Stlyes Inc. estimates that the total annual cost of producing shirts given equat

Question

Stlyes Inc. estimates that the total annual cost of producing shirts given equation TC = 5,000 + 4,100Q - 8Q2 + 0.004Q^3. If the market price is constant, what is the shutdown level of output? What is the minimum price if the firm can accept?

Explanation / Answer

TC = 5000 + 4100Q - 8Q^2 + 0.004Q^3 So, FC = 5000 VC = 4100Q - 8Q^2 + 0.004Q^3 AVC = 4100 - 8Q + 0.004Q^2 (AVC = VC/Q) Shutdown level of output is reached when AVC is minimum and anymore production starts decreasing profit. for minima, d(AVC)/dQ = = => -8 + 0.004*2Q = 0 => Q = 1000 (shutdown level of output i.e optimum output level) (ANSWER) Minimum price acceptable will be = minimum AVC + contribution per unit at that level. = (4100-8*1000+0.004*1000000) + (FC/!000) (since Q = 1000 for minimum AVC, and putting it in eqn of AVC above) = (8100-8000) + (5000/1000) = 100+ 5 =105 (unit of currency) (ANSWER)

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