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Derivation of average cost AC and marginal cost MC

cost chart


Consider the following schedule

Output (Q)Total Cost (TC)Average Cost (AC)Margin Cost (MC)
1
10
1010
2
18
98
3
24
8
6
4
28
7
4
5
30
6
2
6
36
6
6
7
49
7
13
8
64
8
15
9
81
9
17
10100
10
19

In the above schedule, the total cost average cost and marginal cost are shown. The schedule shows that both average and marginal costs are declines with the rise in units of output. The average cost is minimum when the level of output is 6. At that level both average and marginal costs are equal. The marginal cost rises from its minimum points. The minimum marginal cost is equal to 2 when the output is 5 units.

cost derivation


Average cost also rises from its minimum point. The minimum average cost is 6 when the level of output is 6. This clearly shows that both curves decline up to a certain limit and move upwards. In the above figure average cost decreases up to 6 units of output then increases but marginal cost decreases up to 5 units of output then increases. This means both average and marginal cost curves are U-shaped average cost is equal to marginal cost and the average cost is minimum. In other words, the MC curve passes through the minimum point of the AC curve. AC decreases till MC is less than AC and starts increasing when MC becomes more than the AC.

Relation between AC and MC

Some different relationship exists between AC and MC. The relationship between them may be pointed out as:

1. Both mc and ac fall at a certain range of output and rises afterward.

2. When AC falls, MC also falls, but at a certain range of output, MC rise even though AC continues to fall.

3. So long as AC is falling, MC is less than AC.

4. When AC is rising, after the point of intersection, MC will be greater than AC.

5. MC curve cuts the AC cob at the minimum point of the curve.

Post Navi

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