We know that average product (AP) of an input is equal to the total product or output (Q) divided by the number of units of variable input (N). Therefore,
AP=Q/N
=> 1/AP = N/Q
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Further,
Average variable cost (AVC) = TVC/Q
=>AVC=N?P/Q=P. (N/Q)
Here, ‘P’ is the price per unit of the variable factor.
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Substituting equation (11.1) in equation (11.2) we get
AVC = P. (1/AP)
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Thus, average variable cost is equal to the price of the input multiplied by the reciprocal of its average product. Given the price of the variable input (P), the average variable cost is equal to the reciprocal of the average product. In other words, the average variable cost and average product vary inversely with each other.
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When average product rises in the beginning (as more variable inputs are employed), the average variable cost must be falling. The level of output at which the average product is maximum the average variable cost is minimum. Further, when the average product of the variable input falls, the average variable cost must be rising.
The average variable cost (AVC) curve looks like the average product (AP) curve turned upside down with minimum point of the AVC curve corresponding to the maximum point of AP curve.
Likewise, the marginal cost curve in the short run is a mirror image of the marginal product curve, expressed in monetary terms. To prove it, assume that price of the variable input is constant. Now, the change in total variable cost will occur only due to the change in the amount of the variable input.
Therefore,
MC = d(TVC) /dQ = d(N?P)/dQ
=> MC = P. dN/ dQ
= P/ dQ/dN = P/MP
Thus, marginal cost of production is equal to the price multiplied by the reciprocal of the marginal product of the variable input. Given price of the variable input, marginal cost varies inversely with the marginal product of the variable input.
The fact that marginal product rises initially, reaches a maximum and then falls ensures that the marginal cost curve of a firm first declines, then reaches a minimum and finally rises. The maximum of marginal product corresponds to minimum of marginal cost. The relation between marginal product and marginal cost is quite similar to the relationship between average product and average cost.
The relationship between product curves (average product curve and marginal product curve) and cost curves (average cost curve and marginal cost curve) is graphically shown in Fig. 11.9.
While the marginal product intersects average product from above at its maximum point (if AP rises, MP is greater than AP; if AP falls, MP is less than AP and when AP is at its maximum, MP is equal to AP), the marginal cost intersects average cost from below at its minimum point. Average cost and marginal cost are simply the transformation of average product and marginal product respectively from physical terms into money terms.
