Currently, the issues of the operation of the Internet of Things technology are being actively studied. The operation of a large number of different self-powered sensors is within the framework of a massive machine-type communications scenario using random access methods. Topical issues in this type of communication are: reducing the transmission signal power and increasing the duration of the device by reducing the consumption energy per bit. Formulation and analysis of the tasks of minimizing transmission power and spent energy per bit in systems without retransmissions and with retransmissions to obtain achievability bounds. A model of the system is described, within which four problems of minimizing signal power and energy consumption for given parameters (the number of information bits, the spectral efficiency of the system, and the Packet Delivery Ratio) are formulated and described. The numerical results of solving these optimization problems are presented, which make it possible to obtain the achievability bounds for the considered characteristics in systems with and without losses. The lower bounds obtained by the Shannon formula are presented, assuming that the message length is not limited. The results obtained showed that solving the minimization problem with respect to one of the parameters (signal power or consumption energy per bit) does not minimize the second parameter. This difference is most significant for small information message lengths, which corresponds to IoT scenarios. The results obtained allow assessing the potential for minimizing transmission signal power and consumption energy per bit in random multiple access systems with massive machine-type communications scenarios. The presented problems were solved without taking into account the average delay of message transmission.