JNU-Monopoly-2008

[Ashish Gourav]

Question.>
A monopolist faces a demand curve q= 1/p. He incurs a cost of Rs.3 per unit of output produced. There is no fixed cost. His optimal output choice is

Options.
(a) 2
(b) 3
(c) 0
(d) No such optimal output exists  

Zero should be the answer

MR = P ( 1- 1/mod e ) here elasticity is -1. So putting this in the equation MR = P ( 0)
In monopoly , MR = MC so we get P = 3/0 and thus q = 0

[Sris]

answer is D...
q=1/p
implies..pq=1    TR=1
implies MR=0...(differenciating )
but MC=3
MR not equal to MC
....so no optimal output exists

This is a constant elasticity case. And here we don't use that formula. In these cases we use MR = P ( 1 - 1/ mod e ) = MC

[Ashish Gourav]

[e-mail]

MR = P ( 1 - 1/ mod e ) = MC is the formula derived after substituting the value of elasticity into the profit function.

Maximising the profit function is the more general approach. The elasticity formula is a special case, a shortcut

Correct me if I am wrong.

Gaurav in cases where u have q = ap^e which is constant elasticity case u can't use normal maximisation formula , because there u will always get MR = 0 or an undefined MR wherein u can only get P by this formula. Had the question been q = 50/p and MC = 3 , even the. Profit maximisation formula wud havegiven u MR = 0 and u wud have ended up with the same result as given by Sris. But in this case u cud maximise and find an answer.
I hope u understood the point.
Coming back to this question , even if u go by intuition total revenue I'd 1 and MC = 3, which means producing anything will bring losses and he CAN optimise by producing 0.