Marginal revenue (MR) is the incremental revenue for the last quantity sold, while average revenue (AR) is the mean revenue for all quantity sold. Mathematically:
MR=dTR(Q)/dQ, e.i. MR is the first derivative of the total revenue function TR(Q) with respect to Q; while
AR=TR(Q)/Q, e.i. is total revenue divided by Q.
An interesting property of MR and AR is that when AR is falling, MR is less than AR; when AR is rising, MR is greater than AR. MR and AR intersect where dAR(Q)/dQ=0.