Find optimal consumption choice

Question

John derives utility from hand-cleaning wipes, w, and bottled water,

b, in a function U (w; b) = w^(2/3)*b^(1/3). Handcleaning wipes cost $1 and water costs $2 per bottle. His daily budget is $12.

find the optimal consumption choice

Answer 1

$12 = $1*w + $2*b

U=w^(2/3)*b^(1/3)

U→MAX

MUw/$1=MUb/$2

MUw=2/3 * (b/w)^(1/3)

MUb=1/3 * (w/b)^(2/3)

w=4b

12 =w+2b = 4b+2b=6b

b=12/6=2

w=2*4=8

Check:

8+2*2=8+4=$12

U=4*2^(1/3)=5.03968