Estimating the social welfare under monopoly.

The market demand curve for widgets is P = 100 - 6Q
where Q is the quantity of widgets demanded when the unit price of a widget is P.

Currently only one firm produces in the widget market as a sanctioned monopolist, free to do whatever they wish (as long as they charge a single price per unit for a widget that's the same for every demander).

The monopolist's total cost function is
TC = 50 + 4Q + 2Q2
where Q is the quantity of widgets produced.

Suppose the state (who sanctioned the monopoly) now decrees that the monopolist must price at marginal cost (to simulate a perfectly competitive market).

How much does social welfare change as a result of the change in the state's policy? Who wins and who loses and by how much (candidates for a winner or a loser are the widget firm and the aggregate of consumers)?

Now suppose that you were able to disaggregate the market demand and discovered that it was made up of 10 identical demanders, each of whom had a demand curve of
P = 100 - 60q

where q is the quantity of widgets demanded when the unit price of a widget is P.

What if the firm was again a monopolist and was allowed to implement a two-part tariff. What's the optimal use fee and the optimal entry fee? describe how much more profit does this pricing policy lead to as compared to the simple monopoly price above? Widgets can be non-integers.