Re: Question from ISI 2015 Sample Question Paper

Posted by L on Mar 12, 2015; 10:16am
URL: http://discussion-forum.276.s1.nabble.com/Question-from-ISI-2015-Sample-Question-Paper-tp7595913p7595917.html

For social welfare maximizing tax rate, consumer surplus should be maximized. I am assuming the price of G to be less than 10, otherwise nobody would buy it.
Initial CS = 10-P
After tax CS = 10-[ P(1+t)(1-pt/2rk)^2 + P(pt/2rk (2-pt/2rk)) +TC]

where TC is travelling which you need to calculate by integrating from d to r,
and, respective Prices are multiplied with the proportion of population.
Then, differentiate w.r.t t and you will get welfare maximizing tax rate.
I am getting t=2rk/p, which seems weird because at this tax, d=r, so, everybody is buying from outside. I don't think the approach is wrong, maybe I have done calculation mistake. Please somebody else confirm.

Revenue maximizing is easy. t = 2rk/3p. At this tax, r=d/3.
I don't know about the necessary and sufficient conditions for revenue maximizing rate equal to welfare one.

And Revenue at revenue maximizing rate is independent of P, so elasticity should be zero.