Question

Hi there, I am currently doing a Microeconomics homework question (few actually) and its asking me to calculate the demand of two goods give the utility function of them. The utility function is U(x1,x2)=x1(x2^2), and the price of good x1 is $3,and price of good x2 is $1. Income is $90. Please help me out in the most simple way possible. Thank you so much!

Answer 1

U(x1,x2)=x1(x2^2), MUX1 = x2^2, MUX2 = x1(2*x2)
3*x1 + x2 = 90, MUX1/ MUX2 = PX1/PX2, (x2^2)/ x1(2*x2)= 1/3
x2^2 = 2/3x1*x2
x2 = 2/3x1, 3*x1 + 2/3x1 = 90, x1 = 24.5, x2 = 17.5