Suppose a nonlinear price discriminating monopoly can set three prices, depending on the quantity a consumer purchases. The firm's profit is x=P: (Q1) + P2 (Q2 -Q;) + P3 (Q3 - Q2) - mQg, where p, is...

Extracted text: Suppose a nonlinear price discriminating monopoly can set three prices, depending on the quantity a consumer purchases. The firm's profit is x=P: (Q1) + P2 (Q2 -Q;) + P3 (Q3 - Q2) - mQg, where p, is the high price charged on the first Q, units (first block), p, is a lower price charged on the next Q, -Q, units, p3 is the lowest price charged on the Q, - Q, remaining units, Q, 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. Let demand be p= 90 - Q. The profit-maximizing prices for the nonlinear price discriminating monopoly are P1 = S P2 = S and P3 = 5 (Enter numeric responses using real numbers rounded to two decimal places.)