BS and the users. Based on backward induction, the pricing problem of the BS is recast into the non-convex power allocation problem, which is equivalent to the rate allocation problem by variable replacement. Based on the equivalence problem, an optimal price-based power allocation algorithm is proposed to maximize the revenue of the BS. Simulation results show that the proposed algorithm is superior to the existing pricing algorithm in items of the revenue of BS and the number of admitted users.