In: Economics
u(x1, x2) = min {x1/2, x2/3}
if the price of good 1 is $7/unit, the price of good 2 is $4/unit and income is 114..
What is this person's optimal consumption level for good 2?
u(x1, x2) = min{x1/2, x2/3}
At optimal consumption bundle, the condition is:
x1/2 = x2/3
3x1 = 2x2
x1 = (2/3)x2
The additional information provided is:
Px1 = 7
Px2 = 4
M = 114
The budget line is:
x1*Px1 + x2*Px2 = M
7x1 + 4x2 = 114
7(2/3)x2 + 4x2 = 114
(14/3)x2 + 4x2 = 114
(26/3)x2 = 114
x2 = 114*3/26
x2 = 13.15385
Hence, the person's optimal consumption level for good 2 is 13.15385
Hence, the correct answer is 13.15385