(1) consider a second-price, sealed-bid auction with a seller who has one unit of the object which he values at s and two buyers 1, 2 who have values of v1 and v2 for the object. the values s, v1, v2 are all independent, private values. suppose that both buyers know that the seller will submit his own sealed bid of s (and will keep the item if bid s wins), but they do not know the value of s. the buyers know that the seller must submit his bid before seeing the buyer’s bids and they know that the seller will actually run a second price auction with the three bids he has: his own bid and the two buyer’s bids. each buyer knows his own value but not the other buyer’s value.(b) now suppose that the seller opens the bids from the buyers and then submits his own bid after seeing the bids from the two buyers. the seller runs a second price auction with these bids in the sense that the object is awarded to the highests bidder (one of the two buyers or the seller) and that bidder pays the second highest bid. now is it optimal for the buyers to bid truthfully; that is, should they each bid their true value? give a brief explanation for your answer.

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?