A novel monostatic multiple-input multiple-output (MIMO) dual-function radar communication (DFRC) system is proposed, that uses the available bandwidth efficiently for both sensing and communication. The proposed system, referred to as Shared-Subcarriers DFRC (SS-DFRC) transmits wideband, orthogonal frequency division multiplexing (OFDM) waveforms and allows the transmit antennas to use subcarriers in a shared fashion. A novel, low complexity target estimation approach is proposed to overcome the coupling of radar target parameters and transmitted symbols that arises in that case. When all subcarriers are used in a shared fashion, the proposed system achieves high communication rate but its sensing performance is limited by the size of the receive array. We show that when some of the subcarriers are reserved for exclusive use by one transmit antenna each (private subcarriers), the communication rate can be traded off for improved sensing performance. The latter can be achieved by using the private subcarriers to construct a larger aperture virtual array that yields higher resolution angle estimates. The system is endowed with beamforming capability, via waveform precoding, where the precoding matrix is optimally designed to meet a joint sensing-communication system performance metric.