The market for sweet potatoes consists of 1,000 identical firms. Each firm has a short-run total cost curve of STC = 100 + 100q + 100q², and a short-run marginal cost curve of SMC=100+200q where q is output. What is the minimum level of average variable costs?

Question

Quizplus · Accepted Answer

To find the minimum level of average variable cost, we need to find the level of output where the SMC curve intersects the AVC curve. The AVC curve can be calculated as follows: AVC = STC/q = (100 + 100q + 100q²)/q = 100/q + 100 + 100² At the minimum level of AVC, the derivative of AVC with respect to q is equal to zero: dAVC/dq = -100/q^2 + 100² = 0 Solving for q, we get: q = 10*Sqrt(²) Substituting q into the AVC equation, we get: AVC = 100/(10*Sqrt(²)) + 100 + 100² As ² is positive, AVC will be minimized when q is maximized. Therefore, the minimum level of AVC is: AVC = 100/10 + 100 + 100² = 200 + 100² Therefore, the minimum level of AVC is 200.

The Market for Sweet Potatoes Consists of 1,000 Identical Firms