(40 pt.) a monopolist has a quadratic cost function c(q) = q2 + 12. the market demand is given by q(p) = 24 − p. a. (5 pt.) find inverse demand function p(q) and revenue function r(q). b. (5 pt.) write down the profit maximization problem of this monopolist. c. (10 pt.) determine the monopolist’s choice qm that maximizes profit by investigating the first- and second-order conditions. d. (10 pt.) find the price p m the monopolist would set up and calculate the profit at the monopoly outcome. e. (10 pt.) find market outcome (qc , p c ) in which the monopolist behaves as if in a competitive market, and calculate the profit at this outcome.

Onsider the following subscription behavior information from genie, a web site that provides tools for constructing a family tree (ancestor search). subscriptions cost $9.99 per month, but you are charged for the entire year at the time of purchase. there is a one-year minimum term when you sign up for the service. once purchased, subscriptions are set to renew automatically unless the subscriber cancels them. when a membership renews, it renews for a one-year term and again you are charged for the entire year. there are no variable costs associated with providing this service to an individual customer, but genie does engage in customer relationship activities that they believe will increase customer retention. these customer relationship activities cost genie about $10 per year per customer. based on a sample of 1000 customers that joined genie five years ago, near the time when the company was founded, they were able to determine how many of those customers remained subscribers in the second year, third year etc. based on this information, genie calculated the average annual retention rate to be 20%. genie uses an annual discount rate of 8%. a. last year, genie spent $10,000 placing advertisements on google. genie management believes that these advertisements were responsible for about 300 new subscribers. would you recommend to genie management that they purchase more google ads? b. suppose a newly-introduced loyalty program increases the number of customers that remained to 30%. does this new data change your answer to 9.a? c. do you have any hesitations or concerns about making recommendations to management based on your above estimate of customer lifetime value?

Which of the following services will be provided by a full-service broker but not by a discount broker? i. research of potential investment opportunities ii. purchase and sale of stock at your request iii. recommendation of investments a. i and iii b. ii only c. iii only d. i, ii, and ii

If springfield is operating at full employment who is working a. everyone b. about 96% of the workforce c. the entire work force d. the robots