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PS 4 Solution

# PS 4 Solution - Quantitative Intermediate Microeconomics...

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Quantitative Intermediate Microeconomics Answers to Problem Set #4 1) Answers a) MP L = q/ L= α L α -1 K β 2 q/ 2 L= α ( α -1)L α -2 K β <0 since ( α -1)<0 MP K = q/ K= β L α K β -1 2 q/ 2K = β ( β -1)L α K β -2 <0 since ( βα -1)<0 b) MRTS=MP L/ MP K = α L α -1 K β / β L α K β -1 = α K/ β L c) If both inputs are changed by the proportion m, the new output is (mL) α (mK) β = m α + β L α K β <m L α K β =mq since α + β <1 2) Answers a) No, she does not. The cost relevant to her should be the cost from the moment that a sale is made since it represents the opportunities or resources she is foregoing in making the sale. b) No interest has to be paid, but the firm does sacrifice an interest return it could receive by investing the profits in bonds or in other ways. If the firm could invest its profits elsewhere and receive a return of 10 percent, the opportunity cost of financing out of profits would be as high as financing by borrowing. 3) Answers a) SRTC: SRTC= wL+ vK q=2L 1/2 K 1/2 or L=q 2 /4K^ SRTC=( wq 2 /4K^)+vK^ SRMC= SRTC/ q= wq/2K^

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