Q.A firm has Total Fixed Cost (TFC) of ₹50, constant at every output level. Its Total Variable Cost (TVC) at outputs 1 to 6 units is ₹25, ₹42, ₹55, ₹65, ₹80 and ₹102 respectively. Compute TC, AFC, AVC, AC and MC at each output level, and state the output at which MC is at its minimum.

This is a standard short-run cost-schedule problem: build TC by adding the constant TFC to each TVC figure, then divide through by output for the three averages, and take successive differences of TC (or, equivalently, of TVC) for MC.

Step 1 — Total Cost. Add the constant TFC (₹50) to TVC at each output:

Step 2 — Averages. $AFC = TFC/Q$, $AVC = TVC/Q$, $AC = TC/Q$:

Step 3 — Marginal Cost. MC is the change in TC per extra unit (treating output 0 as TC = TFC = ₹50): 75 − 50 = 25; 92 − 75 = 17; 105 − 92 = 13; 115 − 105 = 10; 130 − 115 = 15; 152 − 130 = 22.

Cross-check (dual solve): MC should equal $ΔTVC/ΔQ$ as well, since TFC never changes. At Q = 5: ΔTVC = 80 − 65 = 15, which matches MC computed from ΔTC (130 − 115 = 15). The two methods agree, confirming the arithmetic.

Reading the MC column, the lowest value is ₹10, reached when output rises from 3 to 4 units. Notice also that AVC is at its lowest tabulated value (₹16.00) at Q = 5, very close to MC (₹15) at that same output — consistent with the rule that MC intersects AVC near its minimum point.

Cross-check MC by computing it two ways — from ΔTC and from ΔTVC — since TFC contributes nothing to the change; both must give the identical figure at every output.

A common slip is computing MC as TC(Q)/Q − TC(Q−1)/(Q−1) (a difference of averages) instead of ΔTC/ΔQ (a difference of totals) — these are not the same thing. Another common error is expecting MC to equal AVC exactly at AVC's minimum in every whole-number table; in a discrete schedule (as here) this holds only approximately, because MC is measured over a one-unit interval rather than at a single point — exact equality is a property of smooth, continuous curves.