Assume that KPM's demand function for coffee is
(1) Q = 1 - p, where p is the price of a cup of espresso.

(a) Assume that the marginal cost of a cup of coffee is 10 cents. Assume that the seller can use a two-part tariff coffee purchasing plan (where plan has a price per cup and an entry fee). Concretely, the amount of money that consumer spends on X cups of espresso is given by T = F + p*X, where F is the entry fee in dollars. Under that plan, what is the profit-maximizing price of a cup of coffee? How many cups will KPM drink? What is the maximum entry fee that the seller can charge KPM to participate in the plan? [Hint: Use the fact the that entry fee should extract consumer's surplus, when possible. Consumer surplus is the area of the triangle above the equilibrium price and the price at which demand equals zero. Given the demand function, that price is equal to p^=1.]

(b) Assume that CAD's demand for coffee is given by (2) Z = 0.5 - p.
What is the profit-maximizing plan (price plus entry fee) that the seller can charge CAD? How many cups of coffee will CAD drink under the plan designed for her?

(c) Assume that the seller cannot differentiate between CAD and KPM. In such a situation, would you expect that KPM will purchase under the plan designed for him (as in point (a), above) or under the plan designed for CAD (as in point (b), above).

(d) What can the seller do to make CAD's plan unattractive to KPM? In answering this question discuss the following ideas (i) participation constraint; (ii) self-selection or individual rationality constraint; (iii) informational rent.