There are two competing Internet-based providers of medical information suitable for patients. ProPatient currently charges $150 per year to subscribers of its service which helps patients learn more about their medical conditions. Its competitor, AskUs Health, currently charges $125 for a similar service. The current level of advertising by ProPatient is $2,500,000. ProPatient has tracked its volume of subscribers as a function of its price, the price of AskUs services, and of its own marketing expenditures designed to promote the service. The marketing department at ProPatient estimated its demand relationship based on these data. Here is the result:

QP = 120,000 - 900PP + 400PA +.02MP

where QP = quantity of subscribers to ProPatient

PP = price charged by ProPatient

PA = price charged by AskUs Health

M P = Marketing expenditures by ProPatient (all values of the independent variables are in dollars)

ProPatient's fixed cost to establish and maintain the business is $10,000,000 plus marketing expenses per year. In addition, there is an incremental expense of $5 for each subscriber.

a. What is the current quantity of subscriptions for ProPatient?

b. Measure the cross price elasticity of demand for ProPatient subscriptions with respect to the price of AskUs service under the current conditions.

c. What is the price elasticity of demand for ProPatient under the current conditions?

d. What is marginal revenue for ProPatient under the current conditions?

e. What is the current level of profits for the company?

f. Given the values of the other variables, is ProPatient charging the optimal price? If not, what is the optimal price?