Monopoly

[Devika]

Please explain!! With steps

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.

How to calculate the MR in this case?

[Devika]

The Demand function is constant elasticity demand function. So, e=-1

MR=P(1-1/|e|), but this is 0.
:s

[Mauli]

here, note that the TR is fixed at 100 . wtever be the price.
ie: TR= (100/Q)*Q = 100
so the max profit will be where he minimises his costs.
MC=1.
TC=MC*Q
   =1*100/P
 the profit will be max if p=20.( u can check that)
here, the profits are 95.
therefore he max profits at q=5.

for this dwl wala part i am not sure..but
MC now becomes 2.
it shifts up.
TR IS STILL THE SAME AT 100.
TC is now 2*100/P
this will also be min when P=20. but now , the profits become 90.
the consumers have an elasticity of -1. that is the dd curve is perfectly elastic .
so, they donot bear the  burden of the tax. the entire tax gets passed on to the producer.
his profits reduce by 5. but he still maximises them at q=5..
someone please cnfrm this part . does it make sense..?
is it that there is no dead wt loss?

[MI]

Hi mauli,

you are right! There is no Dead-weight-loss.

Tax will increase the MC of the monopolist. But TR being constant he is bound to stick to his original production choice.

As same transactions are happening even after tax as before there is no dead-weight-loss.

Consumers are indifferent unless government redistribute the collected tax to them.

cheers :)

[Devika]

Thank you mauli and MI :)

[Mauli]

thanks MI:)