1. Qualtrics is a private survey company. Individuals and companies can pay them a fee to disem- anate a survey to their pool of survey takers, with an assurance of quality responses and statistics. Two different groups of folks use this type of service: wealthy CEOs, who use the data to improve their products and marketing, and poorer university professors, who use the product to conduct research. Both of these groups prefer to have more individuals in their survey sample, as larger samples results in more precise inference (hopefully you all know that). Let Q be the number of individuals included in the sample that Qualtrics sells to a customer. The CEOs have an in- verse demand function of p(Q) = 14000 Q and the professors have an inverse demand curve P(Q) = 9000 Q. The marginal cost for selling surveys Qualtrics is zero. Assume all customers cannot re-sell or share the data. a. Suppose Qualtrics can identify who is a CEO and who is a professor. Qualtrics decides on a "take it or leave" offer: a professor can buy a survey sample of 9000 individuals, or nothing and a CEO can buy a survey sample of 14000 or nothing. What is the maximum price a professor is willing to pay? What is the maximum price a CEO is willing to pay? b. Now suppose Qualtrics cannot tell who is who. The problem is now Qualtrics can't be sure a CEO wouldn't prefer the professor sample survey offer. So Qualtrics decides to implement a pricing scheme to induce CEOs and professors to self-select into a pricing plan. Qualtrics decides to offer a pricing plan for a sample of 9000 and a sample of 14000. What is the highest price a professor will pay for the 9000 survey sample size? How much do CEOs value this survey package? c. What is the maximum price that Qualtrics can for the 14000 survey sample size if it wants CEOs to prefer this package to the offer in (b.), where this offer is the highest amount the professors are willing to pay for the 9000 sample? d. Now suppose that Qualtrics decides to offer a package of a survey sampel size of 6750 to the professors. What is the maximum price it can charge where professors would still be willing to purchase it? e. What is the consumer surplus a CEO would receive from purchasing this professor package of the 6750 sample? f. What is the most Qualtrics could charge for the survey sample of 14000 and still induce CEOs to purchase this offer instead of the survey sample size of 6750? g. If there are an equal number of CEOs and professors, would Qualtrics earn a larger profit from offering professors a sample size of 9000 or 6750?