Question

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. Let MC=0
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?

Answer 1

A) Find the expression for marginal revenue by doubling the coefficient on Qin the inverse demand function. Intensive users: MRI 8 0.2Q Less-intensive users: MRL-10-0.4Q For each group, set MR-MCand solve for Q, then use the inverse demand function to find price .Intensive users: 8 0.2Q-0 QI-40 PI*-8-0.1(40)4 Less-intensive users: 10-0.4Q-0 QL-25 PL*=10-0.2(25)-5 Carolina Atlantic would charge a price of S4 for 40 or more reams of paper:. It would charge a price of S5 fora quantity less than 40

B) Less-intensive users would take advantage of the quantity discount because the consumer surplus gained exceeds the consumer surplus lost. Consumer surplus gained (S1 x25)+0.5(S1 x5)-$27.50 Consumer surplus lost-0.5(10 xS2)-$10.

c) For intensive users, MR-8 (215)Q Set MR=MCand solve for Q 8(2 15)Q0 (2 15)Q8 Q-60 Find price in the inverse demand equation P-8-(1-15)60-4 Carolina Atlantic would now require a purchase of 60 reams of paper in order to qualify for the discounted price of S4. Purchases of a quantity less than 60 will be priced at $5 per ream