Carolina Atlantic sells specialty paper to commercial clients. The paper can be produced at zero marginal cost. Some clients are intensive users who are price-sensitive; their demands are given by P = 8 − 0.1Q, where Q is the number of reams of paper desired per week. Other clients are less-intensive users of paper and have inverse demands given by P = 10 − 0.2Q

a. Carolina Atlantic attempts to separate more-intensive and less-intensive buyers by implementing a quantity discount plan. What price should Carolina Atlantic set for each group? How should the quantity discount plan be structured?

b. Show that the quantity discount plan you outlined in (a) is not incentive-compatible.

c. Suppose, instead, that intensive users had inverse demands given by P = 8 - (1/15)Q. Determine the structure of the quantity discount, and show that the plan is incentive-compatible.

d. Why did the quantity discount plan outlined in (b) fail, while the quantity discount plan outlined in (c) succeeded?