Answer in Microeconomics for Rakhi #179905
March 27th, 2023
Give examples if economic problems that are solved with the help of first and second order difference equation.
i) Utility max problem;“U=Q1Q2”
Subject to; “10Q1+2Q2=240”
Lagrange function
“Z = Q1Q2+ u03bb(240-10Q1-2Q2)”
b) first-order conditions:
“ZQ1 = Q2u2212 u03bb10 = 0\nnn ZQ2 = Q1u2212 u03bb 2 = 0 \nnnZu03bb = 240 u2212 10Q1 u22122 Q2 =0.”
“Zlambda=240-10Q1-2Q2=0”
“ZQ1=Q2- lambda10=0”
“ZQ2=Q1-lambda2=0”
“begin{bmatrix}n 0 & -10 & -2 \n -10 & 0 &1 \n-2 & 1 & 0nend{bmatrix}” “begin{bmatrix}n lambda \n Q1 \ Q2nend{bmatrix}” = “begin{bmatrix}n -240 \n 0 \ 0nend{bmatrix}”
Q1M“=frac{240}{2[-10]}= -12”
Q2M“=frac{240}{2[-2]}=-60”
“lambda=frac{240}{2[-10.-2] }nu200btn =6”
ii.)Second order condition.
