4. Chessathlete.com has a monopoly on a unique holistic health game where players compete in both chess and long-distance runs (which are tracked by their mobile phones). They charge players a monthly flat fee to participate and improve their mental and physical fitness. Past experience revealed that players registering through iPhone and Android devices had a different willingness to pay for membership. For iPhone users, the demand is =79819. For Android users, demand is =1,47035. Chessathlete has a small marginal cost of $2 per user (regardless of the device they are using), which has to do with the cost of server capacity and managing accounts, which they contract out to an external service. The fixed cost Chessathlete must cover each week is $20,000.

(a) Calculate the optimal prices to charge to iPhone and Android users, respectively.

(b) How many memberhips does Chessathlete sell overall at the profit-maximizing prices?

(c) How much profit is Chessathlete able to make? (Hint: Be careful to subtract fixed cost only once, since it applies to the whole company, rather than separately to each market served.)

(d) Now suppose Chessathlete.com cannot tell iPhone and Android users apart, due to a freely available masking technology. Therefore, it has to charge the same price to all customers. What price would maximize its profits, and how many memberships would it sell?

(e) How much profit would it make? How much money (if any) does Chessathlete lose due to the existence of the masking technology?