<p>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 $x_{2}$.</p>

CC BY-SA 3.0
2016-10-20T01:56:56.363Z
Why not just discern whether or not goods are complements/substitutes by examining the utility function directly?
123
CC BY-SA 3.0
2016-10-22T22:09:24.243Z
@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 $p_x x_1 + p_y y_1 + p_x x_2 + p_y y_2 = m$
Eric Chen
CC BY-SA 3.0
2016-10-25T18:47:13.877Z
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
<microeconomics>
Is there a way to identify two goods as complement or substitute simple by calculating their MRS?
Eric Chen
# Is there a way to identify two goods as complement or substitute simple by calculating their MRS?

(Asked by: username_0 on 2016-10-19)

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 $x\_{2}$.

**Tags:** microeconomics

> **Comments:**
> **username_1**: Why not just discern whether or not goods are complements/substitutes by examining the utility function directly?  
> **username_0**: @username_1 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 $p_x x_1 + p_y y_1 + p_x x_2 + p_y y_2 = m$  
> **username_1**: 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.  

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