Question

How to get the answer, explanation

Use the following information to answer the next two questions: The utility function of Ann is U(X,Y) = X(1/2)y(1/2) The utility function of Bob is U(X,Y)= X(3/4)Y(1/4) Also assume that they have the same income and face the same prices for the two goods. V. Consider the (X,Y) consumption bundle that maximizes Ann's utility. At this point, A. Bob also maximizes his utility B. Bob would prefer to consume more of the X-good and less of the y-good C. Bob would prefer to consume more of the y-good and less of the x-good D. Not enough information because the price ratio is not given

Answer 1

At Ann's utility maximization utility consumption bundle, MUx/MUy = Px/Py

As Px/Py is same for both Bob and Ann.

So,

Ann's MUx/MUy = (1/2)*X^-1/2*Y^1/2 / (1/2)*Y^-1/2*X^1/2

MRS = Y/X

While,

MRS of Bob = (3/4)*X^-1/4 * Y^1/4 / (1/4)*X^3/4*Y^-3/4

MRS = 3*Y/X

So, when the consumption bundle when Ann's utility maximizes;

Y/X = Px/Py

While for Bob to maximize his utility it should be 3Y/X = Px/Py

But 3Y/X > Y/X so,

for Bob, MUx/MUy > Px/Py

For Bob to maximize utility, he will buy more of X and less of Y, so as more unit of X leads to reduce MUx due to law of diminishing marginal utility.So,

Ans - B) Bob would prefer more of good X and less of Good Y