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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 thus 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): since consumer Y's demand is twice consumer X's, then 2 x AC = ABCD. As it turns out, the producer is [[indifferent]] to either of these pricing possibilities.
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.
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