Consider a monopolist facing two customer groups. The first has demand p1 = 10 ! q1/2 and the second has demand p2 = 20 ! q2. The firm has marginal cost MC(q) = q, where q = q1 + q2 is the total amount sold.
(a) Suppose it can separate customers into the two groups (third degree price discrimination), each with its own price per unit. How many units does it sell to each group? At what prices?
(b) Suppose instead of MC(q) = q , the firm had exactly 4 units to sell to the two groups (and no costs to worry about; the 4 units are already produced). How should it split the units between the goods?
(c) Suppose it could first degree price discriminate and charge the full willingness to pay for every unit. How many units does it sell to each group? (Back to MC(q) = q = q1 + q2.) (d) 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?