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I have an indicator function $I(D\leq Q)$which is equal to $1$ if $D\leq Q$ and $0$ otherwise. What would be derivative of this function with respect to different variables such as $D$ or $Q$ or $P$ ($D$ is a function of $P$).

Clarification to what I am trying to do:

  • $D$ represents demand which is a function of price, assume $D=a-bp$
  • $Q$ represents quantity or supply, which is assumed to be fixed

$\text{profit} = p\min(D,Q)= PDI(D\lt Q)+PQI(Q\leq D)$

I want to take derivative of profit with respect to price.

Thanks in advance

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    Thank you. I just registered. Also I am trying to delete my answer but can't find how to do it. Sorry2012-05-14

1 Answers 1

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The derivative in the usual sense does not exist at a discontinuity, and is $0$ everywhere else. If you're talking about a derivative in the sense of distributions, $\dfrac{\partial}{\partial D} I(D \le Q) = -\delta(D-Q)$.

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    The second part is the derivative of $f(x)$ away from $x=a$.2012-05-14