ISI question

[bhavya jain]

What is the ans to the following question-
A monopolist has contracted to sell as much his output as he likes to the govt at Rs 100/unit. His sale to the govt is positive. He also sells to pvt buyers at Rs150/unit. What is the price elasticity of demand for the monopolist's products in the pvt market?
is ed=-3?

[don123]

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[Anakin Skywalker]

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[Rajat]

I got -3/2 . Can someone please confirm.

[L]

Here, MC = 100, P = 150

Since,  P(1-1/|E|) = MC
Therefore, |E|=3

[Rajat]

shouldnt MC be 50 ?

[Anakin Skywalker]

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[Anakin Skywalker]

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[L]

My earlier deduction was wrong.
It is the case of third degree price discrimination. So, you have two markets with different demand functions. So, your graph won't be correct in that case. Because, even if MC is constant (=100) it would not be selling below Rs. 150.

Now, what is the meaning of this statement "to sell as much of
its output as it likes to the government at Rs. 100/- per unit"  

Govt. is not deciding the quantity it wants, i.e., it has fixed the price at Rs. 100/unit.
So, it makes sense to take e1=infinity in this market.

SO, P1(1-1/|e1|)  = MC  
=> P1 = MC

Then,  P2(1-1/|e2|) = MC = P1
=> |e2| = 3

It makes sense now. Tell me if there is something wrong in this.

[Anakin Skywalker]

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[Rajat]

I think constant MC is not an assumption but an implication. if the monopolist is selling any quantity at the same price, it should imply that the MC is constant. If this were not the case, MC would keep on increasing with quantity and the monopolist would not be able to maintain constant price.