(a) Before charging a quantity discount to obsessed traders, E*TRADE needs to ensure that its pricing strategy is incentive-compatible. At P_u = $30 per trade, uninterested traders make Q_u trades and receive surplus A. At the quantity and price offered to obsessed traders (Q_o, P_o), their surplus is reduced by area L but increases by area B. Uninterested traders will choose to pay $30 per trade if area B is greater than area L.
(b) Under the pricing policy for uninterested traders, obsessed traders would have to pay both a higher price (P_u = $30 > P_u = $9) and make fewer trades per month (Q_o > Q_u). Therefore, the quantity discount is incentive-compatible for these traders.