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Suppose a nonlinear price discriminating monopoly can set three prices, depending on the quantity a consumer purchases. The firm's profit is * = P1 (Q1 ) + P2 (Q2 - Q1) + P3 (Q3 - Q2) - mQ3. where p, is the high price charged on the first Q, units (first block), p2 is a lower price charged on the next Q2 - Q, units, pg is the lowest price charged on the Q3 - Q2 remaining units, Q3 is the total number of units actually purchased, and m = $10 is the firm's constant marginal and average cost. Use calculus to determine the profit-maximizing P1 . P2. and P3- Let demand be p = 150 - Q. The profit-maximizing prices for the nonlinear price discriminating monopoly are P q = $ . P2 = $ ], and P3 = $ . (Enter numeric responses using real numbers rounded to two decimal places.) Knoebels Amusement Park in Elysburg, Pennsylvania, charges a lump-sum fee, L, to enter its Crystal Pool. It also charges p per trip down a slide on the pool's water slides. Suppose that 350 teenagers visit the park, each of whom has a demand function of q, =6-p, and that 350 seniors also vist, each of whom has a demand function of q2 #5-p. Knoebels's objective is to set L and p so as to maximize its profit given that it has no (non-sunk) cost and must charge both groups the same prices. What are the optimal L and p? The optimal L and p are L=$] and p = $ . (Enter numeric responses using real numbers rounded to three decimal places.) A single-price monopoly faces two consumers with identical demand curves, Roy and Shelly. At the current profit-maximizing price, Roy's consumer surplus equals $64 and Shelly's consumer surplus equals $64. Assume a linear downward-sloping demand curve and a constant marginal cost. By switching to a two-part tariff, the monopolist could increase its total profit by $|. (Enter a numeric response using an integer.)