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Price Discrimination calculations

There is a firm that has pricing control of its output and is able to identify its consumers into two groups. The total quantity demanded for its output is the summation of the quantity demanded by the two groups, therefore Qtotal = Q1 + Q2 where Qtotal is the 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?

Solution Preview

Yes, always assume MC = MR = P. You are on the right track for the rest of it, but if you do the math it will be more obvious what is going on.

Since AC = MC = 120, we know the cost function is given by C(Q) = 120 Q.
Also, we can solve
for the inverse demand functions to be:
(1/3) P = 200 - Q1
P(Q) = 600 - 3Q1
and
(1/6)P = 100 - Q2
P ...

Solution Summary

Price Discrimination calculations based on total quantity demanded and demand functions for two groups

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