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Unformatted text preview: MC = 8/7q Set MC = MR : 8/7q = 15 q = 7(15)/8 answer to 12b (optimal output) = 13.125 Find cost: C(q = 13.125) = 63 + 4/7(13.125 2 ) = 161.4735 Find profit: answer to 12b(profit) = 15q  C(q;P) =15 (105/8) (63 + 4/7[105/8] 2 ) = 35.4375 Now we can write entire cost function the answer to 12a Region 1 (q10.5) C(q;P) = 12q MC = 12 Region 2 (q10.5) C(q;P) = 63 + 4/7q 2 MC = 8/7q What is the shadow price on K 7? C(q;P) = Min qK + 4L s.t. qKL K k Humor me and pretend italicized k is k bar :o) Want dc/d k (shadow price) C(q;P) =9 k + 4q 2 / k Dc/d k = 9 4q 2 / k 2 At optimal production (q = 13.125, k = 7) Dc/d k = 9 4(13.125 2 /7 2 ) = 5.0625...
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 Summer '09
 TOMASSINI

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