Consider a monopolist facing two customer groups. The first has demand p1 = 10 - q/2 and the second has demand p2 = 20 - q. The firm has marginal cost MC(q) = q, where q = q1 + q2 is the total amount sold.
Suppose a regulator could set one per unit price for everyone and knows the demand and marginal cost curves. What price should it set for the two groups to minimize deadweight loss?