PS 3 Solution

PS 3 Solution - Quantitative Intermediate Microeconomics...

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Quantitative Intermediate Microeconomics Answers to Problem Set #3 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) a) Lagrangian: L =P L L+P M M+1+ λ (q-L M) b) First-order conditions (FOC): i) L / L=P L - λ M=0 ii) L / M=P M - λ L=0 iii) L / ∂λ = q-L M=0 c) Dividing the first FOC by the second gives: M /L =P L /P M d) Solving this for M gives M= LP L /P M e) Substituting for M into the third FOC gives: q-L (LP L /P M )=0 or L 2 =P M q/P L f) Solving for conditional demand functions: L* = [qP M /P L ] 1/2 and M*= L*P L /P M =[qP L /P M ] 1/2 . g)
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PS 3 Solution - Quantitative Intermediate Microeconomics...

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