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).