Question

(d) Let qmin denote the value of q that minimizes AC

The demand curve for a product is given by Q = 800 – 0.1P where P denotes price and Q denotes quantity of the product. The industry comprises large number of firms. Each firm's cost function is 

C(q) = 2000 + 500q+ 20q2

(d) Let qmin denote the value of q that minimizes AC. Also, let ACmin denote the value of AC at q = qmin. Find qmin and ACmin

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AC C = 2000 + sooq +zoq? 2000 + Soo + 20g d (AC) = - 2000 20 = 0 da 92 - 2000 + 2092 0 92-100 q=10 qmin = 10 Almin = 2000 +50

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