Example: Suppose a consumerโ€˜s utility function is given by U ( X ,Y ) = ๐‘ฟ^๐Ÿ’ ๐’€^๐Ÿ . Find MRSX,Y

1 answer

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 = ๐›ฟU/๐›ฟX / ๐›ฟU/๐›ฟY

First, let's find ๐›ฟU/๐›ฟX:

๐›ฟU/๐›ฟX = 4X^3 ๐’€^2

Next, let's find ๐›ฟU/๐›ฟY:

๐›ฟU/๐›ฟY = 2X^4 ๐’€

Now we can find MRSX,Y:

MRSX,Y = (4X^3 ๐’€^2) / (2X^4 ๐’€)

Simplifying the expression, we get:

MRSX,Y = 2X^3 / Y