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I'm currently working on the Quantitative Finance course offered on Coursera by Wharton and in one example it states that "through calculus, one can obtain the optimal value of price when p(opt)=(c*b)/(1+b) where c is the production cost and b is the exponent in the power function."

But it fails to explain how that is so? Could someone here please enlighten me? My logic below didn't work out...

  • in my understanding profit max is when MR-MC=0,
  • R=QP=(60000P^(-2.5))*P
  • Pmax=MR-2=(dR/dQ)-2=(-90000P^(-2.5))-2
  • so Pmax = (-1/45000)^(-2/5) but it doesn't :( -- answer given is 3.33

(Apologies for poor formatting, I tried to LaTeX but I don't think it works here? Or maybe I just didn't do it correctly...)

[edit: for the sake of clarity, I thought I'd just include print screens]

print screen

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  • $\begingroup$ Welcome to Quant.SE! Your question is difficult to understand. SE support LaTex. So please use it. $\endgroup$ – Neeraj Feb 10 '16 at 17:01
  • $\begingroup$ You need to specify whether the market is under perfect competition, monopolty ... etc. Could you please provide the question setup? I.e. what is the demand and cost function. $\endgroup$ – phdstudent Feb 10 '16 at 17:02
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OK solved my own problem! The issue was assuming MC = 2... instead,

enter image description here

enter image description here

and when you set that equal to zero you get... p = 10/3 :)

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