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Imagine your firm has the short run total cost function: C = q3 – 3q2 +...

Imagine your firm has the short run total cost function: C = q3 – 3q2 + 10q + 250. At what level of output (quantity of production) is your average variable cost (AVC) minimized?

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Answer #1

At the minimum of average variable cost, marginal cost and average variable cost both are equal.

AVC = MC

Total Cost

TC = q3 - 3q2 + 10q + 250

Total Cost = Fixed Cost + Variable Cost

Fixed Cost = 250

Variable Cost = q3 - 3q2 + 10q

AVC = Variable Cost / Quantity

AVC = q3 - 3q2 + 10q / q

AVC = q2 - 3q + 10

Marginal Cost

MC = dTC / dq

MC = 3q2 - 6q + 10

Equating both MC and AVC

3q2 - 6q + 10 = q2 - 3q + 10

2q2 = 3q

q = 1.5

Hence at 1.5 units, AVC will be minimized

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