Answer in Microeconomics for isaac mensah #179276
March 27th, 2023
a) 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”
c) “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]}=6”