Q.A firm facing the demand relation P = 40 − 3Q sells 1 to 5 units. Prepare a schedule of Total Revenue, Average Revenue and Marginal Revenue, and verify that MR lies below AR (except at the first unit) and falls faster than AR.

Because the demand curve slopes downward, price must be cut to sell more, so AR itself falls with output — and MR falls even faster, since the price cut applies to every unit sold, not only the last one. …

Step 1 — Price at each output, from $P = 40 − 3Q$: Q=1: 37; Q=2: 34; Q=3: 31; Q=4: 28; Q=5: 25.

Step 2 — Total Revenue, $TR = P × Q$: 37, 68, 93, 112, 125.

Step 3 — Average Revenue, $AR = TR/Q$: 37, 34, 31, 28, 25 — identical to price at every output, confirming $AR = P$.

Step 4 — Marginal Revenue, $MR = ΔTR/ΔQ$: 37 − 0 = 37; 68 − 37 = 31; 93 − 68 = 25; 112 − 93 = 19; 125 − 112 = 13.

As a graphical cross-check: since AR here is the straight line P = 40 − 3Q, the corresponding continuous MR line is P = 40 − 6Q (twice the slope) — at Q = 2 this gives MR = 28, reasonably close to the discrete table's 31, the small g …

A frequent mistake is assuming MR must always be below AR, including at the first unit — in fact MR = AR exactly at Q = 1 for any demand curve, and the 'M …