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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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    On what domain is your indicator function defined? What do the variables D, Q, and P represent? Have you verified wether you can derive such function?2012-05-09
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    [Antiderivative and derivative of the Heaviside stepfunction](http://en.wikipedia.org/wiki/Heaviside_step_function#Antiderivative_and_derivative)2012-05-10
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    @Elnaz: Please consider registering, so that you don't log in as two different people and have to get "permission" to edit your own post. Thank you.2012-05-14
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    Thanks for the answers. Please see the clarification made to original question. Also I would be grateful if you briefly explain what you mean by derivative in the sense of distribution. Thanks2012-05-14
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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

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