Question

Let income be I = $90, Px = $2, Py = $1, and utility U = 4X½Y. a.[12] Write down and simplify the two conditions required for utility maximization. b.[6] Compute the optimal consumption bundle for the consumer. What is the level of utility at the optimum?

Answer 1

a> Here we have to maximize the total utility while the consumption bundle cost should be less than the income.

So, we have to maximize 4X½Y given 2X+Y=<90[Price of cons. bundle <=income]

b> For optimal case, 2X+Y=90

So, Y=90-2X

So, we have to maximize 4X½(90-2X)

By taking first derivative, we get 180X^(-1/2)-12X^(1/2)

By making it equal to zero, we get, X=180/12=15

Y=90-30=60

So, he will consume 15 X and 60 Y and utillity will be 4x60xroot(15)=929.5