Relationship between Average Cost, Average Variable Cost, and Marginal Cost in Short-Run

It has been seen that the AC and MC curves are both U-shaped. This shows that they fall steeply at the initial levels of output, reach their minima, and shoot up thereafter as fast as they had dived down. Such behaviour of these curves, in short run, is caused by diminishing returns to variable proportions. Initial increasing returns cause a steep fall in these curves. The decreasing returns that follow thereafter slow down the fall. The curves touch their respective lowest points before shooting up again. Figure 5.9 shows the behaviour of the three curves.

AC and MC are both alike in nature but for three basic differences.

(i) When AC falls, so does MC but at a faster rate. MC < AC so long as AC is falling.

(ii) MC attains its minimum earlier than AC. MC starts rising steeply while AC is still falling to its lowest point. As soon as AC touches its lowest point, MC meets it. Thus, MC = AC where AC is least.

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(iii) When AC rises, so does MC but at a faster rate.

MC > AC so long as AC is rising.

The relative behaviour of AVC and MC can be seen to be the same as that of the AC and MC by simply taking AVC in place of AC throughout the three points mentioned above.

Fig. 5.9: When AC falls, so does MC but at a faster pace, keeping itself below the AC curve. MC reaches its minimum before AC does and it begins to rise thereafter, the way it had fallen. MC rises beyond the output OQ_v while AC continues to fall till it reaches its minimum at the output OQ₂, where it is cut from below by the rising MC. Thus, AC is falling even when MC has begun to rise. Beyond the lowest point on the AC, both the curves rise but MC rises at a faster pace, keeping itself above the AC curve. Behaviour of the AVC is rather modest.

Illustration 5.1 Consider the total cost function

TC = 2 + 3Q – 1.5Q² + 0.5Q³ where Q is in quintals and TC in thousand rupees. Show that MC reaches its I minimum at an output of 1.00 quintal, AVC at an output of 1.50 quintals and AC J reaches its minimum at an output of 2.00 quintals. Also show that MC cuts AVC/ and AC from below at their respective minimum points.

Relationship between AC and MC can also be understood through calculus. For the purpose, let us express the total cost as the product of AC and be output produced.

TC = cQ

Where, c = AC (a function of output Q) and Q = output

Since MC = d(TC)/dQ, differentiating TC with respect to Q we have

MC =d (TC)/dQ = c + Q.(dc/dQ) [By product rule of differentiation]

=AC + Q. (slop [of AC)

When AC falls, its slope is negative; when AC is minimum, its slope is 0, and when AC rises, its slope is positive. With this notion, we can interpret the expression for MC as

(1) MC > AC when slope of AC is positive (AC is rising)

(2) MC = AC when slope of AC = 0 (AC is minimum), and

(3) MC < AC when slope of AC is negative (AC is falling)

The value of AVC at Q = 1.50 quintals can be checked to be 1,875 thousand rupees. The value of MC at Q = 1.50 is also the same. This shows that MC = AVC at Q = 1.50, the level of the output at which AVC is the minimum.

Which is [+3/2] at Q, = 2. This shows that AC is minimum at Q = 2 and its value at Q = 2 is 3.00 while that of MC at this level of output is also 3.00. This shows that the MC cuts AC where AC is least. To sum, MC, AVC and AC attain their minima at

Q= l,

Q = 1.5, and

Q = 2

respectively, and that MC cuts AVC and AC where they are least.