how to find the MRS of
U(x,y)=√xy
To find the Marginal Rate of Substitution (MRS) for a function U(x, y) = √xy, we need to calculate the partial derivatives of this function with respect to x and y.
The MRS represents the rate at which a consumer is willing to trade off one good for another while maintaining a constant level of utility. It is calculated as the ratio of the marginal utility of good x to the marginal utility of good y.
First, we need to find the partial derivatives of the utility function with respect to x and y:
∂u/∂x = 1/(2√xy) * y = 1/(2√xy) * y
∂u/∂y = 1/(2√xy) * x = 1/(2√xy) * x
Next, we calculate the MRS by taking the ratio of the two partial derivatives:
MRS = (∂u/∂x) / (∂u/∂y)
MRS = (1/(2√xy) * y) / (1/(2√xy) * x)
MRS = y / x
Thus, the Marginal Rate of Substitution for the function U(x, y) = √xy is MRS = y / x.