Hi

I'm alswo waiting for an answer on that :)

Because in order to get the MRS you need to calculate the marginal utility (MU), the partial derivative, for x and y. In the first example the utility function is given by y^2+x^2. This results in the following partial derivatives: dU/dy (or y')= 2y^2-1=2y and dU/dx (or x')=2x^2-1 = 2x. In the second example the utility function is given by y * x, resulting in a different differentiation due to the multiplication. The dU/dy (or y')= x * y^1-1 = x and dU/dx ( or x') = x^1-1 * y = y . The difference in the first and second example is mainly caused by the nature of the utility functions. Example one uses y + x and example two uses y*x, this makes a big difference when calculating the partial derivatives.

In case you are still interested: f(x)=y¹ * x¹ -> f'(x)= 1 * y¹ * x^(1-1) -> y¹ -> y You differentiate only partially.

They are doing partial derivative. So when deriving the utility function you make one of the variable a constant.