A Two-part Tariff When Consumer Demand Is Different
We now consider the case where there are two consumers, X and Y. Consumer Y's demand is exactly twice consumer X's demand, and each of these consumers is represented by a separate demand curve, and their combined demand (Dmarket). The firm is the same as in the previous example. We assume that the firm cannot separately identify each consumer - it cannot therefore price discriminate against each of them individually.
The firm would like to follow the same logic as before and charge a per-unit price of Pc while imposing a lump-sum fee equal to area ABCD - the largest consumer surplus of the two consumers. In so doing, however, the firm will be pricing consumer X out of the market, because the lump-sum fee far exceeds his own consumer surplus of area AC. Nevertheless, this would still yield profit equal ABCD from consumer Y.
A solution to pricing consumer X out of the market is to instead charge a lump-sum fee equal to area AC, and continue to charge Pc per unit. Profit in this instance equals twice the area AC (two consumers): 2 x AC. As it turns out, since consumer Y's demand is twice consumer X's, ABCD = 2 x AC. The profit is the same and the producer is indifferent to either of these pricing possibilities, although consumer Y is better off this way since she gets consumer surplus BD.
However, it is possible for the firm to earn even greater profits. Assume it sets the unit price equal to Pm, and imposes a lump-sum fee equal to area A. Both consumers again remain in the market, except now the firm is making a profit on each unit sold - total market profit from the sale of Qm units at price Pm is equal to area CDE. Profit from the lump-sum fee is 2 x A = AB. Total profit is therefore area ABCDE.
Thus, by charging a higher per unit price and a lower lump-sum fee, the firm has generated area E more profit than if it had charged a lower per-unit price and a higher lump-sum fee. Note that the firm is no longer producing the allocatively efficient output, and there is a deadweight loss experienced by society equal to area F - this is a result of the exercise of monopoly power.
Consumer X is left with no consumer surplus, while Consumer Y is left with area B.
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