Gabriel earns $100,000 annually. he also faces a 25% chance of getting sick during any given year. if gabriel falls sick during the year, the cost to him will be $20,000. gabriel has the option of purchasing health insurance to hedge against the risk of illness. gabriel's total utility of income is given by u = ln(y). where y denotes gabriel's annual income. use this information to answer the following questions. be sure to show all your work. [it's safer to round to 4 decimal places for questions on expected utility] calculate gabriel's expected utility if he chooses not to purchase an insurance policy. calculate the actuarially fair insurance premium. calculate gabriel's expected utility if he chooses to purchase an insurance policy at the actuarially fair premium. should gabriel purchase the insurance policy? why or why not? what is the maximum premium gabriel would be willing to pay for the insurance policy? what is gabriel's risk premium?

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?

In order to be thoughtful about the implementation of security policies and controls, leaders must balance the need to reduce with the impact to the business operations. doing so could mean phasing security controls in over time or be as simple as aligning security implementation with the business’s training events.

Suppose that a paving company produces paved parking spaces (q) using a fixed quantity of land (t) and variable quantities of cement (c) and labor (l). the firm is currently paving 1,000 parking spaces. the firm's cost of cement is $3 comma 600.003,600.00 per acre covered (c) and its cost of labor is $35.0035.00/hour (w). for the quantities of c and l that the firm has chosen, mp subscript upper c baseline equals 60mpc=60 and mp subscript upper l baseline equals 7mpl=7. is this firm minimizing its cost of producing parking spaces?