Question

Vincent Price utility function is U(X,Y)=X2Y, which the following marginal utilities: MUX=2XY,   MUY=X2 His income is $200...

  1. Vincent Price utility function is

    U(X,Y)=X2Y,

    which the following marginal utilities:

MUX=2XY,   MUY=X2

His income is $200 and the price of X is $6 and the price of Y is $4.

A) Find Vincent's optimal basket given those price and income

more step by step plz I couldn't understand the other answer that was very close to this answer

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Answer #1

Ans. Utility function, U = X^2 * Y

Marginal utility from X, MUx = dU/dX = 2*X*Y

Marginal utility from Y, MUy = dU/dY = X^2

=> Marginal Rate of Substitution, MRS = dY/dX = MUx/MUy = 2*(Y/X)

As utility maximizing level of consumption,

MRS = Price of X / Price of Y

=> 2*(Y/X) = 6/4

=> Y = (3/4)*X ---> Eq1

Substituting Eq1 in the budget constraint, 6X + 4Y = 200 , we get,

6X + 4*(3/4)*X = 200

=> X = 22.22 units

From Eq1, Y = 16.67 units

Thus, optimal consumption bundle is, (X,Y) = (22.22, 16.67)

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