Both marginal cost (MC) and average cost (AC) are derived from the total cost. They bear unique relationship. The relationship between MC and AC can be stated as under:
(i) When AC falls with increase in output, MC is lower than AC, i.e., MC curve lies below the AC curve. However, it is not necessary that MC should fall throughout this stage. Actually, MC rises earlier than AC.
(ii) When AC rises with increase in output, MC is higher than AC, i.e., MC curve lies above the AC curve.
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(iii) At the level of optimum output, average cost is minimum and constant. Here, MC stands equal to AC, i.e., MC pulls AC horizontally.
(iv) At zero level of output, AC is zero, but, MC is indeterminate.
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It brief, it can be said that MC intersects AC at its minimum point. Both are U-shaped curves on account of the operation of the law of variable proportions. The above relationship between MC and AC can be illustrated with the help of a diagram (see Fig. 11.7).
In Fig. 11.7, as long as AC curve is falling, MC is less than AC, i.e., MC pulls AC downwards. However, MC falls more rapidly and reaches its minimum point ‘A’ earlier than AC reaches its own minimum point ‘B’. Therefore, MC starts rising from point ‘A’ to point ‘B’.
AC is still falling up to point ‘B’. Further, beyond point ‘B’, both MC and AC rise, but, the former rises more sharply. When MC rises above AC, it pulls the latter upwards. Similar relationship holds between MC and AVC too. MC intersects both AVC and AC (from below) at their respective minimum points in that order.
Here, the ray from the origin is also tangent on the corresponding point of total (variable) cost curve The relationship between AC and MC can also be shown with the help of a simple diagram (Fig. 11.8). It shows that so long as the marginal cost curve lies below the average cost curve, the average cost falls (pulled downwards by the marginal cost).
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On the other hand, when marginal cost lies above the average cost curve, the average cost rises (pulled upwards by the marginal cost). When marginal cost is equal to average cost, it is the minimum point of the latter.
It is important to note that as long as the marginal cost is less than average cost, each additional unit of output will add less to total cost in comparison to the average (per unit) cost incurred on the previous units. This lowers the overall average cost of production.
Hence, the average cost will continue to decline as long as the marginal cost is less-than the average cost (whether the marginal cost is itself rising or falling). Further, when the marginal cost exceeds the average cost, each extra unit of output produced ads more to the total cost than the average cost incurred on the previous units, resulting in rise in the overall average cost of production. This leads to a rise in the average cost curve, when the marginal cost is more than the average cost.
Finally, if the additional unit of output produced costs same as the average cost incurred on the previous units, the overall average cost does not change and attains its minimum value. Thus, when the average cost reaches its minimum level, it is equal to the marginal cost.
The relationship between average cost (AC) and marginal cost (MC) can be explained by observing mathematical relationship between them. We know that,
AC = TC/Q
Or, TC = AC. Q
Further, marginal cost is the first derivative of total cost with respect to output. Therefore,
Assuming that AC > 0 and Q > 0, the relationship between AC and MC can be written as,
(i) When the slope of AC curve is negative (i.e., AC curve is falling), MC will be less than AC and thus lie below AC.
(ii) When the slope of AC is positive (i.e., AC is rising), MC will be greater than AC and lie above it.
(iii) When the slope of AC is equal to zero (i.e., AC is minimum), MC is equal to AC.
Similar relationship holds between AVC and MC. Here d/dQ (AVC) = 1/q [MC – AVC] would imply (assuming AVC, Q > 0)
(i) MC < AVC =>d (AVC)/dQ < 0, i.e., AVC is falling
(ii) MC > AVC =>d/dQ (AVC) > 0, i.e., AVC is rising
(iii) MC=AVC=>d/dQ (AVC) = 0, i.e., AVC is minimum
Therefore, MC cuts AVC and AC from below at their respective minimum points.