4.3 Assume that the quantity-discriminating monopoly as in panel a of Figure 10.4 can set three prices, depending on the quantity a consumer purchases.

The firm’s profit is

 = p1Q1 + p2(Q2 - Q1) + p3(Q3 - Q2) - mQ3, where p1 is the high price charged on the first Q1 units

(first block), p2 is a lower price charged on the next Q2 - Q1 units, p3 is the lowest price charged on the remaining Q3 - Q2 units, Q3 is the total number of units purchased, and m = $20 is the firm’s constant marginal and average cost. The monopoly faces the inverse demand function p = 60 - Q. Use calculus to determine the profit-maximizing p1, p2, and p3. C