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Hello. Someone sent this on a discord server that I am on, and I couldn't make heads or tails of this. I found the book it is from on studocu; solutions to Cabral's Industrial Organisations, 2nd Ed. The question has MC = 0.

Is max p just max profit? Because then it would make some sense for me. And how did they derive the first order condition from this? All I found was that (∂π / ∂q) = 0, but please do explain where this comes from? Also, why is consumer surplus just the square of the total demand from a type 1 consumer?

Thank you so much in advance!

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$max_p f(p)$ just means the maximal value of expression of $f(p)$ with regards to $p$ (meaning the value of $f(p)$ is checked over the whole range of $p$'s possible values).

In your case it does indeed mean the maximal profit value the monopolist can attain.

The given first order condition is a derivative of the expression with respect to $p$, divided by 3. Division by 3 is fine since the right hand side of the first order condition is 0, which divided by 3 will remain 0.

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  • $\begingroup$ how do they get 1 - 2p, then? and not just 1 - p? $\endgroup$
    – andromeda
    Jul 27, 2023 at 14:18
  • $\begingroup$ also, I hope you could explain the consumer surplus being (1-p)^2, please? $\endgroup$
    – andromeda
    Jul 27, 2023 at 14:18
  • $\begingroup$ 1. This is the derivative of the function. 2. Please ask new questions as new questions. $\endgroup$
    – Giskard
    Jul 27, 2023 at 19:27
  • $\begingroup$ ... I had already asked that in the original question lol. chill tho, thanks for your help. $\endgroup$
    – andromeda
    Jul 28, 2023 at 5:09

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