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 = ๐ฟU/๐ฟX / ๐ฟU/๐ฟY
First, let's find ๐ฟU/๐ฟX:
๐ฟU/๐ฟX = 4X^3 ๐^2
Next, let's find ๐ฟU/๐ฟY:
๐ฟU/๐ฟY = 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
Example: Suppose a consumerโs utility function is given by U ( X ,Y ) = ๐ฟ^๐ ๐^๐ . Find MRSX,Y
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