Define the demand function which maximizes x -> U(x) as:

$\sum_{i=1}^n$$p_i$$\zeta_i$(p, I) = I

According to my textbook if I differentiate this with respect to $p_j$ I will obtain,

$\zeta_j$(p, I) + $\sum_{i=1}^n$$p_i$$\frac{\partial \zeta_i}{\partial p_j}$(p,I) = 0

I don't understand how I get from the demand function to the output by differentiating w.r.t. $p_j$ do I have to use the chain rule, I tried that, I don't see why the function is equal to zero?


  • 2
    $\begingroup$ Yeah all that is being done is the chain rule and, since the RHS does not contain $p_j$, it becomes zero. Although this is more of a math question and would likely be more appropriate on math.se as it does not really contain economics per se. If I were to answer this question formally it would have no economics, only a math explanation of how to get from A to B $\endgroup$ – Brennan Apr 5 '20 at 16:44
  • $\begingroup$ The $i$ and $j$ subscripts are missing in $\zeta$ (3 occurrences) $\endgroup$ – Bertrand Apr 5 '20 at 17:09

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