Question

A maximizing consumer with preferences u = min (3x, 2y) and an income of 120 dollars pays p_X= 2 for good x and p_Y= 2 for good y. Next month her income will decline to 60 dollars. After the income change x₁ =

Answer 1

solution

             utility function $u=min(x ,2y)$

 and  can be written $x=2y$

 $M=p_xx+p_yy$

 M is total income and p_{x ,} p_y are price of good x and Y

so

      $120=2x+p_yy$

price of p_y changes from 2 to 4

so when $p_y=2$

$120=2x+2y\space\space and \space x=2y$

so

$3x=120 =x=40$

and when p_y is 4 then

$120=2x+4y$

$120=2x+2x$

then $x=30$

so when y changes from 2 to 4 then x will change from 40 to 30 unit