# Is there a way to identify two goods as complement or substitute simple by calculating their MRS? [duplicate]

Suppose, given the utility function $U(x_{1},x_{2})$ with known budget $m$ and price vector $p$. If I calculate MRS from this function, can I get information about whether these two goods are complement or substitute? Seems like when I apply Cobb-Douglas utility function I end up with a function containing both $x_{1}$ and $x_{2}$.

• Why not just discern whether or not goods are complements/substitutes by examining the utility function directly?
– 123
Commented Oct 20, 2016 at 1:56
• @123 It is a two-stage utility function and I try to consider on good over two periods. The function form is $(x_1^\alpha y_1^{1-\alpha})^\rho + (x_2^\alpha y_2^{1-\alpha})^\rho$ subject to $p_x x_1 + p_y y_1 + p_x x_2 + p_y y_2 = m$ Commented Oct 22, 2016 at 22:09
• Perhaps I am missing something but I am still not sure why you cannot just evaluate the utility function here to discern relationships between x and y.
– 123
Commented Oct 25, 2016 at 18:47