1. Suppose that the nonlinear price discriminating monopoly in panel a of figure 12.4 can set three prices, depending on the quantity a consumer purchases. The firm’s profit is
Π=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.
2. The demand a monopoly faces is p=100-Q+A^0.5
Where Q is its quantity, p is its price, and A is its level of advertising. Its marginal cost of production is 10, and its cost of a unit of advertising is 1. What is the firm’s profit equation? Solve for the firm’s profit maximizing price, quantity, and level of advertising.