ISI 2012 PEB Q6) PLEASE HELP

[sam]

6. A monopolist has cost function c(y) = y so that its marginal cost is
constant at Re. 1 per unit. It faces the following demand curve
D (p) =



0; if p > 20
100
p
; if p  20.
Find the profit maximizing level of output if the government imposes a
per unit tax of Re. 1 per unit, and also the dead-weight loss from the
tax.

[sam]

D (p)= 0; if p > 20
       = 100/P ; if p<=20

[AnkitKhanna]

In both the cases that is with and without tax Price to the consumer will be 20
 Hence profit maximizing output will be 5

Dead weight loss can be calculated by calculating the loss in producer surplus and subtracting the gain to the govt. from the tax as there is no change here in consumer surplus

change in producer surplus = (20-19)*5= 5
gain to the govt = 1*5

[sam]

Is there any general way to solve this? What if we are given P=2/q, TC=3q, and we are asked to find profit maximizing output of monopoly?(It was asked in today's isi interview, morning slot). By using the same method we get Q=0. Is it correct?

[Saurabh815]

If Q is quantity of discrete good then it should be equal to 0.
But if its infinitely divisible then don't know...

[AnkitKhanna]

In both the cases if you look at the demand curve it has a constant elasticity =1
In this particular Q profit eqn. is
Profit = R - 3q
Here R is constant
This will be maxm. at q=0, but this is not a maxima
If you read the chapter on monopoly from Hal Varian, this is precisely the reason why a monopolist never operates on part of the demand curve with elasticity<= 1

[Saurabh815]

so what will be the answer?

[sam]

And the second part of the same question was-If there is a perfect competitor firm in the above market and is willing to sell any qty at p=5,then what will be monopolist strategy? Will it be different, if so, why?

[AnkitKhanna]

Well for the first Q I would say the monopolist will charge a P -> infinity and q->0 because q=0 is an assymptote  to the demand curve

In the second case I think the monopolist will charge a price slightly lower than 5 and take the whole market
The change in strategy is due to presence of another competitor who is willing to supply the demand of the market at a price lower than that monopolist would have charged in his absence

[Tanu_Jaiswal]

pls explain

[AnkitKhanna]

In the second case monopolist has become part of a perfect competition market
and selling at less than,market price will give him the whole market (is what I thought)