Consider a monopolist who own an exclusive source of spring water, which produces water at 0 cost. The demand curve of the spring-water is

q = 1pif p > p*

q =1p*if 0 p p*

The monopolist decided to use the membership feeCin addition to the per unit pricepof the water to generate the profit. (If you are a member of Amazon Prime, you have to pay annual membership feeC, and when you buy a good, you payp.)

1. Assume thatp*= 0.4. Suppose that the monopolist chargepmfor a small >0but also chargeC=. If the consumer is willing to purchaseq= 1(pm), paying subscription feeC=, what is the profit of the monopolist?
2. What is the optimal values of membership feeCand unit pricep, ifp*= 0.4? What is the monopolist's maximum profit? Compare the value to the profit you calculated in the first part of the questions.