Monopoly question..pls help

[Shefali]

Suppose that demand curve of monopolist is p=20-4x and cost is C=4x+2.If government imposes a tax @20% of sales find output and price.

Please help me with this.My answer is not matching.Thanks.

[Arushi :))]

whats the answer.???
m getting x = 1.875

[greg]

Is output 2.2 and price 11.2

[Shefali]

ans is x=1.9 and p=12.4
Please explain...

[Arushi :))]

neglect my second reply !
:P
see there is a tax on sales , i.e on total revenue.
so the profit would be = TR - 0.20TR - TC
now, profit would be = 0.80x (20-4x) - 4x -2
diff w.rt x to get optimal x

[Ashima]

Yeah since the govt. is imposing the tax. Price of commodity will go up.

P+0.2x= 20-4x

MR= MC
20-8.4X=4

X= 1.9
P= 12.02

[Shefali]

arushi...still the ans is not matching
and ashima its a sales tax not specific..!

[Arushi :))]

arey its matching ! :/
.80x(20-4x) - 4x-2
16x- 3.2x^2- 4x -2
diff w.r.t x gives
16 - 6.4x -4
putting it equal to zero
12 = 6.4x
implies x = 12/6.4 = 1.875 and this approx 1.9 !!

[Ashima]

Yeah . I first did the way Arushi told. But dint get the answer.

This way the answer is exactly matching. So may be they are considering the sales tax as tax on each quantity sold. :(

[Ashima]

Can we approximate this much . really?

[Arushi :))]

i guess !! If we remove 5 then its 1.88 and rounding off to one decimal place would be 1.9 na

[The Villain]

Here goes..
We have pd=ps+.2ps  ..
therfore ps=p/1.2
Now TR=ps*x
=pd/1.2  * x
now solve ..u'll get ut exact answer...!

[Ashima]

And what is Pd and Ps? I mean I dint get you!

[The Villain]

@Ashima
oo sry..forgot to specify
pd is price paid by consumers and ps is price received by sellers :))

[Shefali]

OKay i got it.Price paid by consumers increase rather than of sellers.
Thanx Ron.Amazing

[greg]

@ashima I think x is the quantity over here. 0.2 of x does not make sense to me. Sales tax will be applied to price only and applying to Selling price also makes sense. Will have to look at dead weight loss for these question.