A monopolist has cost function $c(y) = y$ so that its marginal cost is constant at 1 per unit. It faces the following demand curve $D(p) = \begin{cases} \frac{100}{p}, &\text{if}&p ≤ 20 \\0,&\text{if} &p>20 \end{cases}$
Find the profit maximizing level of output if the government imposes a per unit tax of Re. 1 per unit, and also the deadweight loss from the tax.
$TR=100 \Rightarrow$ $MR=0$ while $MC=1$ before tax is imposed and $2$ after tax is imposed. So, I can't even understand how to calculate profit-maximising output from the usual $MR=MC$ condition.
I can maybe see the profit maximising problem being reduced to cost-minimisation since the total revenue is constant. In which case, firm minimises its cost while earning a positive profit for $q=5$ for both cases of $MC.$
But, I still don't understand how to calculate deadweight loss. Could someone please guide me with this problem?