Example: Suppose a consumer‘s utility function is given by U ( X ,Y ) = 𝑿^𝟒 𝒀^𝟐 . Find MRSX,Y

Answer 1

To find the marginal rate of substitution (MRS) between X and Y, we need to calculate the derivative of the utility function with respect to X divided by the derivative of the utility function with respect to Y:

MRSX,Y = 𝛿U/𝛿X / 𝛿U/𝛿Y

First, let's find 𝛿U/𝛿X:

𝛿U/𝛿X = 4X^3 𝒀^2

Next, let's find 𝛿U/𝛿Y:

𝛿U/𝛿Y = 2X^4 𝒀

Now we can find MRSX,Y:

MRSX,Y = (4X^3 𝒀^2) / (2X^4 𝒀)

Simplifying the expression, we get:

MRSX,Y = 2X^3 / Y