3-14 - PART A Ignore L2 C(q;P = Min 100K 150L1 s.t q1 KL1...

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PART A Ignore L 2 C(q;P) = Min 100K + 150L 1 s.t. q 1 ≤√KL 1 K≤200 Region 2: L 1 = q 1 2 /200 C(q;P) = Min 100(200) + 150(q 1 2 /200) = 20000 + (¾)q 1 2 Find MC MC = (3/2)q 1 Set = MR 275 = 3/2q 1 183 1/3 = 550/3 = q 1 Profit for q 1 only π = 275q 1 - C(q 1 ;P) = 275q 1 – [20000 + (¾)q 1 2 ] = 275(550/3) – 20000 – 3/4(550/3) 2 = 5208.33 PART B Ignore L 1 C(q;P) = Min 100K + 175L 2 s.t. q 2 ≤√ KL 2 K≤200 Region 2: L 2 = q 2 2 /200 C(q;P) = Min 100(200) + 175(q 2 2 /200) = 20000 + (7/8)q 2 2 Find MC MC = (7/4)q 2 Set = MR 300 = (7/4)q 2 171 3/7 = 1200/7 = q 2 Profit for q 2 only π = 300q 2 - C(q 2 ;P) = 300q 2 – [20000 + (7/8)q 2 2 ] = 300(1200/7) – 20000 – 7/8(1200/7) 2 = 5714.29 PART C Now consider both inputs/outputs C(q;P) = Min 100K + 150L 1 +175L 2 s.t. q 1 ≤√KL 1 q 2 ≤√ KL 2 K≤200 Assume its in region 2 , L 1 =q 1 2 /200 where K=200 L 2 = q 2 2 /200
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Substitute: C(q;P) = Min 100(200) + 150 q 1 2 /200 +175 q 2 2 /200 =20,000 + 3/4 q 1 2 + 7/8 q 2 2
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3-14 - PART A Ignore L2 C(q;P = Min 100K 150L1 s.t q1 KL1...

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