There is the firm that has pricing control of its output and is capable to identify its consumers in two groups. The total quantity demanded for its output is the summation of quantity demanded by the two groups, therefore Qtotal = Q1 + Q2 where Qtotal is total quantity demanded, Q1 is the quantity demanded by group 1, and Q2 is the total demanded by group 2. The demand for each group is as follows: Q1=200-(1/3)P Q2=100-(1/6)P where P is the price charged by the firm. The firm also has a constant marginal and average cost of 120 (ATC = MC = 120).

If the firm is unable to identify the two groups what price will it charge all customers? I said 120 because MC=MR. Is this correct?

If the firm is able to identify the two groups and is able to prevent resale between the two groups, what price will the firm charge each group? How do I set up the equation to solve for Q and P for group 1 and 2?

What is the benefit of being able to price discriminate to the firm? Is "the firm can charge each customer the maximum price that the customer is willing to pay for each unit bought" correct?