> #equation , #maths > Perfect Substitute Utility Function U (x,y)=ax+by,Now what is MRS derived from this equation?
Anonymous
Feb 24, 2023

Perfect Substitute Utility Function U (x,y)=ax+by,Now what is MRS derived from this equation?

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Anonymous
Jul 4, 2023

The Marginal Rate of Substitution (MRS) represents the rate at which a consumer is willing to trade one good for another while maintaining the same level of utility. In the case of the utility function U(x, y) = ax + by, where a and b are constants representing the respective marginal utilities of x and y, the MRS can be derived as follows:

MRS = - (MUx / MUy)


To find the marginal utilities, we need to take the partial derivatives of the utility function with respect to x and y.


Taking the partial derivative with respect to x:

MUx = ∂U/∂x = a


Taking the partial derivative with respect to y:

MUy = ∂U/∂y = b


Substituting the marginal utilities into the MRS equation, we get:

MRS = - (a / b)


So, the Marginal Rate of Substitution (MRS) derived from the utility function U(x, y) = ax + by is - (a / b).

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