Answer to Question #243927 in Microeconomics for mehk

Question #243927

Consider the utility function u1(x1, x2, x3) = x21,x32 x3 .

Find a monotone transformation of u1(x1, x2, x3) such that the new utility function is of the form u2(x1, x2, x3) = (x1a, x2b, x3c)

Where a + b + c= 1. 


1
Expert's answer
2021-09-28T20:02:24-0400

Such monotonic transformation can be done so that the powers are added up to 1

We see that

2+3+1=6anda=26=13b=36=12c=162+3+1=6\\and\\a=\frac{2}{6}=\frac{1}{3}\\b=\frac{3}{6}=\frac{1}{2}\\c=\frac{1}{6}

After monotonic transformation of Ui(X1,X2,X3)U^i(X_1,X_2,X_3) the new utility function is U2(X1,X2,X3)=X113,X212,X316U^2(X_1,X_2,X_3)=X_1^{\frac{1}{3}}, X_2^{\frac{1}{2}} ,X_3^{\frac{1}{6}}


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment