Assume that the quantity- discriminating monopoly in panel a of Figure 10.4 can set three prices, depending on the quantity a consumer purchases. The firm’s profit is

p = 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 Q3 – Q2 remaining units, Q3 is the total number of units actually purchased, and m = $ 30 is the firm’s constant marginal and average cost. Use calculus to determine the profit- maximizing p1, p2, and p3.