Q. A monopolist exists in an industry. Its cost is
TC = 100 - 5Q + Q2 and its demand is P = 55 - 2Q.

a. What price would firm set to maximize profit? Compute profit and Consumer Surplus.

In diagram given above blue shaded region is consumer surplus and green shaded region is deadweight loss. As you can see that demand function (P = 55 - 2Q) is dark blue line, pink line is showing marginal revenue (MR = 55 - 4Q) and saffron line is representing marginal cost function (MC = -5 + 2Q). From diagram, you can see that output where MR = MC is Q=10 and this Q=10 cut demand function at P = 35 which is profit maximization quantity and price for monopolist.

b. Compute deadweight loss from monopoly power in part (a).

c. Is this deadweight loss a sufficient reason to regulate monopolies? Does such regulation increase consumer welfare? (You can answer this question in general terms. Don't have to use computations in and b)