Existing control design schemes assume availability of input/output signals over the same sampling interval. However, in many practical situations, and particularly in the chemical industries, this is not the case. Hence, control of multirate systems using existing techniques is limited by the slowest sampled signal(s). Multirate control via lifting techniques utilizes both the multirate input/output data and the single-rate control techniques. In this paper, the issue of concern is - is there an incentive in moving from single-rate control at the slow rate to multirate control and if yes, under what conditions? Also, what are the upper and lower bounds on the performance of multirate systems? The equivalence between multirate and single-rate control systems is established in the LQR framework using lifting techniques. The main result in this paper shows that under no model-plant mismatch, the optimal performance of multirate systems is: ( i ) no worse than the optimal performance of the single-rate systems at the slow sample rate and ( ii ) theoretically identical to the optimal performance of single-rate systems at the fast sample rate.