PS 3 Solution

PS 3 Solution - Quantitative Intermediate Microeconomics...

This preview shows pages 1–2. Sign up to view the full content.

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)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/26/2008 for the course EC 16 taught by Professor Loury during the Fall '07 term at Tufts.

Page1 / 3

PS 3 Solution - Quantitative Intermediate Microeconomics...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online